Superconducting Qubit Circuit Simulation: A Quantum Monte Carlo Approach

Simulating large-scale superconducting quantum circuits remains challenging due to the exponential scaling of the Hilbert space dimension with qubit number. We introduce a real-time stochastic approach using Quantum Monte Carlo (QMC) to simulate open quantum systems coupled to infinite-dimensional baths. Our method exploits the pseudo-sparsity of the density matrix in the computational basis—a feature enhanced by noise—to achieve unbiased stochastic compression and operate within an effective Hilbert space orders of magnitude smaller than 4^N_qubit. We demonstrate our method's capabilities by focusing on superconducting transmon qubit implementations, simulating multiple paradigmatic circuits with different entanglement characteristics, including crosstalk suppression using dynamical decoupling and GHZ state preparations. Theoretical analysis and comparison with exact master equation solutions demonstrate that our QMC method is statistically exact. Furthermore, benchmarking against state-of-the-art quantum trajectory methods shows that QMC offers orders of magnitude improvement in both computational time and memory overhead for large systems (over 16 qubits). Our method enables large-scale, unbiased simulations of noisy quantum circuits, providing an efficient tool for hardware and algorithm development in superconducting quantum computing.