Testing non-isometry is QMA-complete

Authors:
Bill Rosgen
Affiliations:
Centre for Quantum Technologies, National University of Singapore
Venue:
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
Year:
2010

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Abstract

Determining the worst-case uncertainty added by a quantum circuit is shown to be computationally intractable. This is the problem of detecting when a quantum channel implemented as a circuit is close to a linear isometry, and it is shown to be complete for the complexity class QMA of verifiable quantum computation. The main idea is to relate the problem of detecting when a channel is close to an isometry to the problem of determining how mixed the output of the channel can be when the input is a pure state.