Optical Quantum Computers : A Route to Practical Continuous Variable Quantum Information Processing

This Book Is A Current And Rare Treatment Of The Theoretical And Experimental Aspects Of One Of The Most Promising Approaches To Quantum Computation-continuous-variable (cv) Quantum Computation Using Optical Systems. In Addition To Its Pedagogical Value To Those New To Quantum Computing, It Is Also A Practical Handbook For Both Experimentalists And Theorists Working In The Field. Optical Quantum Computers: A Route To Practical Continuous Variable Quantum Information Processing Summarizes Many Recent Experimental Developments And Fills A Gap In Current Literature. This Timely Book: -- Provides Up-to-date Discussions Based On Experiments And Expertise Of The Scientists Building Quantum Computers -- Centers Around The Idea Of Time-domain Quantum Computation -- Highlights Work By The Team From The Furusawa-yoshikawa Laboratory At The University Of Tokyo-one Of The Leading Quantum Computing Labs In The World Researchers, Graduate Students, And Those Working In The Quantum Computing Industry And Its Related Fi Elds Will Fi Nd This An Invaluable Resource. Cover Half Title Title Page Copyright Page PREFACE TABLE OF CONTENTS CHAPTER 1: INTRODUCTION 1.1 BRIEF INTRODUCTION TO QUANTUM COMPUTATION 1.2 QUBITS (DISCRETE VARIABLES) AND MODES (CONTINUOUS VARIABLES) 1.3 BUILDING AN OPTICAL QUANTUM COMPUTER 1.3.1 Optical classical computer 1.3.2 Photonic qubits and optical modes 1.4 ABOUT THIS BOOK REFERENCES CHAPTER 2: QUANTUM OPTICS 2.1 REVISION OF QUANTUM MECHANICS 2.1.1 Schrödinger picture and Heisenberg picture 2.1.2 Mixed states and density matrices 2.1.3 Measurements 2.1.4 Uncertainty principle 2.2 BRIEF REVIEW OF CLASSICAL ELECTROMAGNETISM 2.3 QUANTIZATION OF THE ELECTROMAGNETIC FIELDS 2.3.1 Modes 2.3.2 Transformation of modes 2.3.3 Quadrature 2.4 BASIC QUANTUM STATES AND THEIR REPRESENTATIONS 2.4.1 Review of Bloch sphere of the qubit system 2.4.2 Wigner function 2.4.3 Quadrature eigenstates 2.4.4 Vacuum states 2.4.5 Fock states 2.4.6 Coherent states 2.4.7 Squeezed vacuum states 2.4.8 Schrödinger’s cat states 2.5 QUANTUM OPERATIONS AND UNIVERSALITY 2.5.1 A brief review on operations on qubits systems 2.5.2 Universality and classical simulatability 2.5.3 Weyl–Heisenberg group 2.5.4 Symplectic transformations 2.5.5 Non-Gaussian operations 2.6 HOMODYNE MEASUREMENT 2.7 FOCK BASIS MEASUREMENT 2.8 QUANTUM ENTANGLEMENT 2.8.1 Einstein–Podolsky–Rosen paradox 2.8.2 Quantum entanglement and inseparability 2.8.3 PPT criteria 2.8.4 van Loock–Furusawa criteria REFERENCES CHAPTER 3: QUANTUM TELEPORTATION AND MEASUREMENT-BASED QUANTUM COMPUTATION 3.1 QUANTUM TELEPORTATION PROTOCOL 3.1.1 Half-teleportation circuit 3.1.2 Full-teleportation circuit 3.1.3 Experimental realization of CV quantum teleportation 3.2 MEASUREMENT-BASED QUANTUM COMPUTATION 3.2.1 Quantum operations with halfand full-teleportation 3.2.2 Cluster state quantum computation 3.2.3 Gate teleportation 3.2.4 Non-Gaussian measurement using ancillary states REFERENCES CHAPTER 4: QUANTUM COMPUTATION IN TIME DOMAIN 4.1 ENCODING INFORMATION IN A WAVE PACKET 4.1.1 Treatment of wave packet in the time domain 4.1.2 Frequency-domain treatment of the wave packet 4.1.3 Squeezed vacuum state in the temporal wave packet 4.2 TIME-DOMAIN-MULTIPLEXED CLUSTER STATES 4.2.1 Schematic idea 4.2.2 One-dimensional cluster state 4.2.3 Two-dimensional cluster state 4.2.4 Operations using time-domain-multiplexed cluster states 4.3 LOOP-BASED TIME-DOMAIN QUANTUM COMPUTATION 4.4 QUANTUM OPERATIONS ON THE WAVE PACKET MODE 4.4.1 Dynamic squeezing gate 4.4.2 Quantum nondemolition gate 4.5 OTHER MULTIPLEXING METHODS REFERENCES CHAPTER 5: NON-GAUSSIAN QUANTUM STATES 5.1 INTRODUCTION 5.2 HERALDING GENERATION OF NON-GAUSSIAN STATES 5.2.1 Realistic considerations 5.2.2 Modes of non-Gaussian states generated with the heralding method 5.3 GENERATION OF SUPERPOSITION OF FOCK STATES 5.3.1 Herald generation of the single-photon states 5.3.2 Other single-photon sources 5.3.3 Superposition of the Fock state using displacement beams 5.3.4 Multimode non-Gaussian states and their interferences 5.4 PHOTON SUBTRACTION AND CAT STATE 5.4.1 Basic formulation 5.4.2 Experimental consideration 5.4.3 Superposition between cat state and squeezed vacuum state REFERENCES CHAPTER 6: QUANTUM ERROR CORRECTION IN CONTINUOUS-VARIABLE SYSTEM 6.1 “ANALOG” QUANTUM COMPUTER AND FAULT TOLERANCE 6.2 EXAMPLES OF LOGICAL QUBITS IN THE CV OPTICAL SYSTEM 6.2.1 Qutrit 6.2.2 Coherent state encoding 6.3 GOTTESMAN–KITAEV–PRESKILL QUBIT 6.3.1 Operations and error corrections on GKP qubit 6.3.2 Research studies on the generation of GKP qubits 6.4 ANALOG INFORMATION IN CV QUANTUM ERROR CORRECTION REFERENCES CHAPTER 7: INTEGRATED OPTICS FOR QUANTUM COMPUTER 7.1 MOVING FROM TABLE-TOP TO INTEGRATED OPTICS 7.2 INTERFEROMETER 7.3 OPTICAL DELAY LINE 7.4 SINGLE-PHOTON SOURCE 7.5 SQUEEZED-LIGHT SOURCE 7.6 PHOTON DETECTORS 7.7 HOMODYNE MEASUREMENT 7.8 FEEDFORWARD OPERATION REFERENCES CHAPTER 8: CONCLUSION AND FUTURE PERSPECTIVE 8.1 FROM QUBIT TO CONTINUOUS VARIABLE TO LOGICAL QUBIT 8.2 THE NEXT STEPS 8.3 FINAL REMARKS REFERENCES APPENDIX A: MISCELLANEOUS CALCULATIONS A.1 DERIVATION OF THE HEISENBERG PICTURE TIME EVOLUTION OF ˆA AND ˆ5 A.2 HAMILTONIAN OF THE MONOCHROMATIC MODE A.3 EVOLUTION OF OPERATORS AND BAKER–CAMPBELL–HAUSDORFF FORMULA A.4 PROOF OF THE OVERCOMPLETENESS OF THE COHERENT STATES A.5 MATHEMATICAL TREATMENT OF AN OPTICAL PARAMETRIC OSCILLATOR A.6 MULTIMODE WIGNER FUNCTION AND ANALYSIS OF QUANTUM TELEPORTATION A.7 WIGNER FUNCTIONS OF GKP QUBITS REFERENCES APPENDIX B: EXPERIMENTAL METHODS IN QUANTUM OPTICS EXPERIMENTS B.1 GAUSSIAN BEAM B.2 OPTICAL CAVITY B.2.1 Longitudinal mode B.2.2 Transverse mode B.2.3 Locking optical cavity B.3 PHASE LOCKING OF THE INTERFEROMETER B.3.1 Phase locking with carrier interferences B.3.2 Phase locking with phase modulations B.4 FEEDFORWARD AND CANCELLATION REFERENCES INDEX