Riemannian quantum circuit optimization for Hamiltonian simulation

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.

arXiv comment10 pages, 7 figures

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Cited by in corpus (8)

• Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120 Qubits
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Riemannian quantum circuit optimization based on matrix product operators
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• A Riemannian Approach to the Lindbladian Dynamics of a Locally Purified Tensor Network
• Phase Estimation with Compressed Controlled Time Evolution
• Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering