Riemannian quantum circuit optimization for Hamiltonian simulation
arXiv:2212.07556 · doi:10.1088/1751-8121/ad2d6e
Abstract
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful approximation can lead to relatively deep circuits. Here we start from the insight that for translation invariant systems, the gates in such circuit topologies can be further optimized on classical computers to decrease the circuit depth and/or increase the accuracy. We employ tensor network techniques and devise a method based on the Riemannian trust-region algorithm on the unitary matrix manifold for this purpose. For the Ising and Heisenberg models on a one-dimensional lattice, we achieve orders of magnitude accuracy improvements compared to fourth-order splitting methods. The optimized circuits could also be of practical use for the time-evolving block decimation (TEBD) algorithm.
10 pages, 7 figures
References in corpus (4)
Cited by in corpus (8)
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- A Riemannian Approach to the Lindbladian Dynamics of a Locally Purified Tensor Network
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- Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering