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Hybrid quantum computation in quantum optics

Physical Review A 2008年第2期78卷 022303-022303页

作者： P. van Loock W. J. Munro Kae Nemoto T. P. Spiller T. D. Ladd Samuel L. Braunstein G. J. Milburn National Institute of Informatics 2-1-2 Hitotsubashi Chiyoda-ku Tokyo 101-8430 Japan Optical Quantum Information Theory Group Institute of Theoretical Physics I and Max-Planck Research Group Institute of Optics Information and Photonics Universität Erlangen-Nürnberg Staudtstrasse 7/B2 91058 Erlangen Germany Hewlett-Packard Laboratories Filton Road Stoke Gifford Bristol BS34 8QZ United Kingdom Edward L. Ginzton Laboratory Stanford University Stanford California 94305-4088 USA Computer Science University of York York YO10 5DD United Kingdom Centre for Quantum Computer Technology Department of Physics University of Queensland Brisbane Australia

We propose a hybrid quantum computing scheme where qubit degrees of freedom for computation are combined with quantum continuous variables for communication. In particular, universal two-qubit gates can be implemented deterministically through qubit-qubit communication, mediated by a continuous-variable bus mode (“qubus”), without direct interaction between the qubits and without any measurement of the qubus. The key ingredients are controlled rotations of the qubus and unconditional qubus displacements. The controlled rotations are realizable through typical atom-light interactions in quantum optics. For such interactions, our scheme is universal and works in any regime, including the limits of weak and strong nonlinearities.

关键词： quantum optics

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Any AND-OR formula of size N can be evaluated in time N1/2+o(1) on a quantum computer

Any AND-OR formula of size N can be evaluated in time N1/2+o...

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48th Annual Symposium on Foundations of computer science, FOCS 2007

作者： Ambainis, Andris Childs, Andrew M. Reichardt, Ben W. Špalek, Robert Zhang, Shengyu Department of Computer Science University of Latvia Department of Combinatorics and Optimization Institute for Quantum Computing University of Waterloo Institute for Quantum Information California Institute of Technology NSF Grant PHY-0456720 and ARO Grant W911NF-05-1-0294 United States University of California Berkeley United States

ISBN: (纸本)0769530109

For any AND-OR formula of size N, there exists a bounded-error N 1/2+o(1)-time quantum algorithm, based on a discrete-time quantum walk, that evaluates this formula on a black-box input. Balanced, or "approximately balanced," formulas can be evaluated in O(√N) queries, which is optimal. It follows that the (2 - o(1))th power of the quantum query complexity is a lower bound on the formula size, almost solving in the positive an open problem posed by Laplante, Lee and Szegedy. © 2007 IEEE.

关键词： quantum computers

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Any AND-OR Formula of Size N can be Evaluated in time N^{1/2 + o(1)} on a quantum computer

Any AND-OR Formula of Size N can be Evaluated in time N^{1/2...

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Annual IEEE Symposium on Foundations of computer science

作者： Andris Ambainis Andrew M. Childs Ben W. Reichardt Robert Spalek Shengyu Zhang Department of Computer Science University of Latvia Department of Combinatorics & Optimization Institute for Quantum Computing University of Waterloo Institute for Quantum Information California Institute of Technology University of California Berkeley

For any AND-OR formula of size N, there exists a bounded-error N 1/2+o(1) -time quantum algorithm, based on a discrete-time quantum walk, that evaluates this formula on a black-box input. Balanced, or "approximately balanced," formulas can be evaluated in O(radicN) queries, which is optimal. It follows that the (2-o(1))th power of the quantum query complexity is a lower bound on the formula size, almost solving in the positive an open problem posed by Laplante, Lee and Szegedy.

关键词： quantum computing computer science Spectral analysis Combinatorial mathematics History Databases Algorithms

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quantum Algorithms for Hidden Nonlinear Structures

Quantum Algorithms for Hidden Nonlinear Structures

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Annual IEEE Symposium on Foundations of computer science

作者： Andrew M. Childs Leonard J. Schulman Umesh V. Vazirani Department of Combinatorics & Optimization and Institute for Quantum Computing University of Waterloo Waterloo ONT Canada Department of Computer Science California Institute of Technology Pasadena CA USA Computer Science Division University of California Berkeley CA USA

Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonAbelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an alternative generalization, namely to problems of finding hidden nonlinear structures over finite fields. We give examples of two such problems that can be solved efficiently by a quantum computer, but not by a classical computer. We also give some positive results on the quantum query complexity of finding hidden nonlinear structures.

关键词： quantum computing Polynomials Interference Fourier transforms computer science USA Councils Galois fields Vectors quantum mechanics Level set

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The Communication Complexity of Correlation

The Communication Complexity of Correlation

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Annual IEEE Conference on Computational Complexity

作者： Prahladh Harsha Rahul Jain David McAllester Jaikumar Radhakrishnan Toyota Technological Institute Chicago USA Institute for Quantum Computing and Department of Computer Science University of Waterloo Waterloo Canada University of California Berkeley USA Tata Institute of Fundamental Research Mumbai India

We examine the communication required for generating random variables remotely. One party Alice is given a distribution D , and she has to send a message to Bob , who is then required to generate a value with distribution exactly D . Alice and Bob are allowed to share random bits generated without the knowledge of D . There are two settings based on how the distribution D provided to Alice is chosen. If D is itself chosen randomly from some set (the set and distribution are known in advance) and we wish to minimize the expected communication in order for Alice to generate a value y, with distribution D , then we characterize the communication required in terms of the mutual information between the input to Alice and the output Bob is required to generate. If D is chosen from a set of distributions D , and we wish to devise a protocol so that the expected communication (the randomness comes from the shared random string and Alice coin tosses) is small for each D ϵ D , then we characterize the communication required in this case in terms of the channel capacity associated with the set D . Our proofs are based on an improved rejection sampling procedure that relates the relative entropy between two distributions to the communication complexity of generating one distribution from the other. As an application of these results, we derive a direct sum theorem in communication complexity that substantially improves the previous such result shown by Jain et al. [JRSb].

关键词： Complexity theory Random variables Character generation Mutual information Protocols Entropy Data processing quantum computing Channel capacity Sampling methods

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Single-photon quantum key distribution in the presence of loss

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Physical Review A 2007年第5期75卷 052336-052336页

作者： Marcos Curty Tobias Moroder Center for Quantum Information and Quantum Control Department of Physics and Department of Electrical & Computer Engineering University of Toronto Toronto Ontario Canada M5S 3G4 Institute for Quantum Computing University of Waterloo 200 University Avenue West Waterloo Ontario Canada N2L 3G1 Quantum Information Theory Group Institut für Theoretische Physik I and Max-Planck Research Group Institute of Optics Information and Photonics Universität Erlangen-Nürnberg D-91058 Erlangen Germany

We investigate two-way and one-way single-photon quantum key distribution (QKD) protocols in the presence of loss introduced by the quantum channel. Our analysis is based on a simple precondition for secure QKD in each case. In particular, the legitimate users need to prove that there exists no separable state (in the case of two-way QKD), or that there exists no quantum state having a symmetric extension (one-way QKD), that is compatible with the available measurements results. We show that both criteria can be formulated as a convex optimization problem known as a semidefinite program, which can be efficiently solved. Moreover, we prove that the solution to the dual optimization corresponds to the evaluation of an optimal witness operator that belongs to the minimal verification set of them for the given two-way (or one-way) QKD protocol. A positive expectation value of this optimal witness operator states that no secret key can be distilled from the available measurements results. We apply such analysis to several well-known single-photon QKD protocols under losses.

关键词： SEPARABILITY CRITERION NONORTHOGONAL STATES COHERENT STATES CRYPTOGRAPHY PROTOCOL DIFFERENTIATE SECURITY THEOREM PROOF

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Optimal quantum Circuits for General Phase Estimation

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Physical Review Letters 2007年第9期98卷 090501-090501页

作者： Wim van Dam G. Mauro D’Ariano Artur Ekert Chiara Macchiavello Michele Mosca Departments of Computer Science and Physics University of California Santa Barbara Santa Barbara California 93106-5110 USA Dipartimento di Fisica “A. Volta" and CNISM via Bassi 6 27100 Pavia Italy Mathematical Institute University of Oxford 24-29 St. Giles’ Oxford OX1 3LB United Kingdom and Department of Physics National University of Singapore 2 Science Drive 3 Singapore 117542 Institute for Quantum Computing University of Waterloo N2L 3G1 Waterloo ON Canada St. Jerome’s University N2L 3G3 Waterloo ON Canada and Perimeter Institute for Theoretical Physics N2L 2Y5 Waterloo ON Canada

We address the problem of estimating the phase ϕ given N copies of the phase-rotation gate uϕ. We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a general measurement. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate ϕ˜ for ϕ depends only on the difference ϕ˜−ϕ, the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.

关键词： quantum theory

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Integrated simulations for imploded core heating in fast ignition

Integrated simulations for imploded core heating in fast ign...

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33rd European Physical Society Conference on Plasma Physics 2006, EPS 2006

作者： Johzaki, T. Nagatomo, H. Sakagami, H. Nakamura, T. Mima, K. Nakao, Y. Institute of Laser Engineering Osaka University Osaka 565-0871 Japan Theory and Computer Simulation Center National Institute for Fusion Science Toki 509-5292 Japan Department of Applied Quantum Physics and Nuclear Engineering Kyushu University Fukuoka 812-8581 Japan

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Parallelism for quantum computation with qudits

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Physical Review A 2006年第3期74卷 032334-032334页

作者： Dianne P. O’Leary Gavin K. Brennen Stephen S. Bullock Department of Computer Science and Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 USA and Mathematical and Computational Sciences Division National Institute of Standards and Technology Gaithersburg Maryland 20899 USA IDA Center for Computing Sciences 17100 Science Drive Bowie Maryland 20715-4300 USA Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences A-6020 Innsbruck Austria

Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high-fidelity two-qudit gates. We first describe how to implement parallel single-qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth (time) of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the alkali-metal atoms Rb87 and Cs133. Second, we provide a protocol for implementing parallelized nonlocal two-qudit gates using the assistance of entangled qubit pairs. Using known protocols for qubit entanglement purification, this offers the possibility of high-fidelity two-qudit gates.

关键词： computerS SYSTEMS STATE

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Binary Projective Measurement via Linear Optics and Photon Counting

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Physical Review Letters 2006年第4期97卷 040502-040502页

作者： Masahiro Takeoka Masahide Sasaki Norbert Lütkenhaus Quantum Information Technology Group National Institute of Information and Communications Technology (NICT) 4-2-1 Nukui-kitamachi Koganei Tokyo 184-8795 Japan CREST Japan Science and Technology Agency 1-9-9 Yaesu Chuoh-ku Tokyo 103-0028 Japan Quantum Information Theory Group Institute of Theoretical Physics Universität Erlangen-Nürnberg 91058 Erlangen Germany Institute for Quantum Computing University of Waterloo 200 University Avenue West Waterloo Ontario N2L 3G1 Canada

We investigate the implementation of binary projective measurements with linear optics. This problem can be viewed as a single-shot discrimination of two orthogonal pure quantum states. We show that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. The statement holds in the asymptotic limit of a large number of these physical resources.

关键词： quantum theory

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