Testing Non-Isometry Is Qma-Complete

THEORY OF QUANTUM COMPUTATION, COMMUNICATION, AND CRYPTOGRAPHY（2011）

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摘要

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.

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关键词

quantum channel,quantum circuit,verifiable quantum computation,linear isometry,complexity class QMA,main idea,pure state,worst-case uncertainty,Testing non-isometry

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