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Wiley eBooks

Quantum Computing

Published Oct 12, 1999• 30 citations
Publisher

Abstract

Quantum Computation (S. Braunstein). The Los Alamos Trapped Ion Quantum Computer Experiment (R. Hughes, et al.). Experimental Primer on the Trapped Ion Quantum Computer (D. Weineland, et al.). Measurement and State Preparation via Ion Trap Quantum Computing (S. Schneider, et al.). Photon--Wavepackets as Flying Quantum Bits (K. Gheri, et al.). Quantum Logic Gate Operating on Atomic Scattering by Standing Wave Field in Bragg Regime (A. Khan & M. Zubairy). Models of Quantum Turing Machines (P. Benioff). Space, Time, Parallelism and Noise Requirements for Reliable Quantum Computing (A. Steane). The Quantum Hamming and Hexacodes (Th. Beth & M. Grassl). Tight Bounds on Quantum Searching (M. Boyer, et al.). Making an Empty Promise with a Quantum Computer (H. Chau & H.--K. Lo). Flocks of Quantum Clones: Multiple Copying of Qubits (V. Buzck, et al.). Information Gain vs. State Disturbance in Quantum Theory (Ch. Fuchs). On Multi--Particle Entanglement (N. Linden & S. Popescu). Generalized Coherent States and Phase--Space--Interference in Multi--Mode Systems (M. Gagen). Index.

DOI
10.1002/3527603093

Related papers

Quantum Computing Devices: Principles, Designs, and Analysis

Berthold‐Georg Englert, Bernd Rohwedder, Marlan O. Scully +1 more

Preface FOUNDATIONS OF QUANTUM INFORMATICS Spins: The Stern-Gerlach experiment and spin filter EPR, Bell's inequalities, and hidden variables The Landauer principle QUANTUM COMPUTATION AND QUANTUM SYSTEMS Turing machines and binary logic gates Quantum mechanical systems Hilbert spaces Complex finite dimensional Hilbert Spaces Quantum Turing machines Universality of elementary quantum gates Quantum algorithms Quantum adder and multiplier Quantum error correction codes Lasers: a heuristic introduction Quantum computing devices and requirements TWO-LEVEL ATOMS AND CAVITY QED Two-level atoms Quantization of the electromagnetic field Cavity QED Cavity QED for the quantum phase gate Quantum eraser Quantum disentanglement eraser IMPERFECT QUANTUM OPERATIONS Fidelity Density matrices Time evolution of density matrices Examples of master equations Fidelity calculations ION TRAPS Introduction Ion qubits Summary of ion preparation Coherence Quantum gates Large scale confined-ion quantum computer Trap architecture and performance Teleportation of coherent information Experimental DFS logic gates Quantum error correction by ion traps Summary of ion quantum computation QUANTUM LOGIC USING COLD, CONFINED ATOMS Introduction Atom trapping and detection Atom interactions with external fields Atom trapping Qubits and gates Controlled two-qubit gates Coherence properties of atom gates Assessment QUANTUM DOTS QUANTUM COMPUTING GATES Introduction Electrons in quantum dots microcavity Coupled electron spins Biexciton in a single quantum dot Conclusions LINEAR OPTICS COMPUTERS Classical electrodynamics - Classical computers Quantum electrodynamics - Quantum computers Teleportation Summary and outlook SUPERCONDUCTING QUANTUM COMPUTING DEVICES Introduction Superconductivity More on Cooper pairs and Josephson junctions Superconducting circuits: classical Superconducting circuits: quantum Quantum gates Measurement NMR QUANTUM COMPUTING Nuclear magnetic resonance Basic technology with NMR Solid state NMR Shor's algorithm and its experimental realization Quantum algorithm for lattice-gas systems Conclusion Appendix A: The Fock-Darwin States Appendix B: Evaluation of the exchange energy Appendix C: Transformation of quantum states: SU(2) and SO(3) Appendix D: The Homeomorphism from SU(2) to SO(3)

•Sep 18, 2006•53 citations

Quantum information processing with two trapped cadmium ions.

Patricia J. Lee

Quantum information processing combines information theory with laws of quantum mechanics to provide an interesting new study that promises significant technological advances in the field of computation. The quest for a physical quantum information processor not only tests the limits of quantum mechanics but also motivates the development of new control techniques for quantum systems. This thesis documents the implementation of the necessary components of a quantum computer in a new atomic ion species, while demonstrating an entangling procedure that is uniquely insensitive to certain types of phase noise. Quantum bits are stored in the ground state hyperfine levels of individual trapped cadmium ions, and the collective vibration of the ions in the trap potential form a quantum databus through which information can be transferred. Quantum state measurements and initialization processes are accomplished through optical pumping, and quantum logic operations are performed through interactions with applied electromagnetic fields. The spin-dependent force, which is the underlying principle of many entanglement schemes for trapped ions, is investigated in detail in a series of Schrodinger cat experiments that generates entangled wavepackets well separated in the momentum-position phase space (alpha = 6). Phase control of the interaction in the gate scheme proposed by Molmer and Sorensen results in phase coherence between single-qubit rotations and a robust two-qubit entangling logic gate that can operate on magnetic-field insensitive clock qubits at finite temperature. The coherence time of the clock qubit (∼ 1s) is long compared to the gate time (∼ 100mus). Finally, quantum state tomography is performed on two ions, featuring a set of universal quantum logic gates that is sufficient for any quantum computation, with an entangling gate fidelity of 0.83. The combination of the tools developed here is sufficient to perform universal quantum computation. With the advent of scalable, multi-zone ion trap structures, the concept of a quantum computation device may become reality in the not so distant future.

•Jan 1, 2006•4 citations

Basics of Quantum Computation (Part 1)

Elemér Elad Rosinger

The aim of this textbook is to bridge in regard of quantum computation what proves to be a considerable threshold even to the usual science trained readership between the level of science popularization, and on the other hand, the presently available more encyclopedic textbooks. In this respect the present textbook is aimed to be a short, simple, rigorous and direct introduction, addressing itself only to quantum computation proper.

arXiv:quant-ph/0407064•Jul 8, 2004•1 citation

Efficient optical configurations for trapped-ion entangling gates

Aditya Milind Kolhatkar, Karan K. Mehta

High-fidelity and parallel realization in scalable platforms of the two-qubit entangling gates fundamental to universal quantum computing constitutes one of the largest challenges in implementing fault-tolerant quantum computation. Integrated optical addressing of trapped-ion qubits offers routes to scaling the high-fidelity optical control demonstrated to date in small systems. Here we show that in addition to scaling, capabilities practically enabled by integrated optics can substantially alleviate laser powers required for both light-shift (LS) and Molmer-Sorensen (MS) geometric phase gates acting on long-lived ground-state qubit encodings in a broad range of ion species. In the proposed gate schemes utilizing carrier nulling via ion positioning at phase-stable standing-wave (SW) nodes, our calculations suggest that suppressed spontaneous photon scattering at the SW node allows for gate drives operating at smaller Raman detunings, resulting in approximately an order-of-magnitude reduction in power requirement (and significantly larger in certain parameter regimes) for gates of a given duration and scattering-limited fidelity as compared to conventional running wave (RW)-based approaches. The SW schemes have the additional benefit of simultaneously eliminating undesired coherent couplings that typically limit gate speeds. Our work quantifies power requirements for multiple ion species and enhancements to be expected from carrier-nulled configurations practically enabled by integrated delivery, and informs experiments and systems for realization of fast and power-efficient laser-based entangling gates in scalable platforms.

arXiv:2509.05271•Physical Review A•Feb 12, 2026•2 citations

Quantum computing

J. Eisert, Michael M. Wolf

This article gives an elementary introduction to quantum computing. It is a draft for a book chapter of the "Handbook of Nature-Inspired and Innovative Computing", Eds. A. Zomaya, G.J. Milburn, J. Dongarra, D. Bader, R. Brent, M. Eshaghian-Wilner, F. Seredynski (Springer, Berlin Heidelberg New York, 2006).

arXiv:quant-ph/0401019•Jan 5, 2004•0 citations

The Los Alamos Trapped Ion Quantum Computer Experiment

Richard Hughes, Daniel F. V. James, J.J. Gómez +12 more

The development and theory of an experiment to investigate quantum computation with trapped calcium ions is described. The ion trap, laser and ion requirements are determined, and the parameters required for quantum logic operations as well as simple quantum factoring are described.

arXiv:quant-ph/9708050•Fortschritte der Physik•Jun 1, 1998•70 citations
Quantum Computation (S. Braunstein). The Los Alamos Trapped Ion Quantum Computer Experiment (R. Hughes, et al.). Experimental Primer on the Trapped Ion Quantum Computer (D. Weineland, et al.). Measurement and State Preparation via Ion Trap Quantum Computing (S. Schneider, et al.). Photon--Wavepackets as Flying Quantum Bits (K. Gheri, et al.). Quantum Logic Gate Operating on Atomic Scattering by Standing Wave Field in Bragg Regime (A. Khan & M. Zubairy). Models of Quantum Turing Machines (P. Benioff). Space, Time, Parallelism and Noise Requirements for Reliable Quantum Computing (A. Steane). The Quantum Hamming and Hexacodes (Th. Beth & M. Grassl). Tight Bounds on Quantum Searching (M. Boyer, et al.). Making an Empty Promise with a Quantum Computer (H. Chau & H.--K. Lo). Flocks of Quantum Clones: Multiple Copying of Qubits (V. Buzck, et al.). Information Gain vs. State Disturbance in Quantum Theory (Ch. Fuchs). On Multi--Particle Entanglement (N. Linden & S. Popescu). Generalized Coherent States and Phase--Space--Interference in Multi--Mode Systems (M. Gagen). Index.
Preface FOUNDATIONS OF QUANTUM INFORMATICS Spins: The Stern-Gerlach experiment and spin filter EPR, Bell's inequalities, and hidden variables The Landauer principle QUANTUM COMPUTATION AND QUANTUM SYSTEMS Turing machines and binary logic gates Quantum mechanical systems Hilbert spaces Complex finite dimensional Hilbert Spaces Quantum Turing machines Universality of elementary quantum gates Quantum algorithms Quantum adder and multiplier Quantum error correction codes Lasers: a heuristic introduction Quantum computing devices and requirements TWO-LEVEL ATOMS AND CAVITY QED Two-level atoms Quantization of the electromagnetic field Cavity QED Cavity QED for the quantum phase gate Quantum eraser Quantum disentanglement eraser IMPERFECT QUANTUM OPERATIONS Fidelity Density matrices Time evolution of density matrices Examples of master equations Fidelity calculations ION TRAPS Introduction Ion qubits Summary of ion preparation Coherence Quantum gates Large scale confined-ion quantum computer Trap architecture and performance Teleportation of coherent information Experimental DFS logic gates Quantum error correction by ion traps Summary of ion quantum computation QUANTUM LOGIC USING COLD, CONFINED ATOMS Introduction Atom trapping and detection Atom interactions with external fields Atom trapping Qubits and gates Controlled two-qubit gates Coherence properties of atom gates Assessment QUANTUM DOTS QUANTUM COMPUTING GATES Introduction Electrons in quantum dots microcavity Coupled electron spins Biexciton in a single quantum dot Conclusions LINEAR OPTICS COMPUTERS Classical electrodynamics - Classical computers Quantum electrodynamics - Quantum computers Teleportation Summary and outlook SUPERCONDUCTING QUANTUM COMPUTING DEVICES Introduction Superconductivity More on Cooper pairs and Josephson junctions Superconducting circuits: classical Superconducting circuits: quantum Quantum gates Measurement NMR QUANTUM COMPUTING Nuclear magnetic resonance Basic technology with NMR Solid state NMR Shor's algorithm and its experimental realization Quantum algorithm for lattice-gas systems Conclusion Appendix A: The Fock-Darwin States Appendix B: Evaluation of the exchange energy Appendix C: Transformation of quantum states: SU(2) and SO(3) Appendix D: The Homeomorphism from SU(2) to SO(3)
Quantum information processing combines information theory with laws of quantum mechanics to provide an interesting new study that promises significant technological advances in the field of computation. The quest for a physical quantum information processor not only tests the limits of quantum mechanics but also motivates the development of new control techniques for quantum systems. This thesis documents the implementation of the necessary components of a quantum computer in a new atomic ion species, while demonstrating an entangling procedure that is uniquely insensitive to certain types of phase noise. Quantum bits are stored in the ground state hyperfine levels of individual trapped cadmium ions, and the collective vibration of the ions in the trap potential form a quantum databus through which information can be transferred. Quantum state measurements and initialization processes are accomplished through optical pumping, and quantum logic operations are performed through interactions with applied electromagnetic fields. The spin-dependent force, which is the underlying principle of many entanglement schemes for trapped ions, is investigated in detail in a series of Schrodinger cat experiments that generates entangled wavepackets well separated in the momentum-position phase space (alpha = 6). Phase control of the interaction in the gate scheme proposed by Molmer and Sorensen results in phase coherence between single-qubit rotations and a robust two-qubit entangling logic gate that can operate on magnetic-field insensitive clock qubits at finite temperature. The coherence time of the clock qubit (∼ 1s) is long compared to the gate time (∼ 100mus). Finally, quantum state tomography is performed on two ions, featuring a set of universal quantum logic gates that is sufficient for any quantum computation, with an entangling gate fidelity of 0.83. The combination of the tools developed here is sufficient to perform universal quantum computation. With the advent of scalable, multi-zone ion trap structures, the concept of a quantum computation device may become reality in the not so distant future.
High-fidelity and parallel realization in scalable platforms of the two-qubit entangling gates fundamental to universal quantum computing constitutes one of the largest challenges in implementing fault-tolerant quantum computation. Integrated optical addressing of trapped-ion qubits offers routes to scaling the high-fidelity optical control demonstrated to date in small systems. Here we show that in addition to scaling, capabilities practically enabled by integrated optics can substantially alleviate laser powers required for both light-shift (LS) and Molmer-Sorensen (MS) geometric phase gates acting on long-lived ground-state qubit encodings in a broad range of ion species. In the proposed gate schemes utilizing carrier nulling via ion positioning at phase-stable standing-wave (SW) nodes, our calculations suggest that suppressed spontaneous photon scattering at the SW node allows for gate drives operating at smaller Raman detunings, resulting in approximately an order-of-magnitude reduction in power requirement (and significantly larger in certain parameter regimes) for gates of a given duration and scattering-limited fidelity as compared to conventional running wave (RW)-based approaches. The SW schemes have the additional benefit of simultaneously eliminating undesired coherent couplings that typically limit gate speeds. Our work quantifies power requirements for multiple ion species and enhancements to be expected from carrier-nulled configurations practically enabled by integrated delivery, and informs experiments and systems for realization of fast and power-efficient laser-based entangling gates in scalable platforms.