The Experts below are selected from a list of 29973 Experts worldwide ranked by ideXlab platform
Tomoyuki Morimae - One of the best experts on this subject based on the ideXlab platform.
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Finding resource states of measurement-based Quantum Computing is harder than Quantum Computing
Physical Review A, 2017Co-Authors: Tomoyuki MorimaeAbstract:Measurement-based Quantum Computing enables universal Quantum Computing with only adaptive single-qubit measurements on certain many-qubit states, such as the graph state, the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, and several tensor-network states. Finding new resource states of measurement-based Quantum Computing is a hard task, since for a given state there are exponentially many possible measurement patterns on the state. In this paper, we consider the problem of deciding, for a given state and a set of unitary operators, whether there exists a way of measurement-based Quantum Computing on the state that can realize all unitaries in the set, or not. We show that the decision problem is QCMA-hard, which means that finding new resource states of measurement-based Quantum Computing is harder than Quantum Computing itself (unless BQP is equal to QCMA). We also derive an upperbound of the decision problem: the problem is in a Quantum version of the second level of the polynomial hierarchy.
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Acausal measurement-based Quantum Computing
Physical Review A - Atomic Molecular and Optical Physics, 2014Co-Authors: Tomoyuki MorimaeAbstract:In the measurement-based Quantum Computing, there is a natural "causal cone" among qubits of the resource state, since the measurement angle on a qubit has to depend on previous measurement results in order to correct the effect of byproduct operators. If we respect the no-signaling principle, byproduct operators cannot be avoided. In this paper, we study the possibility of acausal measurement-based Quantum Computing by using the process matrix framework [O. Oreshkov, F. Costa, and C. Brukner, Nature Communications {\bf3}, 1092 (2012)]. We construct a resource process matrix for acausal measurement-based Quantum Computing. The resource process matrix is an analog of the resource state of the causal measurement-based Quantum Computing. We find that the resource process matrix is (up to a normalization factor and trivial ancilla qubits) equivalent to the decorated graph state created from the graph state of the corresponding causal measurement-based Quantum Computing.
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Basics and applications of measurement-based Quantum Computing
2014 International Symposium on Information Theory and its Applications, 2014Co-Authors: Tomoyuki MorimaeAbstract:Measurement-based Quantum Computing is a new model of Quantum Computing proposed by Raussendorf and Briegel in 2001. The standard model of Quantum Computing, namely, the circuit model, starts with the product state, and Quantum gates are applied in order to create entanglement among qubits. The output state is measured only at the end of the Computing to read out the computation result. On the other hand, in the measurement-based model, universal Quantum Computing can be done with the preparation of a multipartite Quantum state and adaptive measurements on each qubit of it. It is shown that the computational power of the measurement-based Quantum Computing is equivalent to the circuit model. However, the measurement-based model has provided new points of view to deepen our understanding of Quantum Computing and to explore further relations between Quantum Computing and other fields of physics and information science. In fact, plenty of new results have been obtained about relations between the measurement-based Quantum Computing and, for example, graph theory, statistical physics, Quantum communication, Quantum cryptography, etc. It's inherent multipartiteness is also expected to be more suitable for multipartite information processing than the traditional circuit model. In this talk, we first review the basics of the measurement-based Quantum Computing, and next explain some recent applications of it to information theory, including acausal network, topological Quantum Computing, and secure cloud Quantum Computing.
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Verification for measurement-only blind Quantum Computing
arXiv: Quantum Physics, 2012Co-Authors: Tomoyuki MorimaeAbstract:Blind Quantum Computing is a new secure Quantum Computing protocol where a client who does not have any sophisticated Quantum technlogy can delegate her Quantum Computing to a server without leaking any privacy. It is known that a client who has only a measurement device can perform blind Quantum Computing [T. Morimae and K. Fujii, Phys. Rev. A {\bf87}, 050301(R) (2013)]. It has been an open problem whether the protocol can enjoy the verification, i.e., the ability of client to check the correctness of the Computing. In this paper, we propose a protocol of verification for the measurement-only blind Quantum Computing.
Jonathan A. Jones - One of the best experts on this subject based on the ideXlab platform.
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Quantum Computing with NMR
Progress in Nuclear Magnetic Resonance Spectroscopy, 2011Co-Authors: Jonathan A. JonesAbstract:A review of progress in NMR Quantum Computing and a brief survey of the literature
Samuel J. Lomonaco - One of the best experts on this subject based on the ideXlab platform.
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Extended topological Quantum Computing
Proceedings of SPIE, 2013Co-Authors: Louis H Kauffman, Samuel J. LomonacoAbstract:This paper gives an account of topological Quantum Computing based on unitary solutions to the Yang-Baxter Equation. We show how Quantum Computing with Majorana Fermions fits into this context.
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Topology and Quantum Computing
Lecture Notes in Physics, 2009Co-Authors: Louis H Kauffman, Samuel J. LomonacoAbstract:This chapter describes relationships between topology and Quantum Computing. It is fruitful to move back and forth between topological methods and the techniques of Quantum information theory.We sketch the background topology, discuss analogies (such as topological entanglement and Quantum entanglement), show direct correspondences between certain topological operators (solutions to the Yang-Baxter equation), and universal Quantum gates. We then describe the background for topological Quantum Computing in terms of Temperley-Lieb recoupling theory. This is a recoupling theory that generalizes standard angular momentum recoupling theory, generalizes the Penrose theory of spin networks and is inherently topological. Temperley-Lieb recoupling theory is based on the bracket polynomial model [2, 3] for the Jones polynomial. It is built in terms of diagrammatic combinatorial topology. The same structure can be explained in terms of the SU(2) q Quantum group and has relationships with functional integration and Witten's approach to topological Quantum field theory. Nevertheless, the approach given here will be unrelentingly elementary. Elementary, does not necessarily mean simple. In this case, an architecture is built from simple beginnings, and this architecture and its recoupling language can be applied to many things including, e.g., colored Jones polynomials, Witten-ReshetikhinTuraev invariants of three manifolds, topological Quantum field theory, and Quantum Computing.
Zhenghan Wang - One of the best experts on this subject based on the ideXlab platform.
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Mathematics of Topological Quantum Computing
arXiv:1705.06206 [cond-mat physics:math-ph physics:quant-ph], 2017Co-Authors: Eric C. Rowell, Zhenghan WangAbstract:In topological Quantum Computing, information is encoded in "knotted" Quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in Quantum Hall liquids by experiments to an accuracy of $10^{-10}$, and harnessed to stabilize Quantum memory. In this survey, we discuss the conceptual development of this interdisciplinary field at the juncture of mathematics, physics and computer science. Our focus is on Computing and physical motivations, basic mathematical notions and results, open problems and future directions related to and/or inspired by topological Quantum Computing.
Antonia Neels - One of the best experts on this subject based on the ideXlab platform.
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Adiabatic topological Quantum Computing
Physical Review A, 2015Co-Authors: Chris Cesare, Steven T. Flammia, Dave Bacon, David Bacon, Andrew J. Landahl, Antonia NeelsAbstract:Topological Quantum Computing promises error-resistant Quantum computation without active error correction. However, there is a worry that during the process of executing Quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded Quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev's surface codes and the more recently discovered color codes. We develop protocols that enable universal Quantum Computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computation size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic Quantum Computing with these topological Quantum Computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.
