Fast classical simulation of Hamiltonian dynamics by simultaneous diagonalization using Clifford transformation with parallel computation

• DOI: 10.1016/j.cpc.2023.108720
• Publication Date: 2023-03-07T21:21:31Z
• Authors: Yoshiaki Kawase; Keisuke Fujii
• Keywords: Hamiltonian (control theory)

Simulating quantum many-body dynamics is important both for fundamental understanding of physics and practical applications information processing. Therefore, classical simulation methods have been developed so far. Specifically, the Trotter-Suzuki decomposition can analyze a highly complex dynamics, if number qubits sufficiently small that main memory store state vector. However, via requires huge steps, each which accesses vector, hence time becomes impractically long. To settle this issue, we propose technique to accelerate simultaneous diagonalization mutually commuting Pauli groups, also attracting lot attention reduce measurement overheads in algorithms. We group Hamiltonian into commputing strings, them are diagonalized computational basis Clifford transformation. Since diagonal operators applied on vector simultaneously with minimum access, method successfully use performance parallel processors such as Graphics Processing Units (GPU). Compared an implementation using one fastest simulators computers, numerical experiments shown our provides few tens times acceleration.