Approximation Methods for Simulation and Equivalence Checking of Noisy Quantum Circuits

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Abstract
In the current noisy intermediate-scale quantum (NISQ) era, simulating and verifying noisy quantum circuits is crucial but faces challenges such as quantum state explosion and complex noise representations, constraining simulation and equivalence checking to circuits with a limited number of qubits. This article introduces an approximation algorithm for simulating and assessing the equivalence of noisy quantum circuits, specifically designed to improve scalability under low-noise conditions. The approach utilizes a novel tensor network (TN) diagram combined with singular value decomposition to approximate the tensors of quantum noises. The implementation is based on Google’s TensorNetwork Python package for contraction. Experimental results on realistic quantum circuits with realistic hardware noise models indicate that our algorithm can simulate and check the equivalence of quantum approximate optimization algorithm (QAOA) circuits with around 200 qubits and 20 noise operators, outperforming state-of-the-art approaches in scalability and speed.
Funding Information
  • Innovation Program for Quantum Science and Technology (2024ZD0300500)
  • Youth Innovation Promotion Association of the Chinese Academy of Sciences (2023116)
  • National Natural Science Foundation of China (62402485)
  • National Natural Science Foundation of China

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