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      Surface codes: Towards practical large-scale quantum computation

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          Abstract

          This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault-tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-NOT. We then describe the single-qubit Hadamard, S and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of appendices in which we provide supplementary information to the main text.

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          Most cited references 18

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          Many-Body Physics with Ultracold Gases

          This article reviews recent experimental and theoretical progress on many-body phenomena in dilute, ultracold gases. Its focus are effects beyond standard weak-coupling descriptions, like the Mott-Hubbard-transition in optical lattices, strongly interacting gases in one and two dimensions or lowest Landau level physics in quasi two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near Feshbach resonances in the BCS-BEC crossover.
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            Scheme for reducing decoherence in quantum computer memory.

             Sarit Shor,  Erez Shor (1995)
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              Fault-tolerant quantum computation by anyons

               A. Kitaev (1997)
              A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.
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                Author and article information

                Journal
                04 August 2012
                2012-10-26
                Article
                10.1103/PhysRevA.86.032324
                1208.0928

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Phys. Rev. A 86, 032324 (2012)
                54 pages, 35 figures, version incorporating referee and community feedback. Additional comments welcome
                quant-ph

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