A compact ion-trap quantum computing demonstrator

I. Pogorelov1, T. Feldker1, Ch. D. Marciniak1, L. Postler1, G. Jacob2, O. Krieglsteiner2, V. Podlesnic1, M. Meth1, V. Negnevitsky3, M. Stadler3, B. Höfer4, C. Wächter4, K. Lakhmanskiy1,5, R. Blatt1,6, P. Schindler1, and T. Monz1,2∗ 1 Institut für Experimentalphysik, 6020 Innsbruck, Austria 2 Alpine Quantum Technologies (AQT), 6020 Innsbruck, Austria 3 Institute for Quantum Electronics, ETH Zürich, 8093 Zürich, Switzerland 4 Fraunhofer-Institut für Angewandte Optik und Feinmechanik IOF, 07745 Jena, Germany 5 Russian Quantum Center, 121205 Moscow, Russia and 6 Institute for Quantum Optics and Quantum Information, 6020 Innsbruck, Austria

Quantum information processing is steadily progressing from a purely academic discipline to- wards applications throughout science and industry. Transitioning from lab-based, proof-of-concept experiments to robust, integrated realizations of quantum information processing hardware is an im- portant step in this process. However, the nature of traditional laboratory setups does not offer itself readily to scaling up system sizes or allow for applications outside of laboratory-grade environments. This transition requires overcoming challenges in engineering and integration without sacrificing the state-of-the-art performance of laboratory implementations. Here, we present a 19-inch rack quan- tum computing demonstrator based on 40Ca+ optical qubits in a linear Paul trap to address many of these challenges. We outline the mechanical, optical, and electrical subsystems. Further, we de- scribe the automation and remote access components of the quantum computing stack. We conclude by describing characterization measurements relevant to quantum computing including site-resolved single-qubit interactions, and entangling operations mediated by the Mølmer-Sørensen interaction delivered via two distinct addressing approaches. Using this setup we produce maximally-entangled Greenberger–Horne–Zeilinger states with up to 24 ions without the use of post-selection or error mitigation techniques; on par with well-established conventional laboratory setups.

I. INTRODUCTION lenge across architectures [14]. These challenges are prominent examples of problems that need to be over- Quantum information processing as a computational come as quantum devices scale to hundreds of qubits. paradigm has been proposed as an efficient means to It has become clear over the last decade that any de- tackle computational challenges throughout science and vice that can outperform classical high-performance com- industry [1–6]. The rapid scaling of the computational puting for tasks relevant in industrial or applied science potential with the number of quantum bits (qubits) is the settings will require substantially more qubits than cur- basis for widespread interest in realizing a quantum in- rent architectures can sustain [27–31]. In addition to a formation processor, or quantum computer. Tremendous large number of qubits, such a device should present the progress has been made both experimentally and theo- user with a hardware-agnostic interface, and require little retically in exploring and demonstrating hallmark capa- to no maintenance by on-site personnel during standard bilities of quantum information processors in numerous operation. Meanwhile, all the basic routines should be architectures [7–12]. Among the most successful of these automated and perform at the level sufficient for fault- architectures are trapped atomic ions, which have already tolerance requirements. Finally, the device should be de- met many requirements for fault-tolerant [13] quantum ployable outside of well-controlled, low-noise laboratory computation [14–18]. conditions with purpose-built infrastructure. Demon- With progressing capabilities among all platforms, strating the capabilities of scalable architectures beyond the attention has recently shifted away from proof-of- laboratory implementations is therefore a crucial next step. arXiv:2101.11390v3 [quant-ph] 7 Jun 2021 principle implementations towards integration and scala- bility of architectures [7,8, 14, 19–23]. The shift in devel- In this work we present the first phase of our efforts to- opment of quantum computers from small-scale, expert- wards a compact, 50-qubit quantum computing demon- user devices to integrated, end user-centric systems is strator based on trapped ions as part of the AQTION analogous to the history of classical computation. It (Advanced Quantum computation with Trapped IONs) presents a host of new challenges such as manufactur- collaboration. It features a 1.7 m × 1 m footprint with ing many, effectively identical qubits, and improving the high mechanical stability, and scalable control electron- scaling in number of control and readout lines, while ics. We describe the hardware concept and integration, maintaining low error rates [24–26]. The minimization and characterize the initial system performance including of resource overhead incurred in quantum control tech- entangling gate operation necessary for quantum compu- niques or quantum error correction is an ongoing chal- tation. For a quantum computer to perform arbitrary compu- tations it is sufficient to implement arbitrary-pair, two- ∗ [email protected] qubit entangling gates in addition to single-qubit rota- 2 tions [32, 33]. In a trapped ion quantum computer these encoded in the electronic state of the valence electron operations are typically the result of interactions with in nuclear spin-free 40Ca+ ions. This choice is moti- laser fields. Addressing individual qubits in a register vated in part by technical considerations such as com- with light beams is thus an essential component of univer- mercially available semiconductor laser sources and high- sal quantum computation efforts in trapped ions [34, 35]. quality optics for all the required transitions. Transitions Meeting the demands of state preparation and measure- wavelengths are in the blue, red and infrared part of the ment [36–38] in a scalable fashion is therefore a major optical spectrum. Compared to transitions wavelength challenge in trapped ion quantum computing. Conse- in the ultraviolet (UV) this has several advantages such quently, the demonstrator leverages industrial expertise as reduced charging of trap electrodes and substantially to accomplish scalable integration of light generation and lower onset of solarization or photodarkening of optical delivery, in particular single-site addressing essential for components. Optical qubits can be directly interacted the trapped-ion implementation. The demands of quan- with using only a single beam compared to more com- tum control and algorithmic compiling on the software plex beam geometries for Raman gates in Zeeman qubits stack with increasing qubit and gate numbers are simi- or hyperfine qubits. larly challenging [39]. A detailed description of the holis- Specifically, the qubit |1i state is the tic software stack of the AQTION platform, spanning |4 S1/2, mJ = −1/2i Zeeman state, which is coupled to device-specific control to hardware-agnostic end user al- the long-lived qubit |0i state |3 D5/2, mJ = −1/2i. This gorithms, is beyond the scope of the present paper and excited state has a lifetime of τ = (1.168 ± 0.007) s [40], will be covered in upcoming publications. and decays via an electric quadrupole transition near This manuscript is structured as follows: In section 729 nm, see Fig.1 a. This transition has the lowest II we present an overview of the physical qubit imple- magnetic field sensitivity in the manifold (5.6 MHz/mT) mentation, as well as the means of control, preparation, and is suitable for an effective two-level system as shown readout, and manipulation as necessary for computation. in Figs1 a and b. In sectionIII we describe the main subsystems by func- The high magnetic field sensitivity compared to clock tional groups, including mechanical, optical, and elec- transitions in hyperfine qubits can be mitigated by proper trical subsystems, as well as automation features of the magnetic shielding and stabilization [41]. A more funda- demonstrator. In section IV we turn to characterization mental limit of this optical qubit used is the lifetime of measurements on the composite system. This manuscript the upper qubit state |3 D5/2, mJ = −1/2i. However, τ is concludes in sectionV, where we outline near-term hard- about 4 orders of magnitude longer than typical 2-qubit ware integration goals to expand this setup into a fully operations (200 µs) and 5 orders of magnitude longer than self-contained, trapped ion-based quantum computing single-qubit operations (15 µs). Thus, in the medium demonstrator. term, gate fidelity is not limited by the fundamental phys- ical properties of the qubit but by the specifics of the technical implementation. II. THE QUBIT SYSTEM Preparation of the qubit system in our demonstrator entails two tasks: First, loading of ions into the trap is The choice of atomic species in a trapped-ion ex- typically performed only when the qubit count has to periment is always based on trade-offs between benefi- be changed. Second, preparation of the electronic and cial physical properties of a given species, and technical motional state of the ions which is performed before every implementation challenges associated with it. Broadly experiment. speaking, atomic qubits can be either optical qubits, a. Ion loading 40Ca+ is loaded into the trap ei- Zeeman qubits or hyperfine qubits. In optical qubits ther from a thermal source or via ablation from a tar- quantum information is encoded in two electronic states get. Either method produces ions with temperatures connected by an electric multipole transition with fre- ranging from hundreds to thousands of Kelvin. Atomic quency in the optical domain, and the excited state is 40Ca features a low-lying excited state connected to long-lived or meta-stable. In Zeeman or hyperfine qubits the ground state via a dipole transition, which enables the information is encoded in magnetic sublevels of elec- isotope-selective, resonantly-enhanced two-photon pho- tronic ground states with transition frequencies in the mi- toionisation at commercially available laser wavelengths crowave to radiowave domain. A species may host several near 423 nm and 375 nm. The ionization process takes different types of qubits distinct in their implementation. place at the center of the trap, where ions are confined Each species and qubit type offers advantages and dis- afterward by the trapping potential. The ions are then advantages which may benefit certain applications more Doppler cooled via an electric dipole cycling transition than others. At this stage no single species or qubit type from 4 S1/2 ↔ 4 P1/2 at 397 nm. A repumping laser near has been identified as ultimately superior. The design 866 nm prevents population trapping in the metastable goals and principles for our trapped-ion demonstrator are 3 D3/2 manifold. Doppler cooling alone may be sufficient largely independent of the choice of ion species or qubit to reach crystallization into a Coulomb crystal depend- type to reflect the flexibility that this fact requires. ing on ion number and confining potential strength. Such In our particular demonstrator we use optical qubits Coulomb crystals of N ions support 3N bosonic motional 3 a mJ b 4P3/2 gling gate provided via the bichromatic Mølmer-Sørensen 3D +5/2 5/2 4P1/2 gate [14, 47]. Both single- and two-qubit gates are imple- 866 nm 854 nm repump quench mented using laser light fields focused onto the ions. The 0 -1/2 effective Hamiltonian governing (near) resonant single- -5/2 qubit interactions in the demonstrator is given by [48]

−iνt † iνt pumping 3D5/2 −i((ω−ωeg )t−ϕ) iη(ae +a e ) sb cooling qubit H = ~Ωσ+e e + h.c.,

397 nm Doppler 3D3/2 where ω and ϕ denote laser field frequency and phase, ν is the motional mode frequency, ωeg is the qubit tran- 729 nm sition frequency, and h.c. denotes the hermitian conju- +1/2 coherent 4S1/2 gates. Further, Ω denotes the Rabi frequency associ- 1 -1/2 4S 1/2 ated with the transition, η is the Lamb-Dicke parame- † ter, a is the phonon creation operator, and σ+ denotes FIG. 1. Energy levels and relevant transitions in 40Ca+ for the atomic (spin) raising operator. This Hamiltonian as- quantum computing demonstrator. a Ground and excited state fine structure manifold with electric quadrupole tran- sumes a well-isolated two-level system for the interaction, sitions for sideband (sb) cooling on the first red sideband, uses the rotating wave approximation [43], and we ne- optical pumping, and the ∆mJ = 0 qubit transition. b glect all other vibrational modes. This Hamiltonian in Ground, excited and auxiliary levels in 40Ca+ with transitions first-order Lamb-Dicke approximation leads to a single- for Doppler cooling and detection, repumping, and quenching qubit unitary propagator of the form of the excited state lifetime during sideband cooling. −i α ~n·~σ R(α) = e 2 ,

where α is an angle that depends on the interaction modes, N of which are parallel to the weakly-confining strength and time, ~n is a unit vector, ~σ = {σx, σy, σz} 2N axial trap direction, and perpendicular to that in the is the Pauli spin vector, and ~n · ~σ quantifies the strength radial trap directions [42]. of the interaction along the three spin directions. In b. State preparation and readout State preparation the atomic eigenbasis this can be expressed in spherical- proceeds in four steps. First, ions are Doppler cooled coordinate form assuming ω = ωeg. at 397 nm and repumped near 866 nm. The mo- tional modes of the ion cloud or Coulomb crystal af-  cos θ/2 −i −iφ sin θ/2 R(θ, φ) = e , ter Doppler cooling will in general be in or close to −ieiφ sin θ/2 cos θ/2 the Lamb-Dicke regime [43]. Second, polarization gra- dient cooling (PGC) is employed using two counter- where θ and φ can be controlled via changing the ampli- propagating, orthogonally-polarized beams blue-detuned tude or interaction time of the laser field, and its phase. from the 4 S1/2 ↔ 4 P1/2 transition [44]. Polarization The propagator lends itself to the interpretation of rotat- gradient cooling results in a thermal state of all mo- ing the state of a qubit on the Bloch sphere, and single- tional modes of typically a few quanta of motion for qubit operations are consequently referred to as single- common trapping parameters much below the Doppler qubit rotations. cooling limit [45]. Optical pumping of the qubit mani- Qubit-qubit interactions in linear ion chains forming fold on the |3 D5/2, mJ = −3/2i → |4 S1/2, mJ = +1/2i along the weakly confining trap axis are mediated via transition redistributes the electronic population from the bosonic bus of shared motional modes through spin- the initial mixed population of Zeeman sublevels to the dependent optical dipole forces [49]. These forces are |4 S1/2, mJ = −1/2i state. The final step of preparation generated via a bichromatic laser field detuned slightly is sideband cooling on selected motional modes close to from the upper and lower sideband transition of a se- the ground state. The targeted modes in sideband cool- lected vibrational mode. The effective Hamiltonian gov- ing may consist of subsets of the N axial modes, or of the erning this interaction is given by 2N radial modes closest to the selected carrier transition X X −i((ωk−ωeg )t−ϕk) that implements a gate operation. The cooling rate in H = ~Ωjkσj+e sideband cooling is increased by quenching the lifetime j=j1,j2 k=1,2 −iνt † iνt of the 3 D5/2 manifold through coupling to the short- eiηj (ae +a e ) + h.c., lived 4 P3/2 level via excitation at 854 nm. State-selective readout is performed optically using fluorescence mea- where j enumerates ions, and k enumerates the laser surements on the Doppler cooling transition, either site- tones. Then, ωk and ϕk denote frequencies and phases of resolved using a camera, or collectively (without spatial the bichromatic laser field, ν the closest motional mode resolution) using an avalanche photodiode (APD). frequency, ηj the Lamb-Dicke parameter for this mode, c. State manipulation The universal gate set em- ωeg the frequency of the qubit transition, and Ωjk the ployed [46] in the demonstrator is spanned by arbi- Rabi frequencies of the kth beam for the jth ion. As † trary single-qubit operations and the two-qubit entan- before, a is the phonon creation operator, σj+ is the 4 atomic (spin) raising operator. In the Lamb-Dicke ap- A. Mechanical assembly and environmental proximation this leads to a two-qubit unitary propagator conditions of the form The primary mechanical assembly is composed of  cos χ 0 0 −i sin χ two industry standard 19-inch racks with a footprint of 0.85 m × 1 m each at a height of 2 m. Modules are −iχS2 0 cos χ −i sin χ 0 U (χ) ≈ x =   , MS e  0 −i sin χ cos χ 0  largely free of moving parts to improve mechanical rigid- −i sin χ 0 0 cos χ ity, and long-term stability. Modules that require manual alignment are equipped with self-arresting slide drawers, such that maintenance does not necessitate disassembly. where χ can be controlled with laser field power or in- The sole external supply to the racks is one standard P 16 A/230 V connector per rack, for a total power con- teraction time and Sx = σj,x is the total spin along j 3.7 kW x. The bichromatic beam parameters should obey cer- sumption of less than per rack. Temperature tain relations to guarantee that the motional state is dis- control inside the racks is provided by forced-air cool- entangled from the ions’ spin states at the end of the ing and passive cooling fins throughout the modules. Air interaction [50, 51]. flow is restricted across free-space optical parts by ap- propriate enclosures. This prevents beam pointing in- stability and phase-fluctuations induced by the moving air column. The racks are closed with doors in standard operation, improving directionality of air flow for better cooling, and protecting the equipment from dust. III. TECHNICAL IMPLEMENTATION

1. Ion trap and vacuum apparatus Demonstrations of many of the requisite capabilities for quantum computation using trapped ions have been 40 + The Ca ions are confined in a linear Paul trap (AQT presented using laboratory setups [14–18]. However, dif- Pine trap) consisting of electrodes machined from gold- ferent design constraints apply when constructing tradi- plated titanium, and an alumina holder which serves as tional laboratory setups or our modular approach. In the mounting and electrical isolation between the electrodes. context of this work, we highlight the following: (i) The The macroscopic trap design of the demonstrator con- demonstrator needs to minimize footprint while main- sists of four blade electrodes and two endcaps, and is a taining mechanical stability to move towards scalability variant of earlier designs employed previously in the Inns- without sacrificing performance. (ii) Implementing mod- bruck ion trapping group [52, 53]. The distance from the ularity with flexible standard interconnects helps in re- center of the trap to the surface of the blade electrodes ducing footprint and increasing rigidity, while also al- is r0 = 0.57 mm, while the endcap-endcap distance is lowing replaceability and reconfiguration without major z0 = 4.5 mm. redesign, or manual realignment. (iii) The demonstrator Radio frequency (RF) voltage is applied to two oppos- needs to be self-contained and rely as little as possible ing blade electrodes, and a positive static (DC) voltage on purpose-built infrastructure. This puts restrictions to the endcaps. A set of additional electrodes allows for on external supplies like power, cooling, or environmen- compensation of stray electric fields in order to reduce tal conditioning of the demonstrator location. (iv) Scal- excess micromotion. The remaining two blade electrodes ability inevitably requires standardization. Utilizing es- are held at a DC potential, but may be supplied with an tablished standards to leverage industrial processes and out-of-phase RF potential for symmetric drive, if desired interfaces is therefore desirable. (v) Hardware-agnostic for complete cancellation of axial micromotion. The trap design and scalability require use of automation, as well features a thermal calcium source (oven) for photoioniza- as remote operability. tion, as well as an ablation target. An in vacuo PT100 In this section we present our composite demonstra- temperature sensor allows for temperature monitoring of tor’s setup whose overall concept is shown in Fig.2. the trap in operation. The demonstrator setup is contained within two indus- The trap assembly uses exclusively non-magnetic try standard 19-inch racks. Connections between the materials, specifically titanium, copper, alumina and modules inside each rack and between the two racks are austenitic stainless steel (grade 1.4429 or equivalent) to achieved via electrical and optical patch cords, respec- minimize distortion of the magnetic environment. tively. One of the two racks primarily houses modules The Paul trap itself is located inside a compact stain- related to generation, switching and routing of the re- less steel spherical octagon vacuum chamber. Six di- quired optical frequencies and is hence designated optics ametrically opposing, non-magnetic fused silica DN40 rack. The second houses the ion trap, associated infras- viewports with an antireflective (AR) coating allow for tructure and drive electronics, thus being designated the low numerical aperture (NA) optical access on the trap trap rack. perimeter with NA ≈ 0.05. Additionally, a viewport 5

FIG. 2. Simplified scale model of quantum computing demonstrator housed in two 19-inch racks with major components labelled. Modules in red correspond to optical systems, green for communication and readout, blue electronics and amplifiers, yellow fiber routing and switching, and purple for miscellaneous core modules. The ’optics rack’ contains primarily light generation, switching and routing modules with associated electronics. It additionally houses the coherent radio frequency (RF) and digital signal generation module. The ’trap rack’ houses the main trap module with associated drive electronics, as well as the communications and remote control hub. Interconnects between modules and racks via electrical and optical patch cords. Semi-transparent red is planned 729 nm light generation module. with a clear aperture of 44.2 mm in the trap mounting relative change in magnetic field strength with temper- −5 −1 flange provides optical access with a medium NA ≈ 0.29 ature is δT B ≈ 1 · 10 K . Furthermore, three sets of for imaging of ions to an avalanche photodiode. From compensation coils along three orthogonal axes allow for the opposing side of the vacuum chamber a re-entrance control and stabilization of the magnetic field at the ion viewport with clear aperture of 71.2 mm at a distance location in both absolute value and gradient. of 18.3 mm to the trap center provides optical access via a NA = 0.6 objective lens (Photon Gear, 18WD Atom Imager Objective) for resolved ion imaging and illumina- 2. Trap support infrastructure and environmental isolation tion. The trap mounting flange is equipped with The Paul trap and accompanying vacuum chamber feedthroughs for electrical connection to the trap are the most critical components with respect to envi- electrodes, calcium oven and the PT100 temperature ronmental disturbances like thermal, mechanical or mag- sensor. Two non-evaporative getter (NEG) pumps netic field fluctuations. The employed 40Ca+ implemen- (SAES NexTorr Z200) provide the main pumping ca- tation maintains sensitivity to magnetic field noise that pacity to the chamber. A small ion getter pump (SAES can limit attainable coherence times. Qubit operations CapaciTorr Z100) additionally pumps noble gases depend on amplitude, phase and frequency of the inter- and provides pressure monitoring. Material selection acting light fields. Therefore, any fluctuations on those for chamber construction was again restricted to low quantities, as for example caused by beam pointing in- magnetic permeability, with the exception of permanent stabilities, will adversely affect operation fidelity. Conse- magnets required for pump operation. quently, these critical components are situated in an envi- Permanent magnets are further used in Halbach and ronmentally isolated housing, as shown in Fig.3, which Helmholtz configuration to provide the quantization field we refer to as the trap drawer. The drawer itself, de- for the qubits. These are mounted directly to the vac- signed at AQT, makes up the bottom layer of the trap uum chamber. The resulting homogeneous field in the rack, and is fastened to it via supports. The supports in trap center has an angle of 66◦ and 34◦ to the trap axis, turn connect to sliding rails on ball bearings through ac- and the imaging axis, respectively. The magnitude of tive vibration damping elements (Accurion Vario) based the total field produced is B0 = 0.50 mT. Temperature- on pre-loaded springs and magnetic repulsion elements. compensated samarium cobalt magnets are employed to Measurements of the isolators’ magnetic fields show that reduce magnetic field fluctuations to a minimum. Their their influence at the ions’ position is below ambient mag- 6

FIG. 3. Schematic of trap drawer detail, focusing on the trap proper and mechanical components, displayed with extended (opened) drawer. Three sets of compensation coils with each a Helmholtz and anti-Helmholtz coil per holder (red) together with four sets of permanent magnets in Helmholtz (blue, left leader) and Halbach (blue, right leader) configuration define and compensate the magnetic environment. µ-metal shielding encloses the trap setup except for penetrations allowing electrical and optical access. Active vibration isolation and thick honeycomb-lattice breadboards provide mechanical stability. A fan outside the shielding provides cooling for components close to the shield. netic field level. The sliding drawer allows for easy ac- a Q-switched (pulsed) laser (Coherent Flare NX) situ- cess during installation and maintenance by clearing the ated outside the magnetic shielding in the trap drawer main rack structure. The majority of the drawer foot- emitting at 515 nm provides highly energetic pulses for print is enclosed in a µ-metal (ASTM A753 Alloy 4) ablation loading [54] of 40Ca+ from the in vacuo tar- shield (supplied by Magnetic Shield Ltd) for magnetic get. Second, a multi-color diode laser (MDL) genera- isolation, which has a limited number of penetrations for tion module (Toptica, MDL pro) provides light for all electrical and optical access. Active instruments and elec- incoherently-driven interactions: Doppler and polariza- tronics that can cause magnetic field noise are outside the tion gradient cooling at 397 nm, line broadening (’lifetime shielded section wherever feasible. quenching’ for the qubit reset) at 854 nm, repumping at 866 nm, and 423 nm light used in the first (resonantly en- hanced, isotope-selective) step for photoionization. This B. Optical subsystems MDL setup is supplemented by a free-running laser diode (Toptica iBeam smart) providing light at 375 nm for the Interaction with and readout of the qubits is primarily second (non-resonant) photoionization step to the contin- undertaken using optical fields in the presented demon- uum. The last major light generation module provides 729 nm strator. The ability to manipulate and read out single light at for sideband cooling, optical pumping, qubits with light is thus central to its operation. Opti- and the coherent qubit control transition. Preliminary cal and optoelectronic subsystems consequently occupy operation of this module uses a tapered amplifier (Top- an appreciable portion of the available space and com- tica, TA pro), which is fed by seed light generated out- plexity. In the following we will discuss the generation side of the rack until the integrated laser source is in- and stabilization of the requisite lasers, present the light stalled. The seed light is derived from an ultra-stable routing and addressing capabilities, and finally summa- titanium sapphire (Ti:Sa) master oscillator (MSquared rize the readout and detection components. SolsTiS) locked to a high-finesse optical cavity, resulting in a linewidth of (3.6 ± 0.4) Hz [38]. The seed light is fed into the TA via optical fiber with active fiber noise can- 500 mW 1. Laser light generation and stabilization cellation [55]. The TA has an output power of at a seed level of 15 mW to 30 mW, which is sufficient to drive the amplifier gain into saturation. The bichro- The demonstrator is equipped with three principal matic light fields required for the Mølmer-Sørensen inter- laser generation modules, as indicated in Fig.4. First, 7 action are generated by supplying a two-tone RF signal to presented in a separate publication. the acousto-optic modulator (AOM) further downstream. Future hardware upgrades will be composed of a com- 2. Light delivery, switching, and addressing Stabilization module The delivery subsystem handles the necessary routing AQT Beech Trap module and spatial distribution of the light colors throughout the setup. This includes collective delivery for all the lasers Toptica MDL pro 515 as well as site-selective (addressing) delivery for coherent 397 qubit control. The system provides control over the tem- poral and intensity profile of the light fields via amplitude 375 423 shaping, amplitude stabilization and amplitude switch- ing. The optical subsystems have been made modular Fiber distribution 854 module whenever possible to provide replaceability and readjust- ment without disturbing other parts of the setup. Inter- 866 module connection is achieved via fiber-optical patch To light routing cords in line with the requirements on stability and modularity. Polarization-maintaining single-mode opti- cal fibers are used for delivery throughout due to the po- larization sensitivity of optical transitions between Zee- man sublevels in the magnetic field. Typically, free-space Toptica TA pro From Ti:Sa FNC optics outperform fiber optics in terms of transmission 729 loss and polarization extinction ratio. This gap in per- 729 module formance grows for shorter wavelengths. Consequently, intermediate free-space optics are employed where fiber- based components perform insufficiently. Figure5 shows FIG. 4. Schematic of principal light generation modules. A a schematic of the delivery subsystem. modified Toptica MDL pro unit produces four of the five laser colors needed for incoherently-driven excitations. Their out- Four main delivery points for optical access are ar- put is fiber-coupled to a frequency stabilization module. A ranged orthogonal to the high NA access ports of the vac- free-running laser diode is additionally installed downstream uum chamber. Each of these is equipped with a fiber col- to provide the final incoherent excitation color. Laser colors limator for delivery. The collective qubit laser at 729 nm within the qubit manifold are generated by a Toptica TA pro following the FAOM propagates through holes in the trap seeded by light from an ultra-stable MSquared SolsTiS Ti:Sa endcaps. On the opposing side is another single-mode master oscillator present in the laboratory. fiber with the two photoionization colors. Delivery of all other collective beams happens at 45◦ to the trap pact, diode-based laser system stabilized to a high-finesse axis. A large-mode-area photonic crystal fiber (PCF) cavity, which is completely contained in the rack. The (NKT Photonics LMA-PM-5) delivers the superimposed pending system upgrade features a specified linewidth of Doppler cooling laser, refreeze laser, one of the two PGC <2 Hz and an output power of >200 mW after fiber noise lasers at 397 nm, as well as the repumping and quench cancellation. lasers at 866 nm and 854 nm, respectively. A single-mode Both ablation loading and photoionization inherently fiber on the opposing port delivers the remaining sec- have no need for stringent frequency stabilization. On ond PGC laser to complete the scheme. The high energy the other hand, all interactions with 40Ca+ require pre- 515 nm light pulses for ablation loading are coupled free- cise control of the absolute frequency of the respective space into the trap from below. The four fiber access lasers to maintain efficient operation. The MDL unit ports are equipped each with a fast and slow photodiode has therefore been extended to provide two fiber-coupled for monitoring power and stabilization close to the ion feedback outputs combining all four frequencies on two position. patch cords, which are fed to a dedicated stabilization Individual control over the amplitude of not only each module. The stabilization unit should provide reliable color, but each laser beam, is required by nature of low-noise frequency locking along with low long-term the gate-based interaction. Amplitude shaping is imple- drift rates. In addition to these general requirements we mented via free-space double-pass AOMs. These shap- need to comply with the demonstrator’s design princi- ing AOMs further provide the individual frequency off- ples, which demand compactness, remote control access, sets required to bridge the detuning between frequency and automation features. The module used here to com- stabilization cavity resonance and required transition fre- ply with these requirements is the AQT Beech module. quency. They are situated inside dedicated rack units as Inside, all lasers are locked to a reference cavity. The cav- part of the switching module. An additional mechani- ity in turn is stabilized via a transfer lock to an atomic cal shutter is inserted in the Doppler cooling beam path, transition in a gas cell. The details of this system will be normally blocking the undiffracted 0th order after the 8

Switching PGC 2 module Fiber distribution module Double pass AOMs Double PGC 1 From light generation Doppler 397 423 PDs 854 375 866 To wavemeter 729

Double pass Addressed

FNC AOMs Switching module Global 729 Fiber AOMs

Single ion 515 addressing Trap module

FIG. 5. Schematic of light delivery, switching and address- ing modules. Light is fiber-delivered to dedicated switching modules utilizing free-space double-pass AOMs, after which overlapping and fiber routing to their final destination is han- dled on a fiber distribution module for incoherent interac- tions. Photodiodes (PDs) are placed throughout the beam- FIG. 6. Simplified illustration of addressing approaches tri- line for continuous power monitoring. The qubit laser system aled, dimensions not to scale. a A fiber-coupled rigid waveg- has similar switching and routing capabilities, with addition uide with microoptics delivers light via a shrinking telescope of fiber noise cancellation (FNC), and fiber AOMs for im- to the main objective and onto the ions. Beam separations proved on/off extinction ratio, bichromatic modulation for are fixed. b A pair of crossed acousto-optic deflectors (AODs) Mølmer-Sørensen interactions, and light field parameter con- with a relay telescope delivers light to the main objective and trol. One of two approaches is used to deliver addressed light, onto the ions. Beam separations are variable. see Figs.8 and6. . switching AOM. Opening the shutter gives access to a is delivered to the ions via free space. For the addressing laser which is red-detuned by ≈ 300 MHz from the main units we trial two different approaches: The first uses a cycling transition, and can be used to re-freeze a molten fixed number of fiber-coupled rigid waveguide channels ion crystal. The light switching modules are followed by with microoptics which are imaged onto the ion. The a dedicated fiber distribution module, where free-space second is based on two crossed acousto-optic deflectors optics are used to overlap and fiber-couple beams into (AOD) for positioning of the addressed beam [56]. An patch cords for final delivery. The fiber distribution and overview of these approaches is shown in Fig.6. The ar- switching modules further incorporate photodiodes for rangement of light fields arriving at the ion location is continuous power monitoring on all colors throughout the shown in Fig.7 and Fig.8. beamline. For the microoptics approach, light is sent to an ad- The beamline for the qubit manipulation laser is built ditional splitting module with a fixed number of output analogously, with the addition of active fiber noise cancel- channels, followed by individual FAOMs for light switch- lation, preceding the switching module. The qubit laser is ing before being fed to the unit. The FAOMs have a split on the switching board into two beams before pass- center frequency of 150 MHz, an on/off extinction ratio ing a respective free-space double-pass AOM: The first of ≈ 40 dB, and imprint the bichromatic sidebands onto goes directly into a fiber-coupled AOM (FAOM) and is the laser, as required for Mølmer-Sørensen interactions. sent to the trap along its symmetry axis for collective op- The presence of an individual FAOM per ion has the erations on all qubits simultaneously. The second is used further benefit of allowing individual control of the light for single-ion addressing. Light from an addressing unit field’s parameters for each channel, to e.g. interact with 9 different motional modes for efficient coupling, to adjust on the cycling transition with these parameters yields a each ion’s Rabi rate, or to compensate for potential in- photon flux of order 500 kcts/s on the APD given the dividual qubit frequency shifts. At the stage presented NA, optical losses and device quantum efficiency. here, the splitting board is composed of a diffractive op- The primary imaging system features a high numeri- tic splitting the input light eightfold. The output fibers cal aperture of NA ≈ 0.5 limited by the trap apertures. of the FAOMs are coupled into a waveguide and imaged This system is used both for site-selective readout, and onto the ion crystal via the main objective lens described manipulation of individual ions (single-site addressing). in section IIIB3. This addressing unit is provided by The system’s main objective is a compound lens designed Fraunhofer IOF. The details of this unit are beyond the to operate near the diffraction limit for the detection light scope of this paper and will be summarized in a forth- at 397 nm as well as at the addressing light at 729 nm.A coming publication. dichroic mirror is used to overlap the two colors through In the AOD approach on the other hand light is this main objective, while compensation optics in the delivered via a single fiber. The two AODs are ori- imaging path correct for abberations introduced by the ented at an angle of ±45◦ with respect to the ion dichroic mirror. Imaging design targets are a magnifica- string symmetry axis. Beam steering without incurring tion of ≈ ×29 at a field of view of 150 µm to match the position-dependent frequency shifts is achieved by utiliz- detector size. The design modulation transfer function ing crossed pairs of AODs where the frequency up-shift exceeds 0.5 at a resolution of 0.5 µm over the full field of from one unit (using +1st diffraction order) is exactly view, well in excess of what is required to resolve single cancelled by the second (using -1st diffraction order). An- ions with a typical spacing of more d0 ≥3 µm. gular deflection through the AODs is converted to trans- The main objective’s mounting provides five degrees lation in the ion plane by action of the main imaging of freedom for precisely aligning the optical axis with objective. Driving the AODs with multiple RF tones al- the ions necessary to achieving these tight specifications. lows for simultaneous addressing of multiple ions at the First, translation perpendicular to the optical axis (X-Y cost of additional beams situated above and below the translation) is achieved via flexure joints in the objec- ion string. These beams have a nonzero frequency shift, tive’s mounting plate, which are actuated via fine-pitch and their number grows quadratically with the number of micrometers. Second, pitch and yaw can be adjusted RF tones applied. Consequently, the power available per using fine-pitch screws with a spring-loaded kinematic beam decreases quadratically with the number of tones three-point mounting. Piezo-electric actuators allow for as well. fine tuning the position on all three adjusters in addi- tion to coarse alignment via thumbscrews. The final de- gree of freedom is translation along the optical axis (Z 3. Imaging optics translation or focusing). Coarse alignment is achieved via the fine-pitch threading used to secure the objec- Optical readout can be performed in two ways: First, tive lens. This thread is guided through a tight-fitting spatially-resolved imaging of the ion string using an tube which affords high repeatability. Fine-adjustment EMCCD camera through use of near-diffraction-limited, is achieved by using the kinematic mount’s three piezo- high-NA objective. Second, not spatially discriminat- electric transducers in tandem for pure translation. Re- ing (collective) light detection through a single-photon- alignment and refocussing using manual thumb screws counting avalanche photo diode and medium NA optics. is typically only necessary after making major changes Both detection paths are situated orthogonally to the to the system. Fine adjustment of the addressing using trap axis and the plane which contains all laser beams the piezo actuators is typically done once a day or after to minimize stray light onto the detectors. Addition- opening of the trap drawer. ally, this arrangement gives the largest possible numer- ical apertures through the vacuum chamber view ports for large collection efficiencies on the imaging systems. C. Electronics, control and automation Both APD and camera are placed outside of the mag- netic shielding, where light exits through penetrations in Access to and control of the experimental platform is the shield. Such an arrangement helps to minimize the managed by a rack-mounted desktop computer which amount of stray magnetic fields close to the trap cham- is accessed via Ethernet. Both racks feature Ethernet ber which may be caused by the readout electronics in switches that connect individual devices to the control the detectors. computer. Readout through the APD serves as a means of detec- The electronic outfitting of the demonstrator setup is tion in trap characterization and system diagnostics, but based largely upon modular components. The demon- is only suitable for small system sizes, and does not offer strator is controlled and driven by both analog and digital site-selectivity. The imaging system employed for APD electronics. The trap blades providing radial confinement readout has a medium numerical aperture NA ≈ 0.29, are driven by a dedicated RF signal generator (Rhode with a magnification of about ×1, and a field of view & Schwarz SMB100B) which is amplified via a helical of about 60 µm. A single ion driven far into saturation resonator [57]. The ion’s secular frequency is actively 10

FIG. 7. Schematic of trap drawer detail, focusing on optical and detection components, displayed with extended (opened) drawer. Optical interfacing with the ions is achieved via fiber delivery for Doppler cooling, polarization gradient cooling, quenching and repumping (red pair), as well as collective qubit laser (blue, left) and photoionization (blue, right). Free-space delivery of the pulsed ablation laser is achieved via access from below (green). Single-site addressing lasers are steered by an addressing unit, and overlapped with the resolved detection path (high-NA objective, yellow) on a dichroic beam combiner (silver). Compensation optics for resolved light counter abberations introduced via the combiner. Collective imaging to an APD leaves at the back of the chamber (purple). Detection electronics and light sources are situated outside the µ-metal shielding. Fiber AOMs allow pulsing and imprinting of bichromatic sidebands onto the qubit lasers. stabilized by a feedback circuit actuating on the supplied Control of Trapped IONs’ (M-ACTION) [59]. It uses a trap RF [58]. In addition, the demonstrator makes use of ’star’ topology as shown in Fig.9, with a central master state-of-the-art phase-coherent digital signal generation, control board that communicates with the control PC real-time control, and in-sequence decision making based via a custom Ethernet protocol, and multiple peripheral on field programmable gate arrays (FPGAs) to perform boards providing RF output [60]. The peripheral boards digital (pulsed) operations. communicate with the master via a low-level low-voltage differential signaling (LVDS)-based protocol through a backplane into which all the boards are inserted. 1. Experimental control electronics The master board is a commercially-available Avnet Zedboard extended with custom boards for digital I/O The laser pulses used for manipulating the states of and board-to-board communication. It is centered the ions are controlled using acousto-optic modulators. around a Xilinx Zynq system-on-chip, which holds both These require radio frequency signals which are precisely an FPGA core used for low-level deterministic signal timed and phase-coherent (inter-pulse, inter-channel, and handling, and a dual-core 667 MHz ARM A9 CPU suit- inter-module). For typical RF pulses several microsec- able for higher-level control and real-time computa- onds in length, the timing resolution needs to be <10 ns tions. These include Boolean decisions such as those to control pulse lengths to better than 1 %, and the tim- in quantum error correction, as well as more sophisti- ing jitter must be below a few hundred picoseconds to cated Bayesian decisions featuring feedback of a contin- ensure repeatability. Digital input/outputs (I/Os) with uous parameter to the experimental hardware [59, 61]. similar timing resolution and jitter are also required, both The FPGA core, on the other hand, monitors the pe- for triggering external devices such as RF switches, shut- ripheral RF boards, and controls the digital I/O that ters or arbitrary waveform generators, and for count- requires precise timing. ing photon-arrival pulses from photomultipliers or APDs. The RF peripheral boards each consist of four direct- These RF and digital signals are manipulated using an digital synthesis (DDS) chips (Analog Devices AD9910), FPGA-based modular experimental control system de- controlled by a standalone FPGA (Xilinx Spartan-6 veloped at ETH Zurich, known as ‘Modular Advanced XC6S150T) with sufficient memory and a pulse sequence 11

sequence detection fulfills the branch conditions. Photon

854 count data from either a camera or APD is used directly → Doppler on the FPGA to determine whether a branch condition B 866 is met. PGC 1 A simple example would be of a state transfer |Si → π 729 375 |Di by means of a 2 pulse. If at the decision making point |Si is measured, that is many photons are scattered in Global 423

Side view the detection window, then the FPGA determines that the condition for state transfer to |Di is met, and exe- cutes a π-pulse to transfer the population into |Di. If on 515 the other hand |Di is detected, that is few photons are PGC 2 scattered, this additional pulse is not executed. A more complicated example is given in the literature [62], which → B APD uses the same hardware in a separate experiment.

729 375 2. Experimental control software Global 423 Top view Top The experiment hardware is operated using two layers Camera 729 Addressed of control software. The lower layer, running on the mas- ter board, is written in C++ and provides access to the functionality of M-ACTION to a Python-based higher FIG. 8. Geometric arrangement of beam delivery, beam polar- layer running on the control PC. This higher layer is ization indicated where required. The Doppler cooling beam, used for day-to-day experimental operation and program- the repumping and quenching beams, as well as PGC beams ming, while the lower layer can be used to implement enter the chamber at 45◦ to the trap axis. The collective high-performance real-time computations, or extend the 729 nm beam is delivered through a hole in the trap endcap. capabilities of M-ACTION. Photoionization beams enter through a hole in the opposing A graphical user interface (UI) gives direct feedback endcap. The medium-NA port is used for collective readout to the operator, and is used for the majority of day- of the whole ion chain with an APD. The high-NA access port to-day experimental control tasks. Script-based imple- is used for single-ion addressing and readout with a camera. mentations of pulse sequences allow for versatile exten- sions to low-level pulse patterns available from the UI. Automated routines for calibration, maintenance and er- processor to independently execute most typical exper- ror handling, such as Rabi frequency tracking, frequency iments without intervention from the master [60]. In drift compensation, and string recrystallization, are sup- situations where intervention from the master board is ported to maintain the system at high fidelity without required, such as when real-time feedback is being car- constant supervision. Quantum circuits are executed via ried out, the latency between an input to the mas- a high-level language made in house, called PySeq, which ter and a change in pulse sequence on the peripheral acts as an intermediary between state-of-the-art frame- cards is around 5 µs. Recent revisions of the RF board works like Cirq [63] and Qiskit [64] and close-to-hardware also feature two analog-to-digital converters, and sup- descriptions on the laser pulse level. PySeq is, similar to port on-board servo regulators for intensity stabilization Qiskit, a Python package and provides a convenient ab- with sample and hold synchronous to the local pulse se- straction layer translating quantum circuit objects like quences. Regulator gains and setpoints may be altered rotations around an axis for a given angle to hardware in-sequence to help cope with external nonlinearities. instructions such as laser pulses with a certain power and The aforementioned RF boards support a single-tone duration. It is expected that this feature, in combination output per channel, requiring multiple channels to be with remote access to the setup, will greatly improve the added together for multi-tone quantum gates. Addition- ease of use for collaborators. ally, the complexity of a pulse is limited by the band- width of the interface between the FPGA and the DDS chips. A new RF generation board using 1 GSa/s DACs IV. SYSTEM CHARACTERIZATION controlled directly by a more powerful FPGA, as well as 32 GB of local memory, is being currently developed to We now turn to characterizing the demonstrator setup. overcome these bottlenecks. A suite of common measures and experiments is used to In-sequence decision making is performed based on evaluate the engineering approaches for the rack-based pre-determined conditional decisions or ’branches’. This architecture. The section begins with outlining standard pre-determination allows FPGA memory management. operation parameters for the ion trap. Measurements on Branches are sub-sequences that are executed if in- the mechanical stability of the rack and the performance 12

Control PC Ethernet

RF peripheral boards Master Zedboard RF outputs Digital outputs 32 32 PID lock statuses 8 Photon counters 8 8 Analog inputs Backplane links (RF stabilization)

FIG. 9. M-ACTION experimental control system. The master board acts as the hub of the system, synchronously running experimental sequences involving the digital I/O and the RF peripheral boards, and managing communications with the control PC. of the active vibration isolation system are presented. The ion gauge’s pressure measurement is performed at We show measurements on imaging system performance, the pump location instead of the ion location. Differ- as well as addressing capabilities using two different ad- ential pressures in ultra-low vacuum conditions can thus dressing unit devices. We finally turn to measurements lead to an underestimation of the pressure at the ion lo- pertaining to the operation of the demonstrator itself, cation. Consequently, we independently determine the such as characterization and compensation of the mag- pressure at the ion location via collision rate measure- netic field gradients, coherence times, ion temperature ments [67, 68]. Collisions with residual thermal atoms and heating rates, and gate performance for single and melt the ion crystal and thus limit the stability of ion pairwise qubit interaction. crystals in the trap. We distinguish between two differ- ent types of collision events: Those that melt the crystal and cause ions to change sites in the refrozen crystal, A. Trapping parameters and those that lead to molecule formation via chemi- cal reactions which changes the number of (bright) ions. Detection of reconfiguration events is done by observ- The Paul trap’s radial confinement voltage is supplied ing the position of non-fluorescing, co-trapped ions (de- to a helical resonator, in order to filter and impedance fect hopping). We measure a collision rate of Γcol = match the RF drive to the trap [57] which results in a (0.0025 ± 0.0011)/s per ion by observing reconfiguration voltage step-up at the trap side. The loaded resonator events in a three ion crystal consisting of two bright oscillates at a drive frequency of ΩRF ≈ 2π× 27.4 MHz. 40Ca+ and one dark, co-trapped ion, which corresponds Pin,max = 10 W −11 It is driven with an input power of up to . to a pressure of pion = (9.7 ± 4.2) · 10 mbar assum- The trap endcaps are supplied with a voltage of up to ing collisions with H2 [68]. This means that even a 50- Vec ≈ 1000 V. An ion trapped in the trap will oscil- ion chain is unlikely to experience a collision during the late at the resulting pseudopotential’s three fundamental qubit coherence time of 100 ms. Ion loss may occur when trap frequencies ωax, and ωrad which can be measured by collisions are sufficiently strong to lead to unstable ion external excitation with oscillating fields (’tickling’) [65] trajectories, or when chemical reactions cause formation or by sideband spectroscopy [66]. These trap frequen- of dark ions. By observing an ion crystal of 32 bright cies are (nearly) identical to the center-of-mass motional 40Ca+ ions over the course of 12 h we observe the loss of excitations of ion clouds or crystals in the three trap di- only one ion from the trap. rections. We determine the secular frequencies for a sin- 40 + gle Ca of ωrad ≈ 2π× 3 MHz in the radial direction with 10 W input power, and ωax ≈ 2π× 1 MHz along the trap axis at about 1000 V endcap voltage. In situ tem- B. Mechanical stability and active damping perature measurements using a PT100 thermistor give a temperature of the trap that depends on RF drive power. Mechanical instability affects quantum computing fi- The temperature reaches about Tmax ≈ 100 °C after sus- delity via a multitude of avenues from light field ampli- tained operation at Pin,max = 10 W. The pressure in the tude fluctuation, lowering of signal-to-noise through blur- vacuum chamber as measured by the pump’s gauge is ring or defocusing in the detection system, to light field 1.5 · 10−11 mbar. The pressure reading does not depend dephasing noise [69–73]. We measure the vibrational sta- on the drive power, indicating little outgassing from ad- bility of the setup using piezo-electric shear accelerome- sorbed contaminants on the trap surfaces. ters (Endevco 7703A-1000) at various locations in the 13 setup. Time series data from the detectors is recorded optical tables. Spectra do show a clear influence of the and Fourier transformed to voltage power spectral densi- operation of cooling fans used in the rack construction. ties in an audio spectrum analyzer (Stanford Research The majority of root-mean-square (RMS) displacement Systems SR1). Voltage spectra are converted to dis- is contributed at low frequencies below 10 Hz. Notably placement spectral densities via the accelerometer sen- these frequencies are also well below the fan rotation fre- sitivity calibration. The measurement is limited by the quencies, indicating that they do not simply originate electronic noise floor of the signal conditioner (Endevco from vibrations of the fans or modulations at the 50 Hz 133) below about 2 Hz. Displacement spectral densities motor drive. Determining the origin of excess vibrations recorded simultaneously in the horizontal and vertical di- caused by the fans and the structured noise at low fre- rections are shown in Fig. 10, along with a reference spec- quencies is part of future upgrade efforts, including DC- trum obtained on an empty, broadband-damped, honey drive fans and improved air flow direction. The perfor- comb-lattice optical table in close proximity. Root-mean- mance is comparable to the empty reference table in spite square (RMS) displacements over the full measurement of the compact, tower-like construction in active opera- bandwidth are shown in Tab.I with electronic back- tion, and validates engineering approaches used in the ground subtracted. demonstrator.

2 10 a ¢ z H 0 p 10 / C. Imaging and detection performance m Noise floor n

¡ -2 10 Optical table

D Demonstrator, fans off S -4 Characterizing the performance of the primary imag- A 10 Demonstrator, fans on ing system provides information about the achievable

1 2 3 signal-to-noise ratio in readout, and the minimal achiev- 10 10 10 able spot size and crosstalk for addressing light. After optimization of the objective alignment we resolve well- 2 10 b separated ions in a 50-ion linear crystal. A typical image ¢ z of an 11-ion crystal with minimal ion-ion separation of H 0 p 10 ≈ 4 µm is shown in Fig. 11 a recorded at the detection /

m wavelength of 397 nm. We determine the achieved imag-

n Noise floor

¡ -2 10 Optical table ing system magnification to be ×29.9 from the known

D Demonstrator, fans off pixel dimensions and calculated ion spacings for the used S -4 A 10 Demonstrator, fans on trap parameters. This is slightly larger than the design magnification of ×29. The high-NA readout optics en- 1 2 3 10 10 10 able camera detection times down to 300 µs at a fidelity Frequency (Hz) of about 99.9 %. We determine the detection fidelity by preparing an FIG. 10. Displacement (amplitude) spectral densities (ASD) ion string either in the bright 4 S1/2, or in the dark 3 D3/2 a parallel to the floor (horizontal) and b perpendicular to manifold by turning off the repumping laser at 866 nm. the floor (vertical) calculated from time series data obtained We elect to pursue this method over creation of the dark with piezo-electric shear accelerometers. Traces show equiva- 729 nm lent displacement spectral density of the electronic noise floor state via excitation using the laser to avoid con- (blue), and spectral densities of typical optical table setup flating operational infidelities in qubit manipulation with in close proximity (orange), demonstrator setup with cooling detection infidelities. After a cooling period we perform a fans turned off (green) and on (red). projective measurement and detect each ion individually on a camera. From the counting statistics in each ion de- tection region we determine the probability of measuring Noise Opt. table Full w/o fans Full w/ fans the prepared state for a given measurement time, that is, RMShor. (nm) 54 21 61 275 measure many (no) photons for the ion prepared in the RMSvert. (nm) 50 33 139 335 bright (dark) state. We estimate the detection crosstalk by determining the probability of measuring a bright TABLE I. Root-mean-square (RMS) displacements over the state in a detection region in between two bright ions full measurement bandwidth for vibration measurements spaced at 5.9 µm. Detecting light above the background shown in Fig. 10. Electronic background subtracted point- in this empty region of space comes solely from detection wise from spectra. crosstalk. At a measurement time of 300 µs we detect no events above the background threshold out of 10000. The overall vibrational stability of the system is sim- Consequently, we conclude that detection crosstalk dur- ilar to traditional optical setups situated on dedicated ing our measurement windows is negligible. 14

a ) . u .

a b (

y t i s n e t n I Ion position (a. u. )

FIG. 11. Detection performance. a Fluorescence image of a linear string containing 11 ions. The axial trap frequency is ωax = 2π × 450 kHz, corresponding to a distance between the two center ions of 4 µm. b Integration over pixel columns shows well-separated ions.

D. Single ion addressing performance frequency increment obtained from the AODs by com- paring the population profile to the known ion distances Addressing capabilities are crucial for the quantum at a given axial center-of-mass mode frequency. The cal- (4.9 ± 0.1) m/MHz computing scheme we pursue. This capability is routinely ibration yields a deflection slope of µ . quantified in terms of the ability to resolve individual A measurement for a 16-ion string with a minimal ion sites along with the crosstalk between individual chan- distance of ≈ 3.4 µm and a total length of ≈ 60 µm nels. In the following, characterization measurements is shown in Fig. 13 a. The intensity profile shown of the microoptics addressing unit and AOD addressing in Fig. 13 b is measured analogously to the microop- units are presented. tics addressing unit’s, yielding a beam waist of w0 ≈ (1.09 ± 0.02) m At this stage we utilize only four of the channels on µ . Next, we characterize the resonant and the microoptics addressing unit. The beams from these off-resonant crosstalk in a 10-ion string with minimal 3.5 m channels are fixed in position, and measuring the beam inter-ion distance of µ . The ratio of the Rabi fre- profile proceeds by moving a single ion electrostatically quencies of the non-addressed ions to the addressed ion c along the trap axis through the beams by scanning the is plotted in Fig. 13 . We obtain an average resonant 0.2 % 1 % endcap voltages. At each position the light intensity is crosstalk of with a maximum of on ion 5 when obtained by measuring the oscillation frequency of Rabi addressing ion 4. The average nearest-neighbor crosstalk 0.5 % oscillations. The Rabi frequency is proportional to the is . This is significantly lower than in the microop- electric field at a given position. Figure 12 a shows the tics addressing unit. The difference may at least partly be estimated light intensity along the trap axis obtained in attributed to the better overall optical quality of macro- this fashion. From a Gaussian fit to a higher-resolution scopic precision optics used in the AOD approach, rather scan shown in Fig. 12 b we calculate a beam waist of than microoptical prototype components. Figure 13 d shows the results of off-resonant crosstalk w0 = (0.81 ± 0.01) µm for all spots. Different coupling efficiencies through FAOMs and waveguides lead to peak measurements. For this measurement we perform a π/2 heights varying across channels. resonant collective -pulse, followed by an addressed AC-Stark pulse of variable length, followed by a collec- We further measure the resonant crosstalk between tive −π/2-pulse. These composite pulses, sometimes re- channels as defined by the ratio of the Rabi frequencies, ferred to as U(3) pulses, are used to reduce the effect Ωadjacent/Ωaddressed when exciting a single ion. For the of crosstalk. The AC-Stark shift is proportional to the four active channels we measure resonant crosstalk be- light field intensity I ∝ E2 while the Rabi frequency is tween 1.9 % and 3.4 % as shown in Fig. 12 c. This is √ proportional to the electric field Ω ∝ I ∝ E. Con- much larger compared to what we would expect from a sequently, we expect the U(3) pulses to produce signif- Gaussian beam with w0 = 0.81 µm or Airy fringes arising icantly smaller crosstalk. The maximum crosstalk mea- from the finite aperture, and implies that the crosstalk is sured is 2.6 × 10−4, thus 20 times lower compared to limited by optical aberrations. the resonant crosstalk. The average crosstalk on nearest- For the AOD addressing unit we scan the addressing neighbors is 1.3 × 10−4. beam over a string of ions by changing the AOD drive frequency. In this measurement we use laser pulses of a fixed power and duration such as to produce a pulse area of < π at the center of the beam. Scanning the beam E. Coherence properties and magnetic fields across an ion will thus produce Rabi oscillations with maximal population in the excited state coinciding with Qubit coherence times are affected by a multitude of maximal intensity. We calibrate the deflection per drive sources. Two common technical sources of decoherence in 15

1 a ) . u . a (

y

t 0.5 i s n e t n I

0 0 7 14 Ion position (µm) 1 2 3 4 b c 1 ) - - - . u . a ( 2 - - y t i s n 3 e - - t n I

4 - - -

4 0 4 2 10− Ion position (µm) 0 2 4×

FIG. 12. Microoptics addressing unit performance. a A single ion’s position is scanned electrostatically along the trap axis by varying the endcap voltages. The square of the Rabi frequency is plotted as a function of this position for four active channels at a distance of 3.4 µm. b Same as a with higher resolution for spot size measurement of the focused addressing beam at 729 nm. By fitting a Gaussian distribution to the data we obtain a beam width of about w0 ≈ 0.8 µm. Dashed black lines indicate the nearest neighbors for a 50-ion crystal at the minimal distance of ≈ 3.2 µm. c Estimates of resonant crosstalk from intensity profiles in a. Entries with ’-’ were not assessed.

0.8 a e P

n o i t 0.4 a l u p o P

0.0 0 30 60 Ion position (µm) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 b c d 1 1 ) 2 2 . u 3 3 . a ( 4 4

y 5 5 t i s 6 6 n e 7 7 t n I 8 8 9 9 10 10 4 0 4 2 4 10− 10− Ion position (µm) 0.0 0.5 1.0× 0.0 1.3 2.6×

FIG. 13. AOD addressing unit performance. a Scan of addressing beam over a 16-ion crystal. The population Pg is used as a proxy for signal intensity, see main text. b Spot size measurement of the focused addressing beam at 729 nm. A single ion’s position is scanned electrostatically along the trap axis by varying the endcap voltages. The square of the Rabi frequency is plotted as a function of this position. By fitting a Gaussian distribution to the data we obtain a beam width of about w0 ≈ 1.1 µm. Dashed black lines indicate the nearest neighbors for a 50-ion crystal at the minimal distance of ≈ 3.2 µm. c Resonant crosstalk measurements in 10-ion crystal with minimal inter ion distance of 3.5 µm. Plotted are the ratios of Rabi frequencies of ions relative to the addressed ion (white on diagonal). d Same as c but using off-resonant, compensating U(3) pulses, see main text. Ions where Rabi oscillations are too slow to fit reliably are set to 0 in the plot to avoid spurious structure. 16 state-of-the-art trapped-ion setups are phase noise from experiments, or mains noise. This is further supported the driving fields, and magnetic field noise. Phase noise by two observations: First, neighboring ion trap exper- may originate either directly from laser frequency insta- iments implementing feedforward to cancel mains noise bility, that is finite linewidth, or can be imparted through see a substantial improvement in coherence times. Sec- e.g. fiber noise or optical path length noise. Magnetic ond, a similar experiment being set up in a neighboring field noise modulating the energy splitting in the qubit building with overall worse environmental control but al- manifold often originates from mains or its harmonics, most no other occupants causing magnetic field noise also switching power supplies, or ground loops. shows increased coherence times. Phase noise in the driving field is ultimately limited by In addition, the spatial homogeneity of the mag- the linewidth of the stabilized laser. Vibrational isola- netic field needs to be investigated to maintain coher- tion, rigid construction principles, fixing of flexible (fiber ence across an extended ion register. Small devia- optics) paths and air current control in free-space are im- tions in the positioning of the employed Halbach and plemented throughout the setup to prevent adding excess Helmholtz configurations may cause a gradient or cur- phase noise. Additionally, fiber noise cancellation is used vature across the trap axis. Likewise, the permanent up to the double pass switching AOM, see sectionIIIB2. magnet of the ion getter pump may cause a magnetic The influence of magnetic field noise depends on field gradient across the ion string. We measure a gradi- two factors: The noise present and the sensitivity of ent ∂zB = (0.111 ± 0.002) mT/m by performing Ramsey the utilized transition to it. The qubit transition spectroscopy on the ground state qubit and then shift- |4 S1/2, mJ = −1/2i ↔ |3 D5/2, mJ = −1/2i is the least ing the equilibrium position of a single ion electrostat- sensitive to magnetic field fluctuations out of the S1/2 ↔ ically. The gradient leads to a frequency shift on the D5/2 manifold, with a slope of 5.6 MHz/mT. This is or- ground state qubit transition of (3.1 ± 0.1) Hz/µm. Ap- ders of magnitude higher than in clock transitions of hy- plying appropriate currents to the compensation coils perfine qubits [74], and therefore magnetic field stability reduces this axial gradient by an order of magnitude as well as homogeneity have to be precisely controlled in to (0.2 ± 0.1) Hz/µm. For the five times less sensi- order to reach sufficient coherence times on the order of tive optical qubit transition this means a gradient of T2 ≈ 100 ms or better. (0.041 ± 0.021) Hz/µm, corresponding to an end-to-end We characterize the temporal magnetic field stability frequency difference of ≈ 8 Hz in a 200 µm chain of 50 by performing Ramsey spectroscopy on the ground state ions, as shown in Fig. 14 a. qubit |4 S1/2, mJ = −1/2i ↔ |4 S1/2, mJ = +1/2i tran- sition in a single ion. This transition has a five times increased sensitivity to the magnetic field with respect to the qubit transition, with a gradient of 28.0 MHz/mT. The optical pulse sequence to access this transition be- F. Ion temperature and motional heating rates gins with a π/2-pulse, which creates an equal superposi- tion state between |0i and |1i.A π-pulse then coherently High fidelity gate operations typically require the ions transfers the population from the optical qubit |0i state to retain coherence in their motional degrees of free- to the |4 S1/2, mJ = +1/2i state. After the Ramsey wait- dom [16, 75–77]. Motional coherence is ultimately lim- ing time the sequence is reversed, which implements the ited by the motional heating rate. We therefore mea- Ramsey time evolution of an effective magnetic dipole sure both the ion temperature, that is phononic mode transition. This sequence yields a significant decrease occupation, and from that the heating rates with side- in sensitivity to optical noise sources, thus isolating the band thermometry [78]. Sideband thermometry can be influence of the magnetic field. Performing Ramsey spec- applied for an average phonon occupation n¯ . 2. Com- troscopy with closed µ-metal shield on the ground state parison of the Rabi oscillations on the red and blue side- qubit and optical qubit yields respective coherence times band of the qubit transition yields the average phonon GS Opt of T2 = (18 ± 1) ms and T2 = (90 ± 30) ms, as shown occupation [48]. After sideband cooling a single ion, in Fig. 14 b and c. This is sufficient to execute about 400 we obtain a phonon number of n¯ph, ax = 0.02 ± 0.01 two-qubit gates or 4000 single-qubit gates during the co- (at ωax = 2π × 1.05 MHz) in the axial direction, and herence time. n¯ph, rad = 0.06 ± 0.02 (at ωrad = 2π × 2.5 MHz) in the Furthermore, we measure no influence of the vibration radial direction. By increasing the time between side- isolation elements on the coherence time of our qubit. band cooling and temperature measurement we obtain The initial decay of fringe contrast is consistent with co- a heating rate of (0.221 ± 0.007)/s in the axial direction Opt herence times in excess of the T2 = (90 ± 30) ms. How- (see Fig. 15 a, and (0.3 ± 0.1)/s in the radial direction. ever, for waiting times longer than 25 ms we observe ac- These heating rates compare favourably with values ob- celerated contrast decay which limits the coherence time tained in other traps operated at room temperature [79] to the value above, and causes the substantial uncer- (see in particular Fig. 8). Measuring heating rates for tainty. The source of this enhanced decay is the subject axial trap frequencies between ωax = 2π × 0.15 MHz and of ongoing investigation, but may be caused by magnetic ωax = 2π ×1.05 MHz, we obtain a power-law dependency α field noise induced by switching magnets in neighboring 1/ωax, with α ≈ 1.7, see Fig. 15 b. 17

1.0 900 a b ) D

( 0.5 P ) z H ( 0.0 π 650

2 1.0

/ c R ω ) D

( 0.5 P 400 0.0 80 10 60 0 13 26 Ion position (µm) Waiting time (ms)

FIG. 14. a Magnetic field gradient before compensation (blue, (3.2 ± 0.1) Hz/µm) and after compensation (red, (0.2 ± 0.1) Hz/µm) on ground state qubit as seen from Ramsey fringe frequency ωR for a fixed detuning as a function of ion position, corrected for linear frequency drift at fixed position. b Decay of Ramsey fringes of dark state population P (D) GS for the ground state qubit over time, resulting in a coherence time of T2 = (18 ± 1) ms. c Same for optical qubit transi- tion. The sensitivity to magnetic fields is five times lower, leading to less impact from magnetic field noise. We determine Opt T2 = (90 ± 30) ms.

around an axis in the Bloch sphere’s equatorial plane, Rˆ Rˆ ¯ a b x y n that is between and , can be implemented via res- )

0.16 s r / e onant excitation on the 729 nm qubit transition. An opti- ( 8 b w t m cal phase imparted using the FAOMs is used to define the u ∆ n /

¯ axis of rotation relative to the first pulse in a sequence, n n o ∆

n which may be defined arbitrarily. The remaining axis, e o 0.08 t ˆ h a 4 Rz, is instead driven by off-resonant AC-Stark pulses. r p

g e π/2 15 s

n Typically we perform rotations in µ , limited by g i t a r a our current control electronics. e e v H A 0.00 0 0 300 600 200 600 1000 In order to characterize the fidelity of these single qubit Waiting time t (ms) ω /2π (kHz) w ax rotations we perform randomized benchmarking on a sin- gle qubit [80], assuming uncorrelated noise. A number of a FIG. 15. Axial heating rates. We calculate the heating n Clifford gates is executed, where each Clifford gate in- rate of ∆¯n/∆tw = (0.221 ± 0.007)/s at ωax = 1.05 MHz by ˆ curs an average cost of 1.875 Rx(π). At the end of the fitting the increase in n¯ over the waiting time tw, where n¯ is determined from sideband thermometry. b Heating rates sequence the Clifford gate which inverts the sequence is are determined as in a as a function of trap frequency. The added, thus creating an identity operation if not for gate α dashed line is a power-law fit 1/ωax, where α ≈ 1.7. errors. Here, we concatenate up to 100 Clifford gates and fit an exponential decay of the form A × pn + 0.5 to the population of the initial state. We assume that G. Single qubit gates the population will decay to a value of 0.5 for a large number of gates. A + 0.5 is then the fidelity of state initialization. The error per Clifford gate is calculated Arbitrary single-qubit rotations are part of the com- as RClif = (1 − p)(1 − 1/d), with d = 2 denoting the plete gate set we chose to implement for universal quan- dimension of the Hilbert space for a single qubit. tum computation capabilities. Qubit rotations are im- plemented differently depending on the sets of qubits re- quired, and on the axis of rotation chosen. For many First we characterize qubit rotations when using the applications rotating all qubits collectively is required. global, axially-aligned beam that drives collective ro- This can be efficiently implemented using a single, col- tations. We obtain a Clifford gate fidelity of FClif = lective beam travelling axially along the spine of the trap, (99.83 ± 0.01) % or Fgate = (99.91 ± 0.01) % per single- co-linearly with the ion string. The single-site-resolving qubit rotation. We perform the same measurement addressing units described in section IVD are used in- on a single ion with the tightly-focused beam from stead if only subsets of qubits need to be rotated. the microoptics addressing unit, and obtain FClif = The mechanism to drive the rotation itself is addition- (99.75 ± 0.02) % and Fgate = (99.86 ± 0.01) %, respec- ally different depending on the axis chosen. A rotation tively. 18

H. Mølmer-Sørensen gate and entanglement 1 generation a

0 The ability to generate entanglement in a determin- Parity istic way is key for quantum computation [81–83], and 1 the missing component to our complete gate set. Dif- 0 π/2 π ferent types of entangling gates have been proposed and demonstrated for trapped-ion qubits [49, 84, 85]. Here, 1 b we utilize the Mølmer-Sørensen gate [47, 50] which gen- erates entanglement through spin-dependent forces gen- 0 erated by a bichromatic light field slightly detuned from Parity a vibrational mode. However, quantifying the degree and 1 depth of entanglement in many-body quantum systems 0 π/4 π/2 generated by any means remains a challenging task [86]. Analysis pulse phase Φ Entanglement witnesses [87, 88] are often used, where the observable crossing a given threshold guarantees multi- FIG. 16. a Parity oscillations after a Mølmer-Sørensen gate partite entanglement of a given depth. Greenberger- on two ions followed by an evaluation pulse with phase Φ. Horne-Zeilinger (GHZ) states are a class of maximally- The amplitude of the parity oscillations is C2 = 0.995 ± 0.011 entangled Schrödinger’s cat states that have the for- with 100 measurements per data point. Together with pop- tunate features of being natively implemented by the ulations P2(SS, DD) = 0.9988 ± 0.0005 we determine a fi- Mølmer-Sørensen gate, and providing a particularly easy- delity of F2 = 0.997 ± 0.006. b Parity oscillations of a 24-ion to-measure entanglement witness. GHZ states further GHZ state with 100 measurements per data point. The par- are highly susceptible to errors and decoherence [89–91], ity contrast drops to C24 = 0.501 ± 0.013, the population to and as such provide a sensitive probe for characterizing P24(S . . . S, D . . . D) = 0.588 ± 0.006. We obtain a fidelity of the performance of our compound system. F24 = 0.544 ± 0.007; more than 6 standard deviations above the 24-partite entanglement threshold of 0.5. Measurement First, we implement Mølmer-Sørensen gates using a uncertainties are below marker size. collective, axially-oriented beam on ion strings from 2 to 24 ions. The state fidelity F after the entan- gling operation provides the entanglement witness with F > 0.5 guaranteeing full-depth entanglement. We char- again not corrected for SPAM errors and without post- acterize the operation using a two-ion crystal. The selection, and is more than six standard deviations above fidelity is directly inferable from the populations in the threshold for 24-partite entanglement [89]. The par- b the |S, Si = |1, 1i and |D,Di = |0, 0i states with ity oscillations are plotted in Fig. 16 . To the best of our knowledge this is the largest GHZ state as well as the P2(SS, DD) = 0.9988 ± 0.0005 as shown in Fig. 16 a, as well as their coherences [89]. The coherences are ob- largest fully-entangled state that has been generated in tained from observing the oscillations in the state’s par- any system without error mitigation or post-selection. ity as the phase of an analysis π/2 pulse is varied be- In the data shown above Mølmer-Sørensen gates were fore projective measurement. Measuring the amplitude carried out on the axial modes of vibration. In order to of this oscillation yields C2 = 0.995 ± 0.011 [89, 92]. create a fully programmable system, we use the radial From those we calculate a single-gate state fidelity modes of vibration for arbitrary-pair, addressed entan- F2 = (P2 + C2)/2 with F = 0.997 ± 0.006. This fidelity gling operations on specific qubits in long ion strings. includes all errors from state preparation and measure- Characterizing the creation of states with addressed op- ment (SPAM) and in particular is achieved without post- erations naturally leads to the question of fidelity metric; selection. A single two-ion Mølmer-Sørensen gate typi- with two prominent candidates. The first is the fidelity cally takes 200 µs. Sustaining the interaction for odd- of, say, GHZ state production where the non-addressed integer multiples of this duration implements repeated sub-register is ignored. This will quantify the action of Mølmer-Sørensen gates. Measuring the fidelity after dif- an entangling gate, but is oblivious to what this opera- ferent numbers of gates, and fitting an exponential decay tion does to the rest of the register. The second, more as shown in Fig. 17 a yields a simple estimator of the stringent choice, would be to determine the fidelity of per- state fidelity with 0.9983 ± 0.0001 per gate. forming an entangling operation on the addressed qubits Larger multi-partite entangled states are subsequently without affecting the idling qubits. This is then the over- produced by applying a single Mølmer-Sørensen gate to lap of the full register state with the ideal register state, multiple ions. We demonstrate the generation of GHZ rather than sub-registers. Given that crosstalk is un- states up to 24 qubits. Measured fidelities are plotted in avoidable we elect to chose the second metric. Fig. 17 b, where pairs of ions are successively added to Initial tests were carried out with the microoptics ad- the existing string and the measurement is repeated. For dressing unit, addressing the two outer ions of a three ion 24 ions we measure P24(S...S,D...D) = 0.588 ± 0.006, crystal. The Mølmer-Sørensen gate with the radially- C24 = 0.501 ± 0.013 and F24 = 0.544 ± 0.007, which is oriented addressing beam yielded a register overlap fi- 19

100.0 a shown in Fig. 18. We achieve fidelities in the range from 97.5 0.969(7) to 0.986(8). Cumulative population in the nom- 95.0 inally non-addressed sub-register for these measurements Axial was below 0.2 %. 92.5 Radial We anticipate that further improvements on radial

State fidelity (%) 90.0 1 4 7 10 13 mode stability, cooling of radial modes, addressing unit Number of gates and mode disentanglement [93–95], should increase the 100.0 b fidelity of the addressed gates. 87.5 75.0 V. CONCLUSION 62.5

GHZ fidelity (%) 50.0 2 8 14 20 26 In this manuscript we have provided a detailed descrip- Number of ions tion of the experimental implementation of a compact, trapped-ion quantum computing demonstrator situated FIG. 17. Mølmer-Sørensen gate performance. a Decay of in two 19-inch racks. We presented mechanical, optical overall state fidelity after repeated, odd-integer application and electrical systems along with characterizing experi- of ≈ 200 µs Mølmer-Sørensen interactions for axial and ra- ments. This experimental platform improves upon con- dial two-ion gates. We infer a single-gate state fidelity of ventional hardware implementations in terms of modular- 0.9983 ± 0.0001 per axial gate and 0.9936 ± 0.0003 per radial ity, integration, and remote control. In our characteriza- gate. b Axial Mølmer-Sørensen gates on linear ion string for tion measurements we find the system performance to be different ion numbers. Pairs of ions are successively added to on par with conventional, laboratory-based hardware im- the existing string and the measurement repeated. mea- plementations in terms of experimentally relevant perfor- surements are performed at an axial center-of-mass mode fre- mance criteria. We find that mechanical stability, optical ω = 2π × 234 kHz quency of ax , to ensure the formation of a readout and addressing performance, heating rates, co- linear string for large number of ions, and were taken consec- utively. measurements are performed at an axial center-of- herence times, and Mølmer-Sørensen entangling fidelities in the current implementation do not suffer relative to mass mode frequency of ωax = 2π × 200 kHz to 1000 kHz on different days. Measurement uncertainties are below marker traditional optical table setups. Using the compound sys- size. tem we are able to produce maximally-entangled Green- berger–Horne–Zeilinger states with up to 24 qubits with 1 2 3 4 a fidelity of (54.4 ± 0.7) %. To our knowledge this is the largest maximally-entangled state yet generated in 1 97.7(9) 98.6(8) 98.0(7) any system without the use of error mitigation or post- selection, and demonstrates the capabilities of our sys- 2 97.7(9) 97.0(9) 98.1(7) tem. In addition, we presented site-selective qubit opera- 3 98.6(8) 97.0(9) 96.8(8) tions to implement a complete gate set for universal quan- tum computation using two distinct approaches to ad- 4 98.0(7) 98.1(7) 96.8(8) dressing: A microoptics approach with fixed, rigid waveg- uides, and an acousto-optic deflector approach. Both of these approaches offer advantages over the other in par- ticular settings. FIG. 18. Full register overlap fidelity of states produced using The microoptics approach readily offers itself for si- AOD addressing unit in 4-ion crystal. There is no meaning- multaneous multi-site addressing without producing off- ful distinction between pair (1,4) and (4,1) as opposed to in axis spots which can lead to resonant and off-resonant single-site addressing. Consequently, the matrix is symmetric. crosstalk. The power scaling in such a scenario is linear in the number of channels, assuming a suitable power distribution system is at hand. Parallel radial sideband delity of F2 = 0.989 ± 0.005 for a single gate. Again cooling is one direct beneficiary of such capabilities, as is concatenating multiple gates and fitting an exponential direct generation of interaction between more than two 0 decay yields a fidelity of F2 = 0.9936 ± 0.0003 per gate as qubits. Individual control over amplitude, phase, and plotted in Fig. 17 a. F2 is the fidelity of Mølmer-Sørensen frequency of each channel is a fundamental advantage of 0 gate including SPAM errors, while F2 is approximately this approach but requires one FAOM per qubit. The po- the pure fidelity per gate operation without SPAM errors. sitional stability is not affected by the oscillator stability With the AOD addressing unit we measure all of RF sources, and extension to larger registers are not pairwise-entangling gates in a 4-ion crystal. We calibrate limited by the speed of sound or similar quantities such the gate on the two outer ions and use the same set of pa- as in AOD-based devices. rameters for all gates. The register overlap fidelities are The AOD approach on the other hand is technologi- 20 cally simpler, thus offering superior performance at this enable us to increase this number to the AQTION con- stage. Optical quality of macroscopic components is of- trol target of 50 qubits and beyond. We have already ten also superior to microoptics, in particular in proto- demonstrated basic capabilities of control in larger qubit typing scenarios such as here, which reduces abberations. chains as shown in Fig. 19 b, with a 50 ion chain al- The addressing is inherently flexible, such that it can be ready crystallized in our trap. In the long term, we hope adjusted for qubit registers from 2 ions to 40 ions in our a configuration. Adjustment of power and optical phase of individual channels is possible without an optical modu- b lator per ion, which significantly reduces the technologi- cal overhead compared to the microoptics approach. This unit is fed by a single fiber, and no prior power distri- FIG. 19. Ion images of a 24 and b 50 ions in the demonstra- bution capabilities are required. The switching speed in tor. The 24-ion chain was used to demonstrate 24-partite en- AODs is limited ultimately by the speed of sound in the tanglement within the setup without the use of post-selection deflecting crystal, which therefore also limits the speed or error mitigation. 50-ion chains are the mid-term control at which operations can be performed. The quadratic target and can already be trapped and cooled. Non-uniform power loss for multi-site addressing, and off-axis spots brightness stems from the finite size of the detection beam. limit this technology to the simultaneous addressing of a small number of ions. that the demonstrator’s features and engineering solu- With both of these approaches we demonstrate single- tions mean that ion trap-based quantum computers may qubit and pairwise-entangling gates on registers up to be situated in any space with reasonable environmental 10 ions. From randomized benchmarking we obtain a stability and vibrational level. Quantum computation F = (99.86 ± 0.01) % fidelity of gate per addressed single- with qubit count exceeding 100 is feasible based on our ion gate. Measurements of resonant crosstalk were shown architecture and this characterization of its first imple- to be below 1% across the entire 10-ion register with the mentation. AOD approach, while non-resonant crosstalk was mea- sured to be less than 1.25 × 10−4 in the same string. Together with the pairwise entangling operations with VI. ACKNOWLEDGEMENTS fidelities between 97% and 99% we show all the basic operations for a fully programmable quantum system. We gratefully acknowledge funding from the EU Benchmarking of larger registers, and with more com- H2020-FETFLAG-2018-03 under Grant Agreement no. plete suites of benchmarking tools [96] will be undertaken 820495. We also acknowledge support by the Austrian as part of the next round of hardware integration and Science Fund (FWF), through the SFB BeyondC (FWF software improvements. Project No. F7109), and the IQI GmbH. This project These near and mid-term upgrades to the hardware has received funding from the European Union’s Hori- and software stacks will further improve upon the demon- zon 2020 research and innovation programme under the strator’s capabilities. Use of an external master oscil- Marie Skłodowska-Curie grant agreement No 840450. lator to generate the narrow-linewidth qubit laser will P.S. and M.M. acknowledge support from the Austrian no longer be required after installation of the, compact Research Promotion Agency (FFG) contract 872766. diode-laser source which is currently under construction P.S., T.M. and R.B. acknowledge funding by the Office as part of the AQTION collaboration. Similarly, single- of the Director of National Intelligence (ODNI), Intelli- site addressing capabilities will be improved in mode gence Advanced Research Projects Activity (IARPA), via quality and number of channels. This will allow the setup US ARO grant no. W911NF-16-1-0070 and W911NF- to implement more complex algorithms by moving from 20-1-0007, and the US Air Force Office of Scientific Re- axial gates to radial quantum gates enhanced by estab- search (AFOSR) via IOE Grant No. FA9550-19-1- 7044 lished quantum control techniques [97, 98]. Upgrades LASCEM. to M-ACTION, as well as complimentary developments All statements of fact, opinions or conclusions con- to the control and remote access software stack will en- tained herein are those of the authors and should not able easier access to the demonstrator capabilities in a be construed as representing the official views or policies hardware-agnostic fashion. of the funding agencies. Already, the device presented is capable of operating with qubit numbers on par with state-of-the-art conven- tional laboratory setups. An image of such a qubit regis- REFERENCES ter is shown in Fig. 19 a. The mid-term upgrades should

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