2003/05/09 by Janzing, Dominik, Wocjan, Pawel, Beth, Thomas · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.quant-ph/0305050
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.