DOCSLIB.ORG

Circuit Quantum Electrodynamics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Circuit Quantum Electrodynamics Abstract Circuit Quantum Electrodynamics David Isaac Schuster 2007 This thesis describes the development of circuit quantum electrodynamics (QED), architecture for studying quantum information and quantum optics. In circuit QED a superconducting qubit acting as an artificial atom is electrostatically coupled to a 1D transmission line resonator. The large effective dipole moment of the qubit and high energy density of the resonator allowed this system to reach the strong coupling limit of cavity QED for the first time in a solid-state system. Spectroscopic investigations explore effects of different regimes of cavity QED observing physics such as the vacuum Rabi mode splitting, and the AC Stark effect. These cavity QED effects are used to control and measure the qubit state, while protecting it from radiative decay. The qubit can also be used to measure and control the cavity state, as shown by experiments detecting and generating single photons. This thesis will describe the theoretical framework, implementation, and measurements of the circuit QED system. Circuit Quantum Electrodynamics A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by David Isaac Schuster Dissertation Director: Professor Robert J. Schoelkopf May 2007 c 2007 by David Schuster. All rights reserved. Acknowledgements I would first like to thank my advisor Rob Schoelkopf. He gave me the freedom to explore an amazing world of quantum physics, while his guidance prevented me from ever feeling lost in all of its complexity. He taught me what it means to be a scientist, and the importance of eliminating ground loops. I will always remember our late night brainstorming sessions, and his willingness to suspend more critical demands to provide advice. Most of all I thank him for creating RSL and giving me the opportunity to participate. I have been fortunate to work with many amazing people in the course of this research. In particular, most of the work presented in this thesis was the joint effort of Andreas Wallraff and myself. His influence on me runs deep extending from small things like my (near fanatical) use of mathematica and my much improved graphics design skills to the way I now approach experimental questions. More importantly, Andreas has become one of my closest friends. More recent work, presented in sections 4.3, 8.3.1, and 9.3, related to the “Transmon” was performed with my evil twin, Andrew Houck. His scientific abilities are matched only by his unbounded enthusiasm, and hopefully the former is as contagious as his excitement. I thank Alexandre Blais and Jay Gambetta for teaching me everything I know about cavity QED and quantum measurement. Their patience exceeds even Andrew’s optimism. I also owe a great debt to Luigi Frunzio for teaching me everything I know about the dark arts of fabrication. Steve Girvin has an uncanny ability to make tangible connections between theory and experiment, while simultaneously telling a hilarious story. Similarly, I often found myself emerging from Michel Devoret’s office with new understanding of a question much deeper than the one with which I had entered. Dan Prober is to be thanked not only for his direct role in helping to convince me to come to Yale, serving on my committee, and advising me throughout my time here, but also for helping to build such an amazing community on the 4th floor. My lab mates have made graduate school the best of times, providing help, camaraderie, and close 1 2 friendship. All of my friends from graduate, undergraduate, and high school have provided invaluable support. I would especially like to thank my roommate(s) Matt and Sam for their tolerance and friendship. Most importantly I would like to thank my family, who have encouraged my curiosity and provided me with unending love. Finally, I thank Carol who helped me to grow as a person as well as a scientist. Contents 1 Introduction 18 1.1 QuantumComputation .............................. .... 18 1.2 CavityQuantumElectrodynamics . ........ 21 1.3 QuantumCircuits ................................. .... 26 1.4 CircuitQuantumElectrodynamics . ......... 29 1.5 ThesisOverview .................................. .... 32 2 Cavity Quantum Electrodynamics 34 2.1 DispersiveLimit ................................. ..... 37 2.2 StrongDispersiveInteractions. ........... 41 3 Cavity QED with Superconducting Circuits 45 3.1 TransmissionLineCavities . ........ 45 3.1.1 TheLCROscillator .............................. .. 46 3.1.2 Transmission Line as Series of LC Circuits. .......... 47 3.1.3 CapacitivelyCoupledLCRResonator . ....... 49 3.1.4 Capacitively Coupled Transmission Line Resonator . ............. 51 3.1.5 CoplanarWaveguideCavities . ...... 53 3.1.6 KineticInductance. .. .. .. .. .. .. .. .. .. .. .. .. .... 55 3.1.7 IntrinsicResonatorLosses . ....... 56 3.1.8 QuantizationoftheLCOscillator . ....... 60 3.2 CooperPairBox ................................... ... 61 3.2.1 ChargeBasis ................................... 61 3.2.2 PhaseBasis.................................... 65 3 CONTENTS 4 3.2.3 SplitCPB...................................... 66 3.3 CouplingCPBtoCavity............................. ..... 68 3.3.1 Comparisonwith Traditional CavityQED . ........ 71 3.4 MeasurementTheory............................... ..... 73 3.4.1 Quantum Non-Demolition Measurements . ....... 73 3.4.2 Mapping Qubit State onto Cavity State . ....... 73 3.4.3 Distinguishing Cavity States . ....... 75 3.4.4 SmallPhaseShiftLimit . .... 77 3.4.5 OptimizingSNR ................................. 78 4 Decoherence in the Cooper Pair Box 82 4.1 RelaxationandHeating .. .. .. .. .. .. .. .. .. .. .. .. ...... 82 4.1.1 VoltageNoise.................................. .. 83 4.1.2 VoltageNoiseInsideaCavity . ...... 85 4.1.3 MaterialLoss.................................. .. 89 4.1.4 DipoleRadiation ............................... ... 91 4.2 Dephasing....................................... ... 92 4.2.1 ChargeNoise ................................... 95 4.2.2 FluxNoise ..................................... 100 4.2.3 Critical Current/Josephson Energy 1/f Noise.................. 101 4.2.4 EC Noise ...................................... 102 4.2.5 SummaryofCooperpairboxdecoherence . ....... 102 4.3 Transmon ........................................ 103 4.3.1 ChargeDispersion .............................. .. 103 4.3.2 Anharmonicity ................................. 105 4.3.3 TransmonasaJosephsonOscillator . ....... 108 4.3.4 TransmonforCircuitQED . .. 111 4.3.5 OtherSourcesofDecoherence. ...... 115 4.3.6 TransmonSummary ............................... 117 5 Design and Fabrication 119 5.1 Cavity.......................................... 119 CONTENTS 5 5.1.1 DesignConsiderations . ..... 119 5.1.2 OpticalLithography . .... 123 5.1.3 DepositionandLiftoff . .... 126 5.1.4 Substrates.................................... 127 5.2 CooperPairBox ................................... .. 129 5.2.1 JosephsonEnergy ............................... 129 5.2.2 ChargingEnergyandVoltageDivision . ........ 130 5.2.3 ElectronBeamLithography . ..... 133 5.2.4 VeilofDeath ................................... 135 5.3 Transmon ........................................ 137 5.4 PrintedCircuit BoardsandSample Holders . ........... 137 6 Measurement Setup 141 6.1 CryogenicsandFiltering. ........ 143 6.2 PulseSynthesis .................................. ..... 146 6.3 Demodulation.................................... .... 147 6.3.1 DigitalHomodyne ............................... 148 7 Characterization of CQED 154 7.1 Cavity.......................................... 154 7.1.1 TemperatureDependence . .... 155 7.1.2 MagneticFieldDependence . ..... 157 7.2 Cooperpairbox ................................... .. 159 7.2.1 ChargeNoise ................................... 164 7.2.2 MeasuredCPBproperties . .... 166 7.3 Transmon ........................................ 166 8 Cavity QED Experiments with Circuits 169 8.1 ResonantLimit................................... .... 171 8.1.1 Vacuum Rabi Mode Splitting with CPB . ..... 171 8.1.2 Vacuum Rabi Mode Splitting With Transmon . ....... 173 8.2 DispersiveWeakLimit. .. .. .. .. .. .. .. .. .. .. .. .. ...... 177 CONTENTS 6 8.2.1 ACStarkEffect .................................. 177 8.2.2 Off-ResonantACStarkEffect. .... 182 8.2.3 SidebandExperiments . .... 185 8.3 DispersiveStrongLimit . ....... 191 8.3.1 PhotonNumberSplitting . .... 191 8.3.2 Anharmonic Strong Dispersive Limit . ........ 197 9 Time Domain Measurements 200 9.1 SingleQubitGates ................................ ..... 200 9.2 SingleShotReadout ............................... ..... 207 9.3 SinglePhotonSource.............................. ...... 211 10 Future work 220 10.1 EvolutionofCircuitQED . ....... 220 10.1.1 NewCavityandQubitDesigns . ..... 220 10.1.2 ScalingCircuitQED . .... 221 10.1.3 Otherquantumcircuits . ..... 222 10.1.4 HybridCircuitQED .. .. .. .. .. .. .. .. .. .. .. .. .. 223 11 Conclusions 225 Appendices 226 A Operators and Commutation Relations 227 A.1 HarmonicOscillators. ....... 227 A.2 Spin1/2......................................... 227 A.3 Jaynes-CummingsOperators . ....... 227 A.3.1 Interaction with Harmonic oscillator operators . ............. 228 A.3.2 InteractionwithSpin1/2Operators . ........ 228 B Derivation of Dressed State Atom Picture 229 C Mathematica Notebooks 233 C.1 CooperPairBox ................................... .. 233 CONTENTS 7 D Recipes 234 List of Figures 1.1 Relaxation and dephasing of qubits leads to decoherence ..............
Load more

Recommended publications
  • Theory and Application of Fermi Pseudo-Potential in One Dimension
    Theory and application of Fermi pseudo-potential in one dimension The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Wu, Tai Tsun, and Ming Lun Yu. 2002. “Theory and Application of Fermi Pseudo-Potential in One Dimension.” Journal of Mathematical Physics 43 (12): 5949–76. https:// doi.org/10.1063/1.1519940. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:41555821 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA CERN-TH/2002-097 Theory and application of Fermi pseudo-potential in one dimension Tai Tsun Wu Gordon McKay Laboratory, Harvard University, Cambridge, Massachusetts, U.S.A., and Theoretical Physics Division, CERN, Geneva, Switzerland and Ming Lun Yu 41019 Pajaro Drive, Fremont, California, U.S.A.∗ Abstract The theory of interaction at one point is developed for the one-dimensional Schr¨odinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential arXiv:math-ph/0208030v1 21 Aug 2002 and two Fermi pseudo-potentials, one odd under space reflection and the other even.
    [Show full text]
  • Dynamical Control of Matter Waves in Optical Lattices Sune Schøtt
    Aarhus University Faculty of Science Department of Physics and Astronomy PhD Thesis Dynamical Control of Matter Waves in Optical Lattices by Sune Schøtt Mai November 2010 This thesis has been submitted to the Faculty of Science at Aarhus Uni- versity in order to fulfill the requirements for obtaining a PhD degree in physics. The work has been carried out under the supervision of profes- sor Klaus Mølmer and associate professor Jan Arlt at the Department of Physics and Astronomy. Contents Contents i 1 Introduction 3 1.1 Thesis Outline .......................... 3 1.2 Bose-Einstein Condensation .................. 4 2 Experimental Setup and Methods 9 2.1 Overview ............................. 9 2.2 Magneto-Optic Trap and Optical Pumping .......... 9 2.3 Transport with Movable Quadrupole Traps . 13 2.4 Evaporative Cooling ...................... 14 2.5 Absorption Imaging ....................... 15 3 Optical Lattices 17 3.1 Introduction ........................... 17 3.2 AC Stark-shift Induced Potentials . 18 3.2.1 Classical and Semi-Classical Approaches . 18 3.2.2 Dressed State Picture . 20 3.3 Lattice Band Structure ..................... 22 3.3.1 Reciprocal Space Bloch Theorem . 23 3.3.2 The 1D Lattice Band-Structure . 23 4 Lattice Calibration Techniques 27 4.1 Introduction ........................... 27 4.2 Kapitza-Dirac Scattering .................... 28 4.3 Bloch Oscillation and LZ-Tunneling . 30 4.3.1 Bloch Oscillation .................... 31 4.3.2 Landau-Zener Theory . 31 i ii CONTENTS 4.3.3 Experimental Verification of the Landau-Zener Model 32 4.4 Lattice Modulation ....................... 35 4.5 Summary ............................ 35 5 Dynamically Controlled Lattices 39 5.1 Introduction ........................... 39 5.2 Overview ............................. 39 5.3 Controlled Matter Wave Beam Splitter .
    [Show full text]
  • Engineering the Coupling of Superconducting Qubits
    Engineering the coupling of superconducting qubits Von der Fakultät für Mathematik, Informatik und Naturwissenschaften der RWTH Aachen University zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigte Dissertation vorgelegt von M. Sc. Alessandro Ciani aus Penne, Italien Berichter: Prof. Dr. David DiVincenzo Prof. Dr. Fabian Hassler Tag der mündlichen Prüfung: 12 April 2019 Diese Dissertation ist auf den Internetseiten der Universitätsbibliothek verfügbar. ii «Considerate la vostra semenza: fatti non foste a viver come bruti, ma per seguir virtute e conoscenza.» Dante Alighieri, "La Divina Commedia", Inferno, Canto XXVI, vv. 118-120. iii Abstract The way to build a scalable and reliable quantum computer that truly exploits the quantum power faces several challenges. Among the various proposals for building a quantum computer, superconducting qubits have rapidly progressed and hold good promises in the near-term future. In particular, the possibility to design the required interactions is one of the most appealing features of this kind of architecture. This thesis deals with some detailed aspects of this problem focusing on architectures based on superconducting transmon-like qubits. After reviewing the basic tools needed for the study of superconducting circuits and the main kinds of superconducting qubits, we move to the analyisis of a possible scheme for realizing direct parity measurement. Parity measurements, or in general stabilizer measurements, are fundamental tools for realizing quantum error correct- ing codes, that are believed to be fundamental for dealing with the problem of de- coherence that affects any physical implementation of a quantum computer. While these measurements are usually done indirectly with the help of ancilla qubits, the scheme that we analyze performs the measurement directly, and requires the engi- neering of a precise matching condition.
    [Show full text]
  • Scalability and High-Efficiency of an $(N+ 1) $-Qubit Toffoli Gate Sphere
    Scalability and high-efficiency of an (n + 1)-qubit Toffoli gate sphere via blockaded Rydberg atoms Dongmin Yu1, Yichun Gao1, Weiping Zhang2,3, Jinming Liu1 and Jing Qian1,3,† 1State Key Laboratory of Precision Spectroscopy, Department of Physics, School of Physics and Electronic Science, East China Normal University, Shanghai 200062, China 2Department of Physics and Astronomy, Shanghai Jiaotong University and Tsung-Dao Lee Institute, Shanghai 200240, China and 3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China∗ The Toffoli gate serving as a basic building block for reversible quantum computation, has man- ifested its great potentials in improving the error-tolerant rate in quantum communication. While current route to the creation of Toffoli gate requires implementing sequential single- and two-qubit gates, limited by longer operation time and lower average fidelity. We develop a new theoretical protocol to construct a universal (n + 1)-qubit Toffoli gate sphere based on the Rydberg blockade mechanism, by constraining the behavior of one central target atom with n surrounding control atoms. Its merit lies in the use of only five π pulses independent of the control atom number n which leads to the overall gate time as fast as 125ns and the average fidelity closing to 0.999. The maximal filling number of control atoms can be∼ up to n = 46, determined by the spherical diame- ter which is equal to the blockade radius, as well as by the nearest neighbor spacing between two trapped-atom lattices. Taking n = 2, 3, 4 as examples we comparably show the gate performance with experimentally accessible parameters, and confirm that the gate errors mainly attribute to the imperfect blockade strength, the spontaneous atomic loss and the imperfect ground-state prepa- ration.
    [Show full text]
  • 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]
  • Free-Electron Qubits
    Free-Electron Qubits Ori Reinhardt†, Chen Mechel†, Morgan Lynch, and Ido Kaminer Department of Electrical Engineering and Solid State Institute, Technion - Israel Institute of Technology, 32000 Haifa, Israel † equal contributors Free-electron interactions with laser-driven nanophotonic nearfields can quantize the electrons’ energy spectrum and provide control over this quantized degree of freedom. We propose to use such interactions to promote free electrons as carriers of quantum information and find how to create a qubit on a free electron. We find how to implement the qubit’s non-commutative spin-algebra, then control and measure the qubit state with a universal set of 1-qubit gates. These gates are within the current capabilities of femtosecond-pulsed laser-driven transmission electron microscopy. Pulsed laser driving promise configurability by the laser intensity, polarizability, pulse duration, and arrival times. Most platforms for quantum computation today rely on light-matter interactions of bound electrons such as in ion traps [1], superconducting circuits [2], and electron spin systems [3,4]. These form a natural choice for implementing 2-level systems with spin algebra. Instead of using bound electrons for quantum information processing, in this letter we propose using free electrons and manipulating them with femtosecond laser pulses in optical frequencies. Compared to bound electrons, free electron systems enable accessing high energy scales and short time scales. Moreover, they possess quantized degrees of freedom that can take unbounded values, such as orbital angular momentum (OAM), which has also been proposed for information encoding [5-10]. Analogously, photons also have the capability to encode information in their OAM [11,12].
    [Show full text]
  • Design of a Qubit and a Decoder in Quantum Computing Based on a Spin Field Effect
    Design of a Qubit and a Decoder in Quantum Computing Based on a Spin Field Effect A. A. Suratgar1, S. Rafiei*2, A. A. Taherpour3, A. Babaei4 1 Assistant Professor, Electrical Engineering Department, Faculty of Engineering, Arak University, Arak, Iran. 1 Assistant Professor, Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran. 2 Young Researchers Club, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran. *[email protected] 3 Professor, Chemistry Department, Faculty of Science, Islamic Azad University, Arak Branch, Arak, Iran. 4 faculty member of Islamic Azad University, Khomein Branch, Khomein, ABSTRACT In this paper we present a new method for designing a qubit and decoder in quantum computing based on the field effect in nuclear spin. In this method, the position of hydrogen has been studied in different external fields. The more we have different external field effects and electromagnetic radiation, the more we have different distribution ratios. Consequently, the quality of different distribution ratios has been applied to the suggested qubit and decoder model. We use the nuclear property of hydrogen in order to find a logical truth value. Computational results demonstrate the accuracy and efficiency that can be obtained with the use of these models. Keywords: quantum computing, qubit, decoder, gyromagnetic ratio, spin. 1. Introduction different hydrogen atoms in compound applied for the qubit and decoder designing. Up to now many papers deal with the possibility to realize a reversible computer based on the laws of 2. An overview on quantum concepts quantum mechanics [1]. In this chapter a short introduction is presented Modern quantum chemical methods provide into the interesting field of quantum in physics, powerful tools for theoretical modeling and Moore´s law and a summary of the quantum analysis of molecular electronic structures.
    [Show full text]
  • Quantum Noise in Quantum Optics: the Stochastic Schr\" Odinger
    Quantum Noise in Quantum Optics: the Stochastic Schr¨odinger Equation Peter Zoller † and C. W. Gardiner ∗ † Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria ∗ Department of Physics, Victoria University Wellington, New Zealand February 1, 2008 arXiv:quant-ph/9702030v1 12 Feb 1997 Abstract Lecture Notes for the Les Houches Summer School LXIII on Quantum Fluc- tuations in July 1995: “Quantum Noise in Quantum Optics: the Stochastic Schroedinger Equation” to appear in Elsevier Science Publishers B.V. 1997, edited by E. Giacobino and S. Reynaud. 0.1 Introduction Theoretical quantum optics studies “open systems,” i.e. systems coupled to an “environment” [1, 2, 3, 4]. In quantum optics this environment corresponds to the infinitely many modes of the electromagnetic field. The starting point of a description of quantum noise is a modeling in terms of quantum Markov processes [1]. From a physical point of view, a quantum Markovian description is an approximation where the environment is modeled as a heatbath with a short correlation time and weakly coupled to the system. In the system dynamics the coupling to a bath will introduce damping and fluctuations. The radiative modes of the heatbath also serve as input channels through which the system is driven, and as output channels which allow the continuous observation of the radiated fields. Examples of quantum optical systems are resonance fluorescence, where a radiatively damped atom is driven by laser light (input) and the properties of the emitted fluorescence light (output)are measured, and an optical cavity mode coupled to the outside radiation modes by a partially transmitting mirror.
    [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]
  • A Theoretical Study of Quantum Memories in Ensemble-Based Media
    A theoretical study of quantum memories in ensemble-based media Karl Bruno Surmacz St. Hugh's College, Oxford A thesis submitted to the Mathematical and Physical Sciences Division for the degree of Doctor of Philosophy in the University of Oxford Michaelmas Term, 2007 Atomic and Laser Physics, University of Oxford i A theoretical study of quantum memories in ensemble-based media Karl Bruno Surmacz, St. Hugh's College, Oxford Michaelmas Term 2007 Abstract The transfer of information from flying qubits to stationary qubits is a fundamental component of many quantum information processing and quantum communication schemes. The use of photons, which provide a fast and robust platform for encoding qubits, in such schemes relies on a quantum memory in which to store the photons, and retrieve them on-demand. Such a memory can consist of either a single absorber, or an ensemble of absorbers, with a ¤-type level structure, as well as other control ¯elds that a®ect the transfer of the quantum signal ¯eld to a material storage state. Ensembles have the advantage that the coupling of the signal ¯eld to the medium scales with the square root of the number of absorbers. In this thesis we theoretically study the use of ensembles of absorbers for a quantum memory. We characterize a general quantum memory in terms of its interaction with the signal and control ¯elds, and propose a ¯gure of merit that measures how well such a memory preserves entanglement. We derive an analytical expression for the entanglement ¯delity in terms of fluctuations in the stochastic Hamiltonian parameters, and show how this ¯gure could be measured experimentally.
    [Show full text]
  • Quantum Computation and Complexity Theory
    Quantum computation and complexity theory Course given at the Institut fÈurInformationssysteme, Abteilung fÈurDatenbanken und Expertensysteme, University of Technology Vienna, Wintersemester 1994/95 K. Svozil Institut fÈur Theoretische Physik University of Technology Vienna Wiedner Hauptstraûe 8-10/136 A-1040 Vienna, Austria e-mail: [email protected] December 5, 1994 qct.tex Abstract The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applicationsto quantum computing. Standardinterferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed. hep-th/9412047 06 Dec 94 1 Contents 1 The Quantum of action 3 2 Quantum mechanics for the computer scientist 7 2.1 Hilbert space quantum mechanics ..................... 7 2.2 From single to multiple quanta Ð ªsecondº ®eld quantization ...... 15 2.3 Quantum interference ............................ 17 2.4 Hilbert lattices and quantum logic ..................... 22 2.5 Partial algebras ............................... 24 3 Quantum information theory 25 3.1 Information is physical ........................... 25 3.2 Copying and cloning of qbits ........................ 25 3.3 Context dependence of qbits ........................ 26 3.4 Classical versus quantum tautologies .................... 27 4 Elements of quantum computatability and complexity theory 28 4.1 Universal quantum computers ....................... 30 4.2 Universal quantum networks ........................ 31 4.3 Quantum recursion theory ......................... 35 4.4 Factoring .................................. 36 4.5 Travelling salesman ............................. 36 4.6 Will the strong Church-Turing thesis survive? ............... 37 Appendix 39 A Hilbert space 39 B Fundamental constants of physics and their relations 42 B.1 Fundamental constants of physics ..................... 42 B.2 Conversion tables .............................. 43 B.3 Electromagnetic radiation and other wave phenomena .........
    [Show full text]
  • Quantum Inductive Learning and Quantum Logic Synthesis
    Portland State University PDXScholar Dissertations and Theses Dissertations and Theses 2009 Quantum Inductive Learning and Quantum Logic Synthesis Martin Lukac Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Part of the Electrical and Computer Engineering Commons Let us know how access to this document benefits ou.y Recommended Citation Lukac, Martin, "Quantum Inductive Learning and Quantum Logic Synthesis" (2009). Dissertations and Theses. Paper 2319. https://doi.org/10.15760/etd.2316 This Dissertation is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. For more information, please contact [email protected]. QUANTUM INDUCTIVE LEARNING AND QUANTUM LOGIC SYNTHESIS by MARTIN LUKAC A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in ELECTRICAL AND COMPUTER ENGINEERING. Portland State University 2009 DISSERTATION APPROVAL The abstract and dissertation of Martin Lukac for the Doctor of Philosophy in Electrical and Computer Engineering were presented January 9, 2009, and accepted by the dissertation committee and the doctoral program. COMMITTEE APPROVALS: Irek Perkowski, Chair GarrisoH-Xireenwood -George ^Lendaris 5artM ?teven Bleiler Representative of the Office of Graduate Studies DOCTORAL PROGRAM APPROVAL: Malgorza /ska-Jeske7~Director Electrical Computer Engineering Ph.D. Program ABSTRACT An abstract of the dissertation of Martin Lukac for the Doctor of Philosophy in Electrical and Computer Engineering presented January 9, 2009. Title: Quantum Inductive Learning and Quantum Logic Synhesis Since Quantum Computer is almost realizable on large scale and Quantum Technology is one of the main solutions to the Moore Limit, Quantum Logic Synthesis (QLS) has become a required theory and tool for designing Quantum Logic Circuits.
    [Show full text]