Fast equivalence checking of quantum circuits of Clifford gates

• URL: http://arxiv.org/abs/2308.01206v1
• Date: Wed, 2 Aug 2023 15:10:48 GMT
• Title: Fast equivalence checking of quantum circuits of Clifford gates
• Authors: Dimitrios Thanos, Tim Coopmans, Alfons Laarman
• Abstract summary: checking whether two quantum circuits are equivalent is important for the design and optimization of quantum-computer applications with real-world devices. We consider quantum circuits consisting of Clifford gates, a practically-relevant subset of all quantum operations which is large enough to exhibit quantum features such as entanglement. We present a deterministic algorithm that is based on a folklore mathematical result and demonstrate that it is capable of outperforming previously considered state-of-the-art method.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Checking whether two quantum circuits are equivalent is important for the design and optimization of quantum-computer applications with real-world devices. We consider quantum circuits consisting of Clifford gates, a practically-relevant subset of all quantum operations which is large enough to exhibit quantum features such as entanglement and forms the basis of, for example, quantum-error correction and many quantum-network applications. We present a deterministic algorithm that is based on a folklore mathematical result and demonstrate that it is capable of outperforming previously considered state-of-the-art method. In particular, given two Clifford circuits as sequences of single- and two-qubit Clifford gates, the algorithm checks their equivalence in $O(n \cdot m)$ time in the number of qubits $n$ and number of elementary Clifford gates $m$. Using the performant Stim simulator as backend, our implementation checks equivalence of quantum circuits with 1000 qubits (and a circuit depth of 10.000 gates) in $\sim$22 seconds and circuits with 100.000 qubits (depth 10) in $\sim$15 minutes, outperforming the existing SAT-based and path-integral based approaches by orders of magnitude. This approach shows that the correctness of application-relevant subsets of quantum operations can be verified up to large circuits in practice.

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