身份检查已完成QMA
Identity check is QMA-complete
摘要：
我们定义问题的身份检查：给定一个量子线路的经典描述，确定它是否几乎等价于身份。明确地说，任务是决定相应的酉是否接近于关于算子范数的单位矩阵的复数倍。我们证明了这个问题是QMA完全的。这个问题的一个推广是等价性检验：给定量子线路的两种描述和一个公共不变子空间的描述，判断电路对这个子空间的约束是否几乎一致。我们表明，等价性检查也在QMA，因此QMA完全。
英文摘要：
We define the problem identity check: Given a classical description of a quantum circuit, determine whether it is almost equivalent to the identity. Explicitly, the task is to decide whether the corresponding unitary is close to a complex multiple of the identity matrix with respect to the operator norm. We show that this problem is QMA-complete. A generalization of this problem is equivalence check: Given two descriptions of quantum circuits and a description of a common invariant subspace, decide whether the restrictions of the circuits to this subspace almost coincide. We show that equivalence check is also in QMA and hence QMA-complete.
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