Introduction to Experimental Quantum Measurement with Superconducting Qubits

Quantum technology has been rapidly growing due to its potential revolutionary applications. In particular, superconducting qubits provide a strong light-matter interaction as required for quantum computation and in principle can be scaled up to a high level of complexity. However, obtaining the full benefit of quantum mechanics in superconducting circuits requires a deep understanding of quantum physics in such systems in all aspects. One of the most crucial aspects is the concept of measurement and the dynamics of the quantum systems under the measurement process. This document is intended to be a pedagogical introduction to the concept of quantum measurement from an experimental perspective. We study the dynamics of a single superconducting qubit under continuous monitoring. We demonstrate that weak measurement is a versatile tool to investigate fundamental questions in quantum dynamics and quantum thermodynamics for open quantum systems.

[1]  Are dynamical quantum jumps detector dependent? , 2011, Physical review letters.

[2]  A. N. Korotkov,et al.  Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback , 2012, Nature.

[3]  Alexander N. Korotkov,et al.  Decoherence suppression by quantum measurement reversal , 2010 .

[4]  C. Caves Quantum limits on noise in linear amplifiers , 1982 .

[5]  Mazyar Mirrahimi,et al.  Extending the lifetime of a quantum bit with error correction in superconducting circuits , 2016, Nature.

[6]  C. Bender,et al.  PT -symmetric quantum field theory in D dimensions , 2018, Physical Review D.

[7]  W. Zurek The Environment, Decoherence and the Transition from Quantum to Classical , 1991 .

[8]  How many atoms get excited when they decay , 2017, 1702.08824.

[9]  J. Koski,et al.  Experimental observation of the role of mutual information in the nonequilibrium dynamics of a Maxwell demon. , 2014, Physical review letters.

[10]  Demetrios N. Christodoulides,et al.  Non-Hermitian physics and PT symmetry , 2018, Nature Physics.

[11]  I. S. Oliveira,et al.  Experimental Rectification of Entropy Production by Maxwell's Demon in a Quantum System. , 2016, Physical review letters.

[12]  E. Lutz,et al.  Information: From Maxwell’s demon to Landauer’s eraser , 2015 .

[13]  Yong-Su Kim,et al.  Protecting entanglement from decoherence using weak measurement and quantum measurement reversal , 2012 .

[14]  Jens Eisert,et al.  Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems , 2015, Reports on progress in physics. Physical Society.

[15]  C. Jarzynski,et al.  Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies , 2005, Nature.

[16]  T. Sagawa,et al.  Thermodynamics of information , 2015, Nature Physics.

[17]  C. Jarzynski Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[18]  Kurt Jacobs,et al.  A straightforward introduction to continuous quantum measurement , 2006, quant-ph/0611067.

[19]  J. Anders,et al.  Quantum thermodynamics , 2015, 1508.06099.

[20]  E. Lucero,et al.  Planar Superconducting Resonators with Internal Quality Factors above One Million , 2012, 1201.3384.

[21]  Todd A. Brun Continuous measurements, quantum trajectories, and decoherent histories , 2000 .

[22]  K. Mølmer,et al.  Correlations of the Time Dependent Signal and the State of a Continuously Monitored Quantum System. , 2015, Physical review letters.

[23]  Alexandre Blais,et al.  Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect , 2007, 0709.4264.

[24]  Leigh S. Martin,et al.  Quantum dynamics of simultaneously measured non-commuting observables , 2016, Nature.

[25]  Michael Tinkham,et al.  Introduction to Superconductivity , 1975 .

[26]  Franco Nori,et al.  Decoherence-Free Interaction between Giant Atoms in Waveguide Quantum Electrodynamics. , 2017, Physical review letters.

[27]  G. Milburn,et al.  Quantum Measurement and Control , 2009 .

[28]  M. Barbieri,et al.  Experimental extractable work-based multipartite separability criteria , 2017 .

[29]  Alexander N. Korotkov,et al.  Quantum Bayesian approach to circuit QED measurement , 2011, 1111.4016.

[30]  K J Resch,et al.  Experimental feedback control of quantum systems using weak measurements. , 2009, Physical review letters.

[31]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[32]  I. Tinoco,et al.  Equilibrium Information from Nonequilibrium Measurements in an Experimental Test of Jarzynski's Equality , 2002, Science.

[33]  K. Mølmer,et al.  Homodyne monitoring of postselected decay , 2017, 1705.04287.

[34]  L Frunzio,et al.  Generating single microwave photons in a circuit. , 2007, Nature.

[35]  K. Murch,et al.  Mapping quantum state dynamics in spontaneous emission , 2015, Nature Communications.

[36]  Luigi Frunzio,et al.  Realization of three-qubit quantum error correction with superconducting circuits , 2011, Nature.

[37]  N. Gisin,et al.  Quantum Communication , 2007, quant-ph/0703255.

[38]  F. Wellstood,et al.  An analysis method for asymmetric resonator transmission applied to superconducting devices , 2011, 1108.3117.

[39]  P. Rouchon,et al.  Observing quantum state diffusion by heterodyne detection of fluorescence , 2015, 1511.01415.

[40]  Behavior of eigenvalues in a region of broken-PT symmetry , 2017, 1702.03811.

[41]  Alexander N. Korotkov,et al.  Measuring a transmon qubit in circuit QED: Dressed squeezed states , 2016, 1606.04204.

[42]  Peter W. Milonni,et al.  Why spontaneous emission , 1984 .

[43]  Measurement induced entanglement and quantum computation with atoms in optical cavities. , 2003, Physical review letters.

[44]  Jens Koch,et al.  Understanding degenerate ground states of a protected quantum circuit in the presence of disorder , 2014, 1402.7310.

[45]  C. Degen,et al.  Watching the precession of a single nuclear spin by weak measurements. , 2018, 1806.08243.

[46]  A. Jordan,et al.  Mapping the optimal route between two quantum states , 2014, Nature.

[47]  Zijun Chen,et al.  Measurement-Induced State Transitions in a Superconducting Qubit: Beyond the Rotating Wave Approximation. , 2016, Physical review letters.

[48]  Mazyar Mirrahimi,et al.  Real-time quantum feedback prepares and stabilizes photon number states , 2011, Nature.

[49]  K. Murch,et al.  Characterizing a Statistical Arrow of Time in Quantum Measurement Dynamics. , 2018, Physical review letters.

[50]  P. Rouchon,et al.  Anatomy of fluorescence: quantum trajectory statistics from continuously measuring spontaneous emission , 2015, 1511.06677.

[51]  K. Funo,et al.  Information-to-work conversion by Maxwell’s demon in a superconducting circuit quantum electrodynamical system , 2017, Nature Communications.

[52]  Lan Yang,et al.  Exceptional points enhance sensing in an optical microcavity , 2017, Nature.

[53]  Jamie K. Hobbs,et al.  Observation of entanglement between a single trapped atom and a single photon , 2004 .

[54]  Comment on "On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator" [J. Math. Phys. 48, 032701 (2007)] , 2016 .

[55]  L Frunzio,et al.  High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity. , 2010, Physical review letters.

[56]  T. Paterek,et al.  The classical-quantum boundary for correlations: Discord and related measures , 2011, 1112.6238.

[57]  M. Raizen,et al.  Comprehensive Control of Atomic Motion , 2009, Science.

[58]  E. Lutz,et al.  Heat and Work Along Individual Trajectories of a Quantum Bit. , 2017, Physical review letters.

[59]  M Naghiloo,et al.  Achieving Optimal Quantum Acceleration of Frequency Estimation Using Adaptive Coherent Control. , 2017, Physical review letters.

[60]  K. B. Whaley,et al.  Supplementary Information for " Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits " , 2014 .

[61]  J. Bird,et al.  A review of progress in the physics of open quantum systems: theory and experiment , 2015, Reports on progress in physics. Physical Society.

[62]  K. Murch,et al.  Bath engineering of a fluorescing artificial atom with a photonic crystal , 2018, Physical Review A.

[63]  C. Bender,et al.  Analytic structure of eigenvalues of coupled quantum systems , 2017, 1702.03839.

[64]  K. Mølmer,et al.  Quantum smoothing for classical mixtures , 2016, 1607.00319.

[65]  David Schuster,et al.  Circuit quantum electrodynamics , 2007 .

[66]  P. Hänggi,et al.  Fluctuation theorems: work is not an observable. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[67]  David Schuster,et al.  Time- and Site-Resolved Dynamics in a Topological Circuit , 2015 .

[68]  A. Jordan,et al.  Fluctuation theorems for continuous quantum measurements and absolute irreversibility , 2018, Physical Review A.

[69]  Alexandre Blais,et al.  Superconducting qubit with Purcell protection and tunable coupling. , 2010, Physical review letters.

[70]  Euan R. Kay,et al.  A molecular information ratchet , 2007, Nature.

[71]  K. Mølmer,et al.  How many atoms get excited when they decay? , 2013, 1702.08824.

[72]  C. Bender PT symmetry in quantum physics: From a mathematical curiosity to optical experiments , 2016 .

[73]  Yogesh N. Joglekar,et al.  Quantum state tomography across the exceptional point in a single dissipative qubit , 2019, Nature Physics.

[74]  Pierre Rouchon,et al.  Observing a quantum Maxwell demon at work , 2017, Proceedings of the National Academy of Sciences.

[75]  K. Funo,et al.  Integral quantum fluctuation theorems under measurement and feedback control. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[76]  A. Jordan,et al.  Quantum caustics in resonance fluorescence trajectories , 2016, 1612.03189.

[77]  Vibhor Singh,et al.  Multi-mode ultra-strong coupling in circuit quantum electrodynamics , 2017, npj Quantum Information.

[78]  Jens Koch,et al.  Controlling the spontaneous emission of a superconducting transmon qubit. , 2008, Physical review letters.

[79]  Klaus Molmer,et al.  Bayesian parameter estimation by continuous homodyne detection , 2016, 1605.00902.

[80]  E. Solano,et al.  Circuit quantum electrodynamics in the ultrastrong-coupling regime , 2010 .

[81]  A. Jordan,et al.  Prediction and Characterization of Multiple Extremal Paths in Continuously Monitored Qubits , 2016, 1612.07861.

[82]  C. Macklin,et al.  Observing single quantum trajectories of a superconducting quantum bit , 2013, Nature.

[83]  S. Filipp,et al.  Observation of entanglement between itinerant microwave photons and a superconducting qubit. , 2012, Physical review letters.

[84]  C. Bender,et al.  Series solutions of P T -symmetric Schrödinger equations , 2016, 1601.02446.

[85]  P. Knight,et al.  Introductory quantum optics , 2004 .

[86]  M. Sano,et al.  Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality , 2010 .

[87]  G. Kurizki,et al.  Quantum technologies with hybrid systems , 2015, Proceedings of the National Academy of Sciences.

[88]  David Olaya,et al.  Superconducting nanocircuits for topologically protected qubits , 2009 .

[89]  G. Wendin Quantum information processing with superconducting circuits: a review , 2016, Reports on progress in physics. Physical Society.

[90]  K. Mølmer,et al.  Wave-function approach to dissipative processes in quantum optics. , 1992, Physical review letters.

[91]  Alexander N. Korotkov,et al.  Entanglement of solid-state qubits by measurement , 2003 .

[92]  Andrew W. Cross,et al.  Demonstration of a quantum error detection code using a square lattice of four superconducting qubits , 2015, Nature Communications.

[93]  E. Solano,et al.  Convergence of the multimode quantum Rabi model of circuit quantum electrodynamics , 2017, 1701.05095.

[94]  S. Girvin,et al.  Cavity-assisted quantum bath engineering. , 2012, Physical review letters.

[95]  D. Slichter Quantum Jumps and Measurement Backaction in a Superconducting Qubit , 2011 .

[96]  John M. Martinis,et al.  State preservation by repetitive error detection in a superconducting quantum circuit , 2015, Nature.

[97]  J. Martinis,et al.  Superconducting Qubits: A Short Review , 2004, cond-mat/0411174.

[98]  Michal Horodecki,et al.  The second laws of quantum thermodynamics , 2013, Proceedings of the National Academy of Sciences.

[99]  E. Lutz,et al.  Information Gain and Loss for a Quantum Maxwell's Demon. , 2018, Physical review letters.

[100]  H. Türeci,et al.  Cutoff-Free Circuit Quantum Electrodynamics. , 2017, Physical review letters.

[101]  Shanhui Fan,et al.  Parity–time-symmetric whispering-gallery microcavities , 2013, Nature Physics.

[102]  A. Jordan,et al.  Arrow of Time for Continuous Quantum Measurement. , 2016, Physical review letters.