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      Circuit-Based Quantum Random Access Memory for Classical Data

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          Abstract

          A prerequisite for many quantum information processing tasks to truly surpass classical approaches is an efficient procedure to encode classical data in quantum superposition states. In this work, we present a circuit-based flip-flop quantum random access memory to construct a quantum database of classical information in a systematic and flexible way. For registering or updating classical data consisting of M entries, each represented by n bits, the method requires O( n) qubits and O( Mn) steps. With post-selection at an additional cost, our method can also store continuous data as probability amplitudes. As an example, we present a procedure to convert classical training data for a quantum supervised learning algorithm to a quantum state. Further improvements can be achieved by reducing the number of state preparation queries with the introduction of quantum forking.

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          Quantum Algorithm for Linear Systems of Equations

          Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b(-->), find a vector x(-->) such that Ax(-->) = b(-->). We consider the case where one does not need to know the solution x(-->) itself, but rather an approximation of the expectation value of some operator associated with x(-->), e.g., x(-->)(dagger) Mx(-->) for some matrix M. In this case, when A is sparse, N x N and has condition number kappa, the fastest known classical algorithms can find x(-->) and estimate x(-->)(dagger) Mx(-->) in time scaling roughly as N square root(kappa). Here, we exhibit a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa. Indeed, for small values of kappa [i.e., poly log(N)], we prove (using some common complexity-theoretic assumptions) that any classical algorithm for this problem generically requires exponentially more time than our quantum algorithm.
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            Elementary gates for quantum computation.

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              Quantum principal component analysis

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                Author and article information

                Contributors
                rhee.jk@kaist.edu
                Journal
                Sci Rep
                Sci Rep
                Scientific Reports
                Nature Publishing Group UK (London )
                2045-2322
                8 March 2019
                8 March 2019
                2019
                : 9
                : 3949
                Affiliations
                [1 ]ISNI 0000 0001 2292 0500, GRID grid.37172.30, School of Electrical Engineering, , KAIST, ; Daejeon, 34141 Republic of Korea
                [2 ]ISNI 0000 0001 2292 0500, GRID grid.37172.30, ITRC of Quantum Computing for AI, , KAIST, ; Daejeon, 34141 Republic of Korea
                [3 ]ISNI 0000 0001 0723 4123, GRID grid.16463.36, Quantum Research Group, School of Chemistry and Physics, , University of KwaZulu-Natal, ; Durban, 4000 South Africa
                [4 ]GRID grid.494663.a, National Institute for Theoretical Physics, ; KwaZulu-Natal Durban, 4000 South Africa
                Author information
                http://orcid.org/0000-0002-3177-4143
                Article
                40439
                10.1038/s41598-019-40439-3
                6408577
                30850658
                1d1a3c19-d622-43ec-9549-f4829391541a
                © The Author(s) 2019

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 5 October 2018
                : 11 February 2019
                Funding
                Funded by: FundRef https://doi.org/10.13039/501100003725, National Research Foundation of Korea (NRF);
                Award ID: 2016R1A5A1008184
                Award Recipient :
                Funded by: FundRef https://doi.org/10.13039/501100007108, Korea Advanced Institute of Science and Technology | KAIST Institute for IT Convergence (Korea Advanced Institute of Science and Technology, Institute for IT Convergence);
                Award ID: Science Technology Leading Primary Research Program
                Award ID: Science Technology Leading Primary Research Program
                Award Recipient :
                Funded by: Ministry of Science and ICT, Korea, ITRC support program. Grant Reference Number: IITP-2018-2018-0-01402.
                Funded by: FundRef https://doi.org/10.13039/501100001321, National Research Foundation (NRF);
                Funded by: South African Research Chair Initiative of the Department of Science and Technology
                Funded by: Ministry of Science and ICT, Korea, ITRC support program. Grant Reference Number: IITP-2018-2015-0-00385 and IITP-2018-2018-0-01402.
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