DOCSLIB.ORG

Introduction and Motivation the Transmon Qubits the Combined

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introduction and Motivation the Transmon Qubits the Combined Noise Insensitive Superconducting Cavity Qubtis Pan Zheng, Thomas Alexander, Ivar Taminiau, Han Le, Michal Kononenko, Hamid Mohebbi, Vadiraj Ananthapadmanabha Rao, Karthik Sampath Kumar, Thomas McConkey, Evan Peters, Joseph Emerson, Matteo Mariantoni, Christopher Wilson, David G. Cory - - When driven in the single-photon level, the entire system is in Introduction and Motivation The Transmon Qubits the superposition of the states where the photon exists in either - Circuit quantum electrodynamics (QED) studies the - When the detuning between a qubit and a cavity is much larger of the cavities. The symmetric and antisymmetric superposition interactions between artificial atoms (superconducting qubits) than the coupling strength, the second order dispersive coupling of this collective mode can be used to encode a two level system, and electromagnetic fields in the microwave regime at low causes the cavity frequency depending on the state of the qubit realizing a logical qubit: temperatures [1]. It provides a fundamental architecture for [1]. The dispersive coupling provides possible links between realizing quantum computation. isolated cavities. - When a qubit is placed in a 3D superconducting cavity, the - A transmon qubit is a superconducting charge qubit insensitive cavity acts as both a resonator with low loss and a package to charge noise [5]. In the project they will be fabricated from providing an isolated environment [2]. Coherence times of evaporation deposited aluminum on a sapphire chip. transmon qubits up to ~100 μs have been observed [3]. - Advantages of the logical qubits: - Quantum memories made of 3D cavities have achieved 1) A logical qubit of this form will be immune to the collective coherence times as long as 1 ms [4]. dephasing noise on both cavities as the noise will apply an - We aim to make the long lived cavities into qubits with a identical random rotation on any linear superpostion of the transmon acting as a nonlinear actuator on the cavities. This logical states. gives us the best of both worlds, long lifetimes with control of 2) The logical qubit is expected to have a long coherence time as single photon states. all the quantum information is stored in the high-Q cavities, not the lossy transmon qubit. The 3D Superconducting Cavities 3) The number of photons stored in both cavities may be observed without measuring the logical qubit. This allows - The cylindrical 3D cavity consists of a coaxial cavity and a photon loss to be detected and corrected for. circular waveguide [3]. The Combined System 4) The logical qubit may be controlled by detuning the cavities. - The quarter wavelength (λ/4) coaxial cavity is fabricated from - The two cavities fabricated in a single piece have identical This requires microwave tones only for initialization and ultra high purity aluminum. It has one end shorted and the other frequencies and do not communicate directly with each other. measurement. open. The height of the stub defines the resonance frequency. - The sapphire chip with a transmon qubit on it is placed in the - The cavity seam at the top of the cylinder is coupled to the bridge channel connecting the two cavities. The two ends of the Acknowledgements quarter wavelength stub via a cutoff circular mode in the chip intrude into the cavities at the height of the stub, with the waveguide which exponentially suppresses photon seam losses. coupling strength adjustable via changing the intruding length. - The cavity can be driven by a port opened at the height of the - The transmon qubit in the channel couples to the two cavities stub where the electrical component of the field reaches its in the dispersive regime. It will mix the energy levels in the maximum.. individual cavities into collective energy states . Cavity A Cavity B Cavity Cavity Drive Coupler Drive References [1] S. M. Girvin, Circuit QED: Superconducting Qubits Coupled to Port to drive the cavity Microwave Photons (2014) [2] H. Paik et al. Phys. Rev. Lett. 107, 240501 (2011) [3] C. Rigetti et al. Phys. Rev. B 86, 100506(R) (2012) Bridge [4] M. Reagor et al. Phys. Rev. B 94, 014506 (2016) [5] J. Koch et al. Phys. Rev. A 76, 042319 (2007) .
Load more

Recommended publications
  • Direct Dispersive Monitoring of Charge Parity in Offset-Charge
    PHYSICAL REVIEW APPLIED 12, 014052 (2019) Direct Dispersive Monitoring of Charge Parity in Offset-Charge-Sensitive Transmons K. Serniak,* S. Diamond, M. Hays, V. Fatemi, S. Shankar, L. Frunzio, R.J. Schoelkopf, and M.H. Devoret† Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA (Received 29 March 2019; revised manuscript received 20 June 2019; published 26 July 2019) A striking characteristic of superconducting circuits is that their eigenspectra and intermode coupling strengths are well predicted by simple Hamiltonians representing combinations of quantum-circuit ele- ments. Of particular interest is the Cooper-pair-box Hamiltonian used to describe the eigenspectra of transmon qubits, which can depend strongly on the offset-charge difference across the Josephson element. Notably, this offset-charge dependence can also be observed in the dispersive coupling between an ancil- lary readout mode and a transmon fabricated in the offset-charge-sensitive (OCS) regime. We utilize this effect to achieve direct high-fidelity dispersive readout of the joint plasmon and charge-parity state of an OCS transmon, which enables efficient detection of charge fluctuations and nonequilibrium-quasiparticle dynamics. Specifically, we show that additional high-frequency filtering can extend the charge-parity life- time of our device by 2 orders of magnitude, resulting in a significantly improved energy relaxation time T1 ∼ 200 μs. DOI: 10.1103/PhysRevApplied.12.014052 I. INTRODUCTION charge states, like a usual transmon but with measurable offset-charge dispersion of the transition frequencies The basic building blocks of quantum circuits—e.g., between eigenstates, like a Cooper-pair box. This defines capacitors, inductors, and nonlinear elements such as what we refer to as the offset-charge-sensitive (OCS) Josephson junctions [1] and electromechanical trans- transmon regime.
    [Show full text]
  • Optimization of Transmon Design for Longer Coherence Time
    Optimization of transmon design for longer coherence time Simon Burkhard Semester thesis Spring semester 2012 Supervisor: Dr. Arkady Fedorov ETH Zurich Quantum Device Lab Prof. Dr. A. Wallraff Abstract Using electrostatic simulations, a transmon qubit with new shape and a large geometrical size was designed. The coherence time of the qubits was increased by a factor of 3-4 to about 4 µs. Additionally, a new formula for calculating the coupling strength of the qubit to a transmission line resonator was obtained, allowing reasonably accurate tuning of qubit parameters prior to production using electrostatic simulations. 2 Contents 1 Introduction 4 2 Theory 5 2.1 Coplanar waveguide resonator . 5 2.1.1 Quantum mechanical treatment . 5 2.2 Superconducting qubits . 5 2.2.1 Cooper pair box . 6 2.2.2 Transmon . 7 2.3 Resonator-qubit coupling (Jaynes-Cummings model) . 9 2.4 Effective transmon network . 9 2.4.1 Calculation of CΣ ............................... 10 2.4.2 Calculation of β ............................... 10 2.4.3 Qubits coupled to 2 resonators . 11 2.4.4 Charge line and flux line couplings . 11 2.5 Transmon relaxation time (T1) ........................... 11 3 Transmon simulation 12 3.1 Ansoft Maxwell . 12 3.1.1 Convergence of simulations . 13 3.1.2 Field integral . 13 3.2 Optimization of transmon parameters . 14 3.3 Intermediate transmon design . 15 3.4 Final transmon design . 15 3.5 Comparison of the surface electric field . 17 3.6 Simple estimate of T1 due to coupling to the charge line . 17 3.7 Simulation of the magnetic flux through the split junction .
    [Show full text]
  • A Scanning Transmon Qubit for Strong Coupling Circuit Quantum Electrodynamics
    ARTICLE Received 8 Mar 2013 | Accepted 10 May 2013 | Published 7 Jun 2013 DOI: 10.1038/ncomms2991 A scanning transmon qubit for strong coupling circuit quantum electrodynamics W. E. Shanks1, D. L. Underwood1 & A. A. Houck1 Like a quantum computer designed for a particular class of problems, a quantum simulator enables quantitative modelling of quantum systems that is computationally intractable with a classical computer. Superconducting circuits have recently been investigated as an alternative system in which microwave photons confined to a lattice of coupled resonators act as the particles under study, with qubits coupled to the resonators producing effective photon–photon interactions. Such a system promises insight into the non-equilibrium physics of interacting bosons, but new tools are needed to understand this complex behaviour. Here we demonstrate the operation of a scanning transmon qubit and propose its use as a local probe of photon number within a superconducting resonator lattice. We map the coupling strength of the qubit to a resonator on a separate chip and show that the system reaches the strong coupling regime over a wide scanning area. 1 Department of Electrical Engineering, Princeton University, Olden Street, Princeton 08550, New Jersey, USA. Correspondence and requests for materials should be addressed to W.E.S. (email: [email protected]). NATURE COMMUNICATIONS | 4:1991 | DOI: 10.1038/ncomms2991 | www.nature.com/naturecommunications 1 & 2013 Macmillan Publishers Limited. All rights reserved. ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms2991 ver the past decade, the study of quantum physics using In this work, we describe a scanning superconducting superconducting circuits has seen rapid advances in qubit and demonstrate its coupling to a superconducting CPWR Osample design and measurement techniques1–3.
    [Show full text]
  • Quantum Computers
    Quantum Computers ERIK LIND. PROFESSOR IN NANOELECTRONICS Erik Lind EIT, Lund University 1 Disclaimer Erik Lind EIT, Lund University 2 Quantum Computers Classical Digital Computers Why quantum computers? Basics of QM • Spin-Qubits • Optical qubits • Superconducting Qubits • Topological Qubits Erik Lind EIT, Lund University 3 Classical Computing • We build digital electronics using CMOS • Boolean Logic • Classical Bit – 0/1 (Defined as a voltage level 0/+Vdd) +vDD +vDD +vDD Inverter NAND Logic is built by connecting gates Erik Lind EIT, Lund University 4 Classical Computing • We build digital electronics using CMOS • Boolean Logic • Classical Bit – 0/1 • Very rubust! • Modern CPU – billions of transistors (logic and memory) • We can keep a logical state for years • We can easily copy a bit • Mainly through irreversible computing However – some problems are hard to solve on a classical computer Erik Lind EIT, Lund University 5 Computing Complexity Searching an unsorted list Factoring large numbers Grovers algo. – Shor’s Algorithm BQP • P – easy to solve and check on a 푛 classical computer ~O(N) • NP – easy to check – hard to solve on a classical computer ~O(2N) P P • BQP – easy to solve on a quantum computer. ~O(N) NP • BQP is larger then P • Some problems in P can be more efficiently solved by a quantum computer Simulating quantum systems Note – it is still not known if 푃 = 푁푃. It is very hard to build a quantum computer… Erik Lind EIT, Lund University 6 Basics of Quantum Mechanics A state is a vector (ray) in a complex Hilbert Space Dimension of space – possible eigenstates of the state For quantum computation – two dimensional Hilbert space ۧ↓ Example - Spin ½ particle - ȁ↑ۧ 표푟 Spin can either be ‘up’ or ‘down’ Erik Lind EIT, Lund University 7 Basics of Quantum Mechanics • A state of a system is a vector (ray) in a complex vector (Hilbert) Space.
    [Show full text]
  • Higher Levels of the Transmon Qubit
    Higher Levels of the Transmon Qubit MASSACHUSETTS INSTITUTE OF TECHNirLOGY by AUG 15 2014 Samuel James Bader LIBRARIES Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2014 @ Samuel James Bader, MMXIV. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Signature redacted Author........ .. ----.-....-....-....-....-.....-....-......... Department of Physics Signature redacted May 9, 201 I Certified by ... Terr P rlla(nd Professor of Electrical Engineering Signature redacted Thesis Supervisor Certified by ..... ..................... Simon Gustavsson Research Scientist Signature redacted Thesis Co-Supervisor Accepted by..... Professor Nergis Mavalvala Senior Thesis Coordinator, Department of Physics Higher Levels of the Transmon Qubit by Samuel James Bader Submitted to the Department of Physics on May 9, 2014, in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics Abstract This thesis discusses recent experimental work in measuring the properties of higher levels in transmon qubit systems. The first part includes a thorough overview of transmon devices, explaining the principles of the device design, the transmon Hamiltonian, and general Cir- cuit Quantum Electrodynamics concepts and methodology. The second part discusses the experimental setup and methods employed in measuring the higher levels of these systems, and the details of the simulation used to explain and predict the properties of these levels. Thesis Supervisor: Terry P. Orlando Title: Professor of Electrical Engineering Thesis Supervisor: Simon Gustavsson Title: Research Scientist 3 4 Acknowledgments I would like to express my deepest gratitude to Dr.
    [Show full text]
  • In Situ Quantum Control Over Superconducting Qubits
    ! In situ quantum control over superconducting qubits Anatoly Kulikov M.Sc. A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in 2020 School of Mathematics and Physics ARC Centre of Excellence for Engineered Quantum Systems (EQuS) ABSTRACT In the last decade, quantum information processing has transformed from a field of mostly academic research to an applied engineering subfield with many commercial companies an- nouncing strategies to achieve quantum advantage and construct a useful universal quantum computer. Continuing efforts to improve qubit lifetime, control techniques, materials and fab- rication methods together with exploring ways to scale up the architecture have culminated in the recent achievement of quantum supremacy using a programmable superconducting proces- sor { a major milestone in quantum computing en route to useful devices. Marking the point when for the first time a quantum processor can outperform the best classical supercomputer, it heralds a new era in computer science, technology and information processing. One of the key developments enabling this transition to happen is the ability to exert more precise control over quantum bits and the ability to detect and mitigate control errors and imperfections. In this thesis, ways to efficiently control superconducting qubits are explored from the experimental viewpoint. We introduce a state-of-the-art experimental machinery enabling one to perform one- and two-qubit gates focusing on the technical aspect and outlining some guidelines for its efficient operation. We describe the software stack from the time alignment of control pulses and triggers to the data processing organisation. We then bring in the standard qubit manipulation and readout methods and proceed to describe some of the more advanced optimal control and calibration techniques.
    [Show full text]
  • Superconducting Transmon Machines
    Quantum Computing Hardware Platforms: Superconducting Transmon Machines • CSC591/ECE592 – Quantum Computing • Fall 2020 • Professor Patrick Dreher • Research Professor, Department of Computer Science • Chief Scientist, NC State IBM Q Hub 3 November 2020 Superconducting Transmon Quantum Computers 1 5 November 2020 Patrick Dreher Outline • Introduction – Digital versus Quantum Computation • Conceptual design for superconducting transmon QC hardware platforms • Construction of qubits with electronic circuits • Superconductivity • Josephson junction and nonlinear LC circuits • Transmon design with example IBM chip layout • Working with a superconducting transmon hardware platform • Quantum Mechanics of Two State Systems - Rabi oscillations • Performance characteristics of superconducting transmon hardware • Construct the basic CNOT gate • Entangled transmons and controlled gates • Appendices • References • Quantum mechanical solution of the 2 level system 3 November 2020 Superconducting Transmon Quantum Computers 2 5 November 2020 Patrick Dreher Digital Computation Hardware Platforms Based on a Base2 Mathematics • Design principle for a digital computer is built on base2 mathematics • Identify voltage changes in electrical circuits that map base2 math into a “zero” or “one” corresponding to an on/off state • Build electrical circuits from simple on/off states that apply these basic rules to construct digital computers 3 November 2020 Superconducting Transmon Quantum Computers 3 5 November 2020 Patrick Dreher From Previous Lectures It was
    [Show full text]
  • Superconducting Phase Qubits
    Noname manuscript No. (will be inserted by the editor) Superconducting Phase Qubits John M. Martinis Received: date / Accepted: date Abstract Experimental progress is reviewed for superconducting phase qubit research at the University of California, Santa Barbara. The phase qubit has a potential ad- vantage of scalability, based on the low impedance of the device and the ability to microfabricate complex \quantum integrated circuits". Single and coupled qubit ex- periments, including qubits coupled to resonators, are reviewed along with a discus- sion of the strategy leading to these experiments. All currently known sources of qubit decoherence are summarized, including energy decay (T1), dephasing (T2), and mea- surement errors. A detailed description is given for our fabrication process and control electronics, which is directly scalable. With the demonstration of the basic operations needed for quantum computation, more complex algorithms are now within reach. Keywords quantum computation ¢ qubits ¢ superconductivity ¢ decoherence 1 Introduction Superconducting qubits are a unique and interesting approach to quantum computation because they naturally allow strong coupling. Compared to other qubit implementa- tions, they are physically large, from » 1 ¹m to » 100 ¹m in size, with interconnection topology and strength set by simple circuit wiring. Superconducting qubits have the advantage of scalability, as complex circuits can be constructed using well established integrated-circuit microfabrication technology. A key component of superconducting qubits is the Josephson junction, which can be thought of as an inductor with strong non-linearity and negligible energy loss. Combined with a capacitance, coming from the tunnel junction itself or an external element, a inductor-capacitor resonator is formed that exhibits non-linearity even at the single photon level.
    [Show full text]
  • EE214/PHYS220 Quantum Computing Lecture 1: Introduction Textbook: N
    EE214/PHYS220 Quantum Computing Lecture 1: Introduction Textbook: N. D. Mermin, Quantum computer science (Cambridge Univ. Press, 2007) (errata at http://www.lassp.cornell.edu/mermin/errata-1-12-12.pdf); http://www.lassp.cornell.edu/mermin/qcomp/CS483.html (lecture notes) Other resources: http://www.theory.caltech.edu/~preskill/ph219/ (lecture notes, Caltech course) http://inst.eecs.berkeley.edu/~cs191 (lecture notes, UC Berkeley course) M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000) G. Benenti, G. Casati, and G. Strini, Principles of Quantum Computation and Information, Vol. I: Basic Concepts (World Scientific, 2005) Prospects for Quantum Computing (QC): not really clear Pessimistic view: never, possibly limited to very small QCs as servers for quantum cryptography networks Optimistic view: in 20-50 years large-scale QCs, capable of factoring large integers Very optimistic (overoptimistic): will partially or completely replace general-purpose computers What QC can do efficiently 1) Factoring large integers (exponential speedup) Best classical: exp[ log / ], 1 3 more∼ accurately exp log log log , log base 2 1⁄3 64 2⁄3 Quantum: log (Shor’s∼ algorithm)9 2) Search in unsorted database3 (quadratic speedup) ∼ Classical: (simply check all) Quantum: (Grover’s algorithm) ∼ 3) Simulation of quantum∼ systems (for study of materials, etc.) 4) Possibly something else important (still area of active research) Current status: numbers 15 and 21 “factored” (also 143 with adiabatic QC) 14 well-entangled qubits (trapped ions, 2011), <25 qubits quantum algorithms with 9 superconducting qubits (2015), 1,000 D-Wave “qubits” Truly interdisciplinary effort: physics, engineering, computer science, mathematics Classical vs.
    [Show full text]
  • Measurement of Superconducting Qubits and Causality Alexander Korotkov University of California, Riverside
    Michigan State Univ., 09/21/15 Measurement of superconducting qubits and causality Alexander Korotkov University of California, Riverside Outline: Introduction (causality, POVM measurement) Circuit QED setup for measurement of superconducting qubits (transmons, Xmons) Qubit evolution due to measurement in circuit QED (simple and better theories) Experiments Alexander Korotkov University of California, Riverside Causality principle in quantum mechanics objects a and b observers A and B (and C) observers have “free will”; A B they can choose an action A choice made by observer A can affect light a b evolution of object b “back in time” cones time However, this retroactive control cannot pass space “useful” information to B (no signaling) C Randomness saves causality (even C Our focus: continuous cannot predict result of A measurement) |0 collapse Ensemble-averaged evolution of object b cannot depend on actions of observer A |1 Alexander Korotkov University of California, Riverside Werner Heisenberg Books: Physics and Philosophy: The Revolution in Modern Science Philosophical Problems of Quantum Physics The Physicist's Conception of Nature Across the Frontiers Niels Bohr Immanuel Kant (1724-1804), German philosopher Critique of pure reason (materialism, but not naive materialism) Nature - “Thing-in-itself” (noumenon, not phenomenon) Humans use “concepts (categories) of understanding”; make sense of phenomena, but never know noumena directly A priori: space, time, causality A naïve philosophy should not be a roadblock for good physics,
    [Show full text]
  • Arxiv:1408.2168V2
    Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED∗ Ming Hua, Ming-Jie Tao, and Fu-Guo Deng† Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing normal University, Beijing 100875, China (Dated: August 21, 2018) Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is, the controlled-phase (c-phase) gate on two microwave-photon resonators and the controlled-controlled phase (cc-phase) gates on three resonators, resorting to quantum resonance operations, without any drive field. Compared with previous works, our universal quantum gates have the higher fidelities and shorter operation times in theory. The numerical simulation shows that the fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our cc-phase gate is 99.25% within about 73.3 ns. PACS numbers: 03.67.Lx, 03.67.Bg, 85.25.Dq, 42.50.Pq Quantum computation and quantum information processing have attached much attention [1] in recent years. A quantum computer can factor an n-bit integer exponentially faster than the best known classical algorithms and it can run the famous quantum search algorithm, sometimes known as Grover’s algorithm, which enables this search method to be speed up substantially, requiring only O(√N) operations, faster than the classical one which requires O(N) operations [1].
    [Show full text]
  • Virtualized Logical Qubits: a 2.5D Architecture for Error-Corrected Quantum Computing
    2020 53rd Annual IEEE/ACM International Symposium on Microarchitecture (MICRO) Virtualized Logical Qubits: A 2.5D Architecture for Error-Corrected Quantum Computing Casey Duckering, Jonathan M. Baker, David I. Schuster, and Frederic T. Chong University of Chicago {cduck, jmbaker, david.schuster, ftchong}@uchicago.edu Abstract—Current, near-term quantum devices have shown execution. These efforts are directed at enabling NISQ (Noisy great progress in the last several years culminating recently with Intermediate-Scale Quantum) [2] algorithms to demonstrate a demonstration of quantum supremacy. In the medium-term, the power of quantum computing. Machines in this era are however, quantum machines will need to transition to greater reliability through error correction, likely through promising expected to run some important programs and have recently techniques like surface codes which are well suited for near-term been used to by Google to demonstrate “quantum supremacy” devices with limited qubit connectivity. We discover quantum [3]. memory, particularly resonant cavities with transmon qubits Despite this, these machines will be too small for error arranged in a 2.5D architecture, can efficiently implement surface correction and unable to run large-scale programs due to codes with substantial hardware savings and performance/fidelity gains. Specifically, we virtualize logical qubits by storing them in unreliable qubits. The ultimate goal is to construct fault- layers of qubit memories connected to each transmon. tolerant machines capable of executing thousands of gates Surprisingly, distributing each logical qubit across many and in the long-term to execute large-scale algorithms such memories has a minimal impact on fault tolerance and results as Shor’s [4] and Grover’s [5] with speedups over classical in substantially more efficient operations.
    [Show full text]