05 05 0 v 1 9 M ay 2 00 3 “ Identity check ” is QMA - complete
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چکیده
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. 1 Stating the problem “equivalence check” So far there is only one QMA-complete problem known, namely the 3-local Hamiltonian problem [1, 2, 3]. Here we give another example that occurs naturally in the problem of constructing quantum networks from elementary gates: Let U be a quantum network acting on n qubits that consists of two-qubit gates
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تاریخ انتشار 1996