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  • 1
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    Improved Classical Simulation of Quantum Circuits Dominated by Clifford Gates (2016)
    American Physical Society (APS)
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    Publication Date: 2016-06-21
    Description: Author(s): Sergey Bravyi and David Gosset We present a new algorithm for classical simulation of quantum circuits over the Clifford + T gate set. The runtime of the algorithm is polynomial in the number of qubits and the number of Clifford gates in the circuit but exponential in the number of T gates. The exponential scaling is sufficiently m… [Phys. Rev. Lett. 116, 250501] Published Mon Jun 20, 2016
    Keywords: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society (APS)
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  • 2
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    Gapped and gapless phases of frustration-free spin-12 chains (2015)
    American Institute of Physics (AIP)
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    Publication Date: 2015-06-19
    Description: We consider a family of translation-invariant quantum spin chains with nearest-neighbor interactions and derive necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit. More precisely, let ψ be an arbitrary two-qubit state. We consider a chain of n qubits with open boundary conditions and Hamiltonian H n ( ψ ) which is defined as the sum of rank-1 projectors onto ψ applied to consecutive pairs of qubits. We show that the spectral gap of H n ( ψ ) is upper bounded by 1/( n − 1) if the eigenvalues of a certain 2 × 2 matrix simply related to ψ have equal non-zero absolute value. Otherwise, the spectral gap is lower bounded by a positive constant independent of n (depending only on ψ ). A key ingredient in the proof is a new operator inequality for the ground space projector which expresses a monotonicity under the partial trace. This monotonicity property appears to be very general and might be interesting in its own right. As an extension of our main result, we obtain a complete classification of gapped and gapless phases of frustration-free translation-invariant spin-1/2 chains with nearest-neighbor interactions.
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics (AIP)
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  • 3
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    Polynomial-Time Classical Simulation of Quantum Ferromagnets (2017)
    American Physical Society (APS)
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    Publication Date: 2017-09-09
    Description: Author(s): Sergey Bravyi and David Gosset We consider a family of quantum spin systems which includes, as special cases, the ferromagnetic X Y model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any model in this family can be efficiently approximated to a giv... [Phys. Rev. Lett. 119, 100503] Published Fri Sep 08, 2017
    Keywords: General Physics: Statistical and Quantum Mechanics, Quantum Information, etc.
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society (APS)
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