2023/08/06 by Haijun Liao, Liao, Hai-Jun, Kang Wang +7 · 5 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2308.03082
openalex publication_date 2023/08/06 · openalex created_date 2023/08/09 · openalex updated_date 2026/07/28
We perform classical simulations of the 127-qubit kicked Ising model, which was recently emulated using a quantum circuit with error mitigation [Nature 618, 500 (2023)]. Our approach is based on the projected entangled pair operator (PEPO) in the Heisenberg picture. Its main feature is the ability to automatically identify the underlying low-rank and low-entanglement structures in the quantum circuit involving Clifford and near-Clifford gates. We assess our approach using the quantum circuit with 5+1 trotter steps which was previously considered beyond classical verification. We develop a Clifford expansion theory to compute exact expectation values and use them to evaluate algorithms. The results indicate that PEPO significantly outperforms existing methods, including the tensor network with belief propagation, the matrix product operator, and the Clifford perturbation theory, in both efficiency and accuracy. In particular, PEPO with bond dimension χ=2 already gives similar accuracy to the CPT with K=10 and MPO with bond dimension χ=1024. And PEPO with χ=184 provides exact results in 3 seconds using a single CPU. Furthermore, we apply our method to the circuit with 20 Trotter steps. We observe the monotonic and consistent convergence of the results with χ, allowing us to estimate the outcome with χ→∞ through extrapolations. We then compare the extrapolated results to those achieved in quantum hardware and with existing tensor network methods. Additionally, we discuss the potential usefulness of our approach in simulating quantum circuits, especially in scenarios involving near-Clifford circuits and quantum approximate optimization algorithms. Our approach is the first use of PEPO in solving the time evolution problem, and our results suggest it could be a powerful tool for exploring the dynamical properties of quantum many-body systems.