CIRCUIT QUANTUM ELECTRODYNAMICS

Circuit Quantum Electrodynamics (cQED), the study of the interaction between superconducting circuits behaving as artificial atoms and 1-dimensional transmission-line resonators, has shown much promise for quantum information processing tasks. For the purposes of quantum computing it is usual to approximate the artificial atoms as 2-level qubits, and much effort has been expended on attempts to isolate these qubits from the environment and to invent ever more sophisticated control and measurement schemes. Rather than focussing on these technological aspects of the field, this thesis investigates the opportunities for using these carefully engineered systems for answering questions of fundamental physics.

[1]  Franco Nori,et al.  Generation and control of Greenberger-Horne-Zeilinger entanglement in superconducting circuits. , 2006, Physical review letters.

[2]  E. Jaynes,et al.  Comparison of quantum and semiclassical radiation theories with application to the beam maser , 1962 .

[3]  V. P. Belavkin,et al.  Measurements continuous in time and a posteriori states in quantum mechanics , 1991 .

[4]  N. Mermin.  Quantum mysteries revisited , 1990 .

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

[6]  Jens Koch,et al.  Coupling superconducting qubits via a cavity bus , 2007, Nature.

[7]  J. Raimond,et al.  Manipulating quantum entanglement with atoms and photons in a cavity , 2001 .

[8]  L. Mandel,et al.  Multiatom and transit-time effects on photon-correlation measurements in resonance fluorescence , 1978 .

[9]  Erik Lucero,et al.  Emulation of a Quantum Spin with a Superconducting Phase Qudit , 2009, Science.

[10]  S. Girvin,et al.  Wiring up quantum systems , 2008, Nature.

[11]  Pérès.  Separability Criterion for Density Matrices. , 1996, Physical review letters.

[12]  Thompson,et al.  Observation of normal-mode splitting for an atom in an optical cavity. , 1992, Physical review letters.

[13]  P. Grangier,et al.  Experimental Tests of Realistic Local Theories via Bell's Theorem , 1981 .

[14]  H. Paul,et al.  Measuring the quantum state of light , 1997 .

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

[16]  H. Weinfurter,et al.  Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement , 2000, Nature.

[17]  Marco Barbieri,et al.  Simplifying quantum logic using higher-dimensional Hilbert spaces , 2009 .

[18]  Simon Regard,et al.  ["Less is more"]. , 2013, Revue medicale suisse.

[19]  Paolo Silvestrini,et al.  Macroscopic quantum coherence and quantum computing , 2001 .

[20]  Mohan Sarovar,et al.  High-fidelity measurement and quantum feedback control in circuit QED (10 pages) , 2005, quant-ph/0508232.

[21]  G. Rupper,et al.  Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity , 2004, Nature.

[22]  Morin,et al.  Vacuum Rabi splitting as a feature of linear-dispersion theory: Analysis and experimental observations. , 1990, Physical review letters.

[23]  Giacomo Mauro D'Ariano,et al.  Quantum calibration of measurement instrumentation. , 2004, Physical review letters.

[24]  J. Bell.  La nouvelle cuisine , 1990 .

[25]  A. Wallraff,et al.  Fabrication and characterization of superconducting circuit QED devices for quantum computation , 2005, IEEE Transactions on Applied Superconductivity.

[26]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[27]  J. Dowling.  Exploring the Quantum: Atoms, Cavities, and Photons. , 2014 .

[28]  Timothy A. Davis,et al.  Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method , 2004, TOMS.

[29]  Scott Aaronson,et al.  Limits on Efficient Computation in the Physical World , 2004, ArXiv.

[30]  R. Kaul,et al.  Microwave engineering , 1989, IEEE Potentials.

[31]  G. Rempe,et al.  Structure and dynamics in cavity quantum electrodynamics , 1992, QELS 1992.

[32]  M. Scully,et al.  Statistical Methods in Quantum Optics 1: Master Equations and Fokker-Planck Equations , 2003 .

[33]  A N Cleland,et al.  Measurement of the decay of Fock states in a superconducting quantum circuit. , 2008, Physical review letters.

[34]  L. Mandel,et al.  Photon Antibunching in Resonance Fluorescence , 1977 .

[35]  Carmichael,et al.  Quantum trajectory simulations of two-state behavior in an optical cavity containing one atom. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[36]  Ferdinand Helmer,et al.  Measurement-based synthesis of multiqubit entangled states in superconducting cavity QED , 2009, 0902.0341.

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

[38]  J. Martinis,et al.  Maximally entangling tripartite protocols for Josephson phase qubits , 2008, 0804.3159.

[39]  D. DiVincenzo,et al.  Experimental demonstration of an oscillator stabilized Josephson flux qubit. , 2006, Physical review letters.

[40]  J. E. Mooij,et al.  Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits , 2007, Nature.

[41]  C. Monroe,et al.  Quantum interference of photon pairs from two remote trapped atomic ions , 2006, quant-ph/0608047.

[42]  L. Tian,et al.  Nonperturbative atom-photon interactions in an optical cavity , 1994 .

[43]  K. Lendi,et al.  Quantum Dynamical Semigroups and Applications , 1987 .

[44]  G. W. Snedecor.  STATISTICAL METHODS , 1967 .

[45]  M. Devoret,et al.  Quantum coherence with a single Cooper pair , 1998 .

[46]  R. J. Schoelkopf,et al.  Measuring the decoherence of a quantronium qubit with the cavity bifurcation amplifier , 2007, 0706.0765.

[47]  R. J. Schoelkopf,et al.  Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement , 2007 .

[48]  V. Peano,et al.  Dynamical bistability in the driven circuit QED , 2009, 0903.2338.

[49]  Erik Lucero,et al.  Synthesizing arbitrary quantum states in a superconducting resonator , 2009, Nature.

[50]  V. Kulakovskii,et al.  Strong coupling in a single quantum dot–semiconductor microcavity system , 2004, Nature.

[51]  Michel Devoret,et al.  Superconducting quantum bits , 2005 .

[52]  M. Ansmann.  Benchmarking the superconducting Josephson Phase Qubit: The violation of Bell's inequality , 2009 .

[53]  C. Monroe,et al.  Quantum dynamics of single trapped ions , 2003 .

[54]  Marek Zukowski,et al.  Experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger entanglement. , 2003, Physical review letters.

[55]  P. Leek,et al.  Resolving Vacuum Fluctuations in an Electrical Circuit by Measuring the Lamb Shift , 2008, Science.

[56]  J. Koch,et al.  Superfluid–Mott-insulator transition of light in the Jaynes-Cummings lattice , 2009, 0905.4005.

[57]  Stephan L. Mintz,et al.  Fundamental Theories in Physics , 2012, Studies in the Natural Sciences.

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

[59]  R. Simons.  Coplanar waveguide circuits, components, and systems , 2001 .

[60]  J. Martinis,et al.  Rabi oscillations in a large Josephson-junction qubit. , 2002, Physical review letters.

[61]  Y. Pashkin,et al.  Coherent control of macroscopic quantum states in a single-Cooper-pair box , 1999, Nature.

[62]  E. Purcell.  Spontaneous Emission Probabilities at Radio Frequencies , 1995 .

[63]  J. Cirac,et al.  Long-distance quantum communication with atomic ensembles and linear optics , 2001, Nature.

[64]  H. J. Kimble,et al.  Photon blockade in an optical cavity with one trapped atom , 2005, Nature.

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

[66]  P. Joyez,et al.  Manipulating the Quantum State of an Electrical Circuit , 2002, Science.

[67]  Erik Lucero,et al.  Quantum ground state and single-phonon control of a mechanical resonator , 2010, Nature.

[68]  S. Girvin,et al.  Introduction to quantum noise, measurement, and amplification , 2008, 0810.4729.

[69]  R. J. Schoelkopf,et al.  Dispersive measurements of superconducting qubit coherence with a fast latching readout , 2006 .

[70]  Asher Peres.  Bayesian Analysis of Bell Inequalities , 2000 .

[71]  Alexandre Blais,et al.  Quantum information processing with circuit quantum electrodynamics , 2007 .

[72]  M. Blaauboer,et al.  Production of multipartite entanglement for electron spins in quantum dots , 2007, 0707.1267.

[73]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[74]  Zoller,et al.  Monte Carlo simulation of the atomic master equation for spontaneous emission. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[75]  R J Schoelkopf,et al.  Radio-frequency single-electron transistor as readout device for qubits: charge sensitivity and backaction. , 2001, Physical review letters.

[76]  K. Hornberger.  Introduction to decoherence theory , 2006, quant-ph/0612118.

[77]  Adan Cabello.  Bell's theorem with and without inequalities for the three-qubit Greenberger-Horne-Zeilinger and W states , 2002 .

[78]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.

[79]  Dreyer,et al.  Quantum Rabi oscillation: A direct test of field quantization in a cavity. , 1996, Physical review letters.

[80]  Hideaki Takayanagi,et al.  Two-photon probe of the Jaynes-Cummings model and controlled symmetry breaking in circuit QED , 2009 .

[81]  L. Tornberg.  Superconducting qubits - measurement, entanglement, and noise , 2009 .

[82]  L Frunzio,et al.  Approaching unit visibility for control of a superconducting qubit with dispersive readout. , 2005, Physical review letters.

[83]  H. Weinfurter,et al.  Violation of Bell's Inequality under Strict Einstein Locality Conditions , 1998, quant-ph/9810080.

[84]  D. Browne,et al.  Computational power of correlations. , 2008, Physical review letters.

[85]  Vijay Patel,et al.  Quantum superposition of distinct macroscopic states , 2000, Nature.

[86]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[87]  A. Cottet,et al.  Implémentation d'un bit quantique dans un circuit supraconducteur / Implementation of a quantum bit in a superconducting circuit , 2002 .

[88]  M. Sentís.  Quantum theory of open systems , 2002 .

[89]  R. Feynman.  Simulating physics with computers , 1999 .

[90]  David P. DiVincenzo,et al.  Multilevel quantum description of decoherence in superconducting qubits , 2004 .

[91]  F. W. Cummings,et al.  Exact Solution for an N-Molecule-Radiation-Field Hamiltonian , 1968 .

[92]  Erik Lucero,et al.  Violation of Bell's inequality in Josephson phase qubits , 2009, Nature.

[93]  S. Popescu,et al.  Quantum nonlocality as an axiom , 1994 .

[94]  L. DiCarlo,et al.  Demonstration of two-qubit algorithms with a superconducting quantum processor , 2009, Nature.

[95]  A. Winter,et al.  Information causality as a physical principle , 2009, Nature.

[96]  Dehmelt,et al.  Observation of inhibited spontaneous emission. , 1985, Physical review letters.

[97]  A. Korotkov,et al.  Analysis of Bell inequality violation in superconducting phase qubits , 2007, 0707.0036.

[98]  Alexandre Blais,et al.  Quantum trajectory equation for multiple qubits in circuit QED: Generating entanglement by measurementThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008. , 2008, 0812.0218.

[99]  A. Kossakowski,et al.  On quantum statistical mechanics of non-Hamiltonian systems , 1972 .

[100]  Mario Dagenais,et al.  Investigation of two-time correlations in photon emissions from a single atom , 1978 .

[101]  L. Mandel,et al.  Theory of resonance fluorescence , 1976 .

[102]  D. Schuster,et al.  Measurement of the excited-state lifetime of a microelectronic circuit. , 2003, Physical review letters.

[103]  K. Schwab,et al.  Quantum measurement of a coupled nanomechanical resonator–Cooper-pair box system , 2003, cond-mat/0301252.

[104]  J. S. BELLt.  Einstein-Podolsky-Rosen Paradox , 2018 .

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

[106]  E. Sudarshan,et al.  Who's afraid of not completely positive maps? , 2005 .

[107]  F K Wilhelm,et al.  Quantum superposition of macroscopic persistent-current states. , 2000, Science.

[108]  Howard J. Carmichael,et al.  An Open Systems Approach to Quantum Optics: Lectures Presented at the Universite Libre De Bruxelles, October 28 to November 4, 1991 , 1993 .

[109]  John M. Martinis,et al.  Effect of an Adjustable Admittance on the Macroscopic Energy Levels of a Current Biased Josephson Junction , 1989 .

[110]  Luis L. Sánchez-Soto,et al.  COMPLETE CHARACTERIZATION OF ARBITRARY QUANTUM MEASUREMENT PROCESSES , 1999 .

[111]  J. Gambetta,et al.  Two-qubit state tomography using a joint dispersive readout. , 2008, Physical review letters.

[112]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[113]  C. cohen-tannoudji,et al.  Quantum Mechanics: Volume II , 1978 .

[114]  John M. Martinis,et al.  Implementing Qubits with Superconducting Integrated Circuits , 2004, Quantum Inf. Process..

[115]  D. Averin,et al.  Bloch oscillations in small Josephson junctions , 1985 .

[116]  T. Puppe,et al.  Nonlinear spectroscopy of photons bound to one atom , 2008, 0803.2712.

[117]  Kiel T. Williams,et al.  Extreme quantum entanglement in a superposition of macroscopically distinct states. , 1990, Physical review letters.

[118]  Paul Busch,et al.  Lüders theorem for unsharp quantum measurements , 1998, 1304.0054.

[119]  Peter W. Shor,et al.  Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[120]  R. Xu,et al.  Theory of open quantum systems , 2002 .

[121]  A. Wallraff,et al.  Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system , 2008, Nature.

[122]  Denis Vion,et al.  Quantum nondemolition readout using a Josephson bifurcation amplifier , 2007 .

[123]  O. Macedońska,et al.  Notation , 1966, Geometrical Dimensioning and Tolerancing for Design, Manufacturing and Inspection.

[124]  J. Bell.  On the Problem of Hidden Variables in Quantum Mechanics , 1966 .

[125]  Martinis,et al.  Escape oscillations of a Josephson junction switching out of the zero-voltage state. , 1989, Physical review letters.

[126]  Jens Koch,et al.  Randomized benchmarking and process tomography for gate errors in a solid-state qubit. , 2008, Physical review letters.

[127]  Erik Lucero,et al.  Generation of Fock states in a superconducting quantum circuit , 2008, Nature.

[128]  Jens Koch,et al.  Fluxonium: Single Cooper-Pair Circuit Free of Charge Offsets , 2009, Science.

[129]  Michel Devoret,et al.  Circuit‐QED: How strong can the coupling between a Josephson junction atom and a transmission line resonator be? * , 2007, Annalen der Physik.

[130]  Stephen M. Barnett,et al.  Methods in Theoretical Quantum Optics , 1997 .

[131]  Jens Eisert,et al.  Tomography of quantum detectors , 2009 .

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

[133]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[134]  Andrew D. Greentree,et al.  Quantum phase transitions of light , 2006, cond-mat/0609050.

[135]  M. Devoret.  Quantum Fluctuations in Electrical Circuits , 1997 .

[136]  M. Horodecki,et al.  Separability of mixed states: necessary and sufficient conditions , 1996, quant-ph/9605038.

[137]  Jr.,et al.  Multivalued logic gates for quantum computation , 2000, quant-ph/0002033.

[138]  C. Monroe,et al.  Experimental violation of a Bell's inequality with efficient detection , 2001, Nature.

[139]  R. J. Schoelkopf,et al.  Analog information processing at the quantum limit with a Josephson ring modulator , 2008, 0805.3452.

[140]  S. Filipp,et al.  Measurement of Autler-Townes and Mollow transitions in a strongly driven superconducting qubit. , 2008, Physical review letters.

[141]  Jens Koch,et al.  Suppressing Charge Noise Decoherence in Superconducting Charge Qubits , 2007, 0712.3581.

[142]  Carmichael,et al.  Anharmonicity of the vacuum Rabi peaks in a many-atom system. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[143]  Jean-Michel Raimond,et al.  Cavity Quantum Electrodynamics , 1993, Quantum Dynamics of Simple Systems.

[144]  E. Davies.  A model of atomic radiation , 1978 .

[145]  M. Horne,et al.  Experimental Consequences of Objective Local Theories , 1974 .

[146]  M. Kim,et al.  Macroscopic Greenberger-Horne-Zeilinger and W states in flux qubits , 2007, 0705.3991.

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

[148]  H. Carr,et al.  The Principles of Nuclear Magnetism , 1961 .

[149]  Jaromir Fiurasek.  Maximum-likelihood estimation of quantum measurement , 2001 .

[150]  M. Mariantoni,et al.  Two-resonator circuit quantum electrodynamics : A superconducting quantum switch , 2007, 0712.2522.

[151]  Francesco Petruccione,et al.  Stochastic wave-function method versus density matrix: a numerical comparison , 1997 .

[152]  M. Steffen,et al.  Measurement of the Entanglement of Two Superconducting Qubits via State Tomography , 2006, Science.

[153]  Peter Grünwald,et al.  The statistical strength of nonlocality proofs , 2003, IEEE Transactions on Information Theory.