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QCMA hardness of ground space connectivity for commuting Hamiltonians

Gosset, David and Mehta, Jenish C. and Vidick, Thomas (2017) QCMA hardness of ground space connectivity for commuting Hamiltonians. Quantum, 1 . p. 16. ISSN 2521-327X. doi:10.22331/q-2017-07-14-16.

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In this work we consider the ground space connectivity problem for commuting local Hamiltonians. The ground space connectivity problem asks whether it is possible to go from one (efficiently preparable) state to another by applying a polynomial length sequence of 2-qubit unitaries while remaining at all times in a state with low energy for a given Hamiltonian H. It was shown in [Gharibian and Sikora, ICALP15] that this problem is QCMA-complete for general local Hamiltonians, where QCMA is defined as QMA with a classical witness and BQP verifier. Here we show that the commuting version of the problem is also QCMA-complete. This provides one of the first examples where commuting local Hamiltonians exhibit complexity theoretic hardness equivalent to general local Hamiltonians.

Item Type:Article
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Vidick, Thomas0000-0002-6405-365X
Additional Information:This paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. T.V. is supported by NSF CAREER grant CCF-1553477 and an AFOSR YIP award number FA9550-16-1-0495. All authors were partially supported by the IQIM, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028).
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0495
Gordon and Betty Moore Foundation12500028
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Record Number:CaltechAUTHORS:20171011-112512941
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:82282
Deposited By: Joy Painter
Deposited On:11 Oct 2017 18:41
Last Modified:15 Nov 2021 19:49

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