Synthesizing efficient circuits for Hamiltonian simulation

Journal Article · 03 April 2023 · npj Quantum Information

DOI: https://doi.org/10.1038/s41534-023-00697-6 · OSTI ID:1968101

Mukhopadhyay, Priyanka ; Wiebe, Nathan; Zhang, Hong Tao

Abstract We provide an approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations. The total number of gates, especially CNOT, reduce in many cases. We show that it is possible to implement an exponentiated sum of commuting Paulis with at most m (controlled)-rotation gates, where m is the number of distinct non-zero eigenvalues (ignoring sign). Thus we can collect mutually commuting Hamiltonian terms into groups satisfying one of several symmetries identified in this work. This allows an inexpensive simulation of the entire group of terms. We further show that the cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings.

• Sponsoring Organization: USDOE
• OSTI ID: 1968101
• Journal Information: npj Quantum Information, Journal Name: npj Quantum Information Journal Issue: 1 Vol. 9; ISSN 2056-6387
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United Kingdom
• Language: English