Quantum computing with ions
• Introduction to ion trapping and cooling • Trapped ions as qubits for quantum computing and simulation • Qubit architectures for scalable entanglement • Towards topological quantum error correction • Outlook: connectivity and scalability • Rydberg excitation of trapped ions for fast gates • Single ion delivery for fabricating a solid state quantum device
www.quantenbit.de F. Schmidt-Kaler
Mainz, Germany: 40Ca+ Ion qubit choice MICROWAVE HYPERFINE NIST, Hannover, Rydberg 9 + Oxford, Sussex, … UMZ, Stockholm Be : NIST, ETH Ryd. OPTICAL 25Mg+ : NIST, Freiburg 40Ca+ : UIBK, UCB, 43Ca+ : UIBK, Oxford 171 + ETH, PTB Yb : JQI, Sussex, SPIN 88 + Siegen, Duke,… Sr : MIT, Weizmann 40 + 133 + Ca : Oxford, UMZ 128Ba+ : UIBK Ba : UCLA…
P1/2 P1/2 P1/2
D D5/2 5/2 |1> |1> SF‘ |1> S S 1/2 |0> SF |0> 1/2 |0> • Best overall performance so far • Infinite T • Infinite T • Easy readout 1 1 only scattering errors only scattering errors • Requires optical phase stability • complicated level scheme • readout overhead • Limited by metastable lifetime Two qubit gate error budget
Error type Current (%) Countermeasure Prospective (%) Gate detuning 0.3 composite pulses <0.01
Mis-set laser power 0.04 improved calibration <0.01 Unequal illumination 0.002 - - Thermal occupation 0.01 improved cooling <0.01 Heating 0.01 cryogenic trap, noise supp. <0.01 Motional dephasing 0.1 .. 1.0 tech. noise suppression N/A Anharmonic coupling 0.1 spectator mode cooling N/A Scattering >1.0 20 x laser power <0.05 Osc. light shift <0.7 pulse shaping <0.01 Spectator excitation <0.3 pulse shaping <0.01 Laser intensity noise <0.01 - -
Best two-qubit fidelity: 99.9% Benhelm et al., Nature Physics 4, 463 (2008) Ballance et al., PRL 117, 060504 (2016) Gate times: 20µs…100µs Gaebler et al., PRL 117, 060505 (2016) The Mainz trap for qubit register reconfigurations High performance multi-layer ion trap
Fabrication • Laser-cutting of Alumina • Gold evap./galvoplating • 32 segment pairs of uniform geometry • Bonding to capacitor arrays
Performance • 1.5 MHz axial trap frequency @-6V segment voltage • Lowest heating rate: 3 phonon/s @ 4 MHz radial trap frequency • 1 day trapping times High performance multi-layer ion trap
32 segment pairs
Kaushal, et al,
Motional coherence measurement: Fabrication of micro traps
1. Laser cut 2. Ti/Au deposition 3. Laser cut electrodes
4. Electroplating 5. Dicing off edges 6. Stack assembly galvo plating of 10µm of gold Ion movement – qubit register reconfiguration
∆퐸푧= 0.03(1) ℏ휔푧, 80 µs
∆퐸푧= 0.028(2) ℏ휔푧, 30 µs ∆퐸푧= 0.02(1) ℏ휔푧, 42 µs
Shuttle ion crystal Separate two-ion crystal Geometric phase gate 99.5(1)% Merge into two-ion crystal fidelity on radial mode Swap ion positions Shuttle single ion Walter et al., PRL109, 080501 (2012) Kaufmann et al, NJP 16, 073012 (2014) Kaufmann et al, RPA 95, 052319 (2017) Qubit register reconfiguration control
Data flow: Trap Calibration High level QIP command potentials data
Sequence commands Calculate Calculate ion trap voltages positions
Voltage limits Calculate Electrical Slew rate voltage hardware ramps specifications Shuttling voltage ramps Transfer function Filter • Technical constraints compensation • Low motion excitation • Optimum speed Output 2- and 3-qubit shuttle and swapping
Process tomography data
mean process fidelity 99.96(13)%
Kaufmann et al., PRA 95, 052319 (2017) B-Field Sensing with entangled ions
1. Prepare entangled sensor state ۧ↑↓ȁ훹ۧ = ȁ↑↓ۧ + ȁ 2. Accumulate phase ۧ↑↓ȁ훹ۧ = ȁ↑↓ۧ + ei휑ȁ Linear Zeeman effect: ℏ Δ퐵 푥1, 푥2 = 휑ሶ caused by 푔휇퐵 inhomogeneous B-field Interrog. time T = 0 – 3.1 s 3. Individual state readout Estimate relative phase 휑 Use Bayes experimental design for optimum information gain
Ruster et al, PRX 7, 031050 (2017) Inhomogeneity Inhomogeneity cancellation Hilder , et al, Position along trap axis (m) axis Trap Combined Combined Field Compensation Rings Main Ring
Zeeman splitting (MHz) • Inhomogeneity consistent with zero! Inhomogeneity • Dw < (2π)40 Hz for outermost segments (1σ) cancellation • No shuttling-induced phase compensation required • Automatic tracking of frequency drifts, B-field, ….
Seconds of coherence time Sensitivity: 12pT / Hz
Range: 6mm (Hz)
Hilder, et al, Ruster et al, PRX 7, 031050 (2017) “Knitting together” a 4-ion GHZ state
equivalent circuit: |0000> + |1111> |0> H |0>
|0> |0> duration: 3.3 ms
Experimental sequence uses > 300 shuttling operations for SB Full state tomography yields 94.7 % cooling, state preparation, quantum fidelity from about 50k measurements. circuit, state analysis.
Kaufmann et al, PRL 119, 150503 (2017) Experimental sequence for a 4-ion GHZ state
many shuttling op. • 324 segment to segment transports • 8 separation/merge operations
+ many gates: • 12 single qubit gates • 3 two-qubit gates • multiple spin echos
0.5 seconds cohernence for |0000> + |1111>
Monz et al, PRL 106, 130506 (2011) Kaufmann et al, PRL 119, 150503 (2017) Classical control of sequences Quantum error correction Break-even point for useful Quantum error correction?
|ψ> = α|0> + β|1> Channel, incl. correlated & coherent noise, and Bob is asked: Alice perfectly encodes Is it |ψ> or |ψ> ? |ψ> = α|0> + β|1> L L one round of Or, was Igor really a help? imperfect QEC by Igor
Bermudez et al, Phys. Rev. X 7, 041061 Shuttle based color code QEC
Real-space representation of shuttling-based one-species QEC cycle with multi-qubit MS gates
Stabilizer readout
Helpful Igor! Break-even point for useful QEC ?
Topological quantum error correction, using the reconfigured ion quantum register
• Logical qubit using a 7-qubit color code • Improve and adapt hardware and software • Develop strategies to overcome current limitations
Bermudez et al, Phys. Rev. X 7, 041061, Nigg et al., Sci. 234, 302 (2014) Shuttle based PRX 7, 041061 color code QEC Real-space representation of shuttling-based one-species QEC cycle with 2-qubit gates
Stabilizer readout Topological quantum error correction
Bermudez et al, Phys. Rev. X 7, 041061 Nigg et al., Sci. 234, 302 (2014)
Stabilizer Logical qubit using readout 7-data qubit color code
Z(φ1)
Z(φ2)
Fault tolerant Z(φ3)
Syndrome readout Z(φ4)
X Z(φs) X Chao, Reichardt, arXiv:1705.02329 Z(φf) Yoder, Kim, Quantum 1, 2 (2017) Sequence - Fault tolerant syndrome readout Readout quality 6 ions: 90 configurations 41 two-ion transports 158 single ion transport ‘dark’ detection probability 6 two-ion rotation 98.9 % 21 merge/separate 6 two-qubit gates 98.8 % 6 RAP pulses 99.0 % 6 indivdual fluo. det. 98.7 %
X 94.1 %
X 94.2 %
Shelving @729nm for qubit readout affected by shuttling: • Improve shuttling calibration • Implement robust shelving
• Reduce ƞ729 Hilder, et al, Fault tolerant syndrome – partity readout
|1111> Even parity
|1110> Odd parity
Hilder, et al,
EU flagship: Advanced QC with trapped ions • Development of a robust and compact ion-trap quantum computing demonstrator • Scalable quantum hardware and electronics • Holistic software stack from quantum algorithms to device specific operations • Scalable verification and validation • Quantum advantage over classical capabilities • Quantum processors outside the laboratory Key figures, now and future, for trapped ion-QC
• Single shot read-out of spin state better 1 - 10-4 • Single gate fidelity better than 1 - 10-4….10-5..6 mitigating intensity noise, off- resonant excitation, AC Stark shifts • Two qubit gate fidelity 1 – 10-3….10-4..5 mitigating intensity noise, off- resonant excitation, AC Stark shifts • Gate operation time ~ 30µs …. ≤10µs using shaped light fields • Qubit register reconfiguration operations, few µs to 80µs …. ≤1µs optimized electric wave forms • Long coherence times, up to a few seconds …. seconds with dynamical decoupling pulse sequences • Decoherence-free substates, >10s …minutes coherence • Micro-segmented traps, 30 segments … >100 … 1000 segments • Cryogenic ion traps, trapping times of days Mainz plans for scaling up • Cryogenic trap with extended lifetime and low heating rate, for a trap device with 130 trap segments consequent upscaling the shuttle & gate approach • Segmented trap at room temperature with >50 segments and multiple laser-interaction zones combining advantages of long crystal and shuttle approach, with parallel gate & shuttle execution • Ion shuttles out of trap and recapture • Improvement of gate fidelity and gate speed • Machine learning & Qu. computing Mainz, Germany: 40Ca+ Quantum computing with ions
• Introduction to ion trapping and cooling • Trapped ions as qubits for quantum computing and simulation • Qubit architectures for scalable entanglement • Towards topological quantum error correction • Outlook: connectivity and scalability • Rydberg excitation of trapped ions for fast gates • Single ion delivery for fabricating a solid state quantum device
www.quantenbit.de F. Schmidt-Kaler
Mainz, Germany: 40Ca+ Making two or more atoms/ions/spins interact…
How to make fast gate operations ?
Saffman, Walker, Mölmer, RMP 82, 2313 (2010)
long-range and strong: - Coulomb interaction Join advantages for ion trap qubits - Rydberg dipoles with Rydberg excitations and interactions
Müller, Liang, Lesanovsky, Zoller, NJP 10, 093009 (2008) Experimental Challenges for exciting Rydberg states in trapped ions
• Unfriedly wavelenght range 100nm…150nm Develop reliable and narrow VUV source @ 122nm few µW laser power / optimize difficult beam delivery Or multi-step excitation with UV
• Single / few ion crystal Develop electron shelving detection with high single-excitation detection efficiency
• Hostile high electric alternating RF field of a Paul trap Optimized ion trap & optimized trap operation parameters, compensation of electric field (micro-motion compensation)
NJP 13 (2011) 075014 Rydberg excitation
Doppler shift Stark shift
Schmidt-Kaler et al, NJP 13, 075014 (2011) Feldker et al, PRL 115, 173001 (2015) Higgings et al, PRX X 7, 021038 (2017) kicking ion crystals for entanglement
↓ ↑ 휔t 휔t
푉 0 0 0 0 0
1) Excite a superposition of D5/2 (↓) and Rydberg state (↑) 2) Apply electric kick 3) n7 Rydberg polarizabilty results in spin-dependent potential 4) Kick back 5) Observe geometric phase
spin-dependent potential: 2 2 2 16훽 휔↑ = 휔↓ + Δ휔2, Δ휔2 = − 풫 푛 t t 푡 푡 푚 kicking ion crystals for entanglement
↓ ↑ 휔t 휔t
푉 0 0 0 0 0 퐸(푡) Δ휙
푓0 휋
0 푇 푡 Optimize the electric electric kick by tuning: Generate a Rydberg level n, Kick strength f 0 p-phase gate Kick duration t
Vogel, Li, Mokhberi, Lesanowski, Schmidt-Kaler, arXiv:1905.05111 kicking ion crystals for entanglement
↓ ↑ 휔t 휔t
푉 0 0 0 0 0 퐸(푡) Δ휙 푓 휋 0 (↓ + ↑)1 (↓ + ↑)2 (↓↓+ ↓↑+ ↑↓- ↑↑)
0 푇 푡 Optimize the electric electric kick by tuning: Generate a Rydberg level n, Kick strength f 0 p-phase gate Kick duration t
Vogel, Li, Mokhberi, Lesanowski, Schmidt-Kaler, arXiv:1905.05111 Fidelity Rydberg lifetime: 65µs / 370µs
3-kick Bang-Bang control: 60ns
Realistic parameters for sub-µs entangling operation
See also: Ripol, et al, PRL 91, 157901 (2003), Schäfer Phase space elec. kicks et al, Nat. 555, 75 (2018) Quantum computing with ions
• Introduction to ion trapping and cooling • Trapped ions as qubits for quantum computing and simulation • Qubit architectures for scalable entanglement • Towards topological quantum error correction • Outlook: connectivity and scalability • Rydberg excitation of trapped ions for fast gates • Single ion delivery for fabricating a solid state quantum device
www.quantenbit.de F. Schmidt-Kaler
Mainz, Germany: 40Ca+