Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published July 14, 2017 | Published
Journal Article Open

QCMA hardness of ground space connectivity for commuting Hamiltonians

Abstract

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.

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).

Attached Files

Published - 1610.03582v2.pdf

Files

1610.03582v2.pdf
Files (521.2 kB)
Name Size Download all
md5:0cf2411d40a0d254ee7093086d3a07a0
521.2 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 17, 2023