equivalence check
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2010 ◽  
Vol 76 (5) ◽  
pp. 283-301 ◽  
Author(s):  
Christophe Calvès ◽  
Maribel Fernández
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2010 ◽  
Vol 08 (05) ◽  
pp. 807-819
Author(s):  
YU TANAKA

To understand quantum gate array complexity, we define a problem named exact non-identity check, which is a decision problem to determine whether a given classical description of a quantum circuit is strictly equivalent to the identity or not. We show that the computational complexity of this problem is non-deterministic quantum polynomial-time (NQP)-complete. As corollaries, it is derived that exact non-equivalence check of two given classical descriptions of quantum circuits is also NQP-complete and that minimizing the number of quantum gates for a given quantum circuit without changing the implemented unitary operation is NQP-hard.


2005 ◽  
Vol 03 (03) ◽  
pp. 463-473 ◽  
Author(s):  
DOMINIK JANZING ◽  
PAWEL WOCJAN ◽  
THOMAS BETH

We describe a computational problem that is complete for the complexity class QMA, a quantum generalization of NP. It arises as a natural question in quantum computing and quantum physics. "Non-identity-check" is the following decision problem: Given a classical description of a quantum circuit (a sequence of elementary gates), 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 "non-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 non-equivalence check is also in QMA and hence QMA-complete.


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