Riemannian quantum circuit optimization for Hamiltonian simulation

Ayse Kotil, Rahul Banerjee, Qunsheng Huang, Christian B. Mendl

Research output: Contribution to journalArticlepeer-review


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 algorithm.

Original languageEnglish
Article number135303
JournalJournal of Physics A: Mathematical and Theoretical
Issue number13
StatePublished - 29 Mar 2024


  • Riemannian optimization
  • Trotterization
  • quantum circuit optimization
  • quantum simulation


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