Fast reconstruction algorithm based on HMC sampling

In Noisy Intermediate-Scale Quantum (NISQ) era, the scarcity of qubit resources has prevented many quantum algorithms from being implemented on quantum devices. Circuit cutting technology has greatly alleviated this problem, which allows us to run larger quantum circuits on real quantum machines with currently limited qubit resources at the cost of additional classical overhead. However, the classical overhead of circuit cutting grows exponentially with the number of cuts and qubits, and the excessive postprocessing overhead makes it difficult to apply circuit cutting to large scale circuits. In this paper, we propose a fast reconstruction algorithm based on Hamiltonian Monte Carlo (HMC) sampling, which samples the high probability solutions by Hamiltonian dynamics from state space with dimension growing exponentially with qubit. Our algorithm avoids excessive computation when reconstructing the original circuit probability distribution, and greatly reduces the circuit cutting post-processing overhead. The improvement is crucial for expanding of circuit cutting to a larger scale on NISQ devices.