NISQ algorithm for the matrix elements of a generic observable

Journal Article · 29 October 2023 · SciPost Physics

DOI: https://doi.org/10.21468/SciPostPhys.15.4.180 · OSTI ID:2204078

Erbanni, Rebecca ^[1]; Bharti, Kishor ^[2]; Kwek, Leong-Chuan ^[3]; Poletti, Dario ^[4]

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1. Singapore University of Technology and Design
2. University of Maryland, College Park
3. Nanyang Technological University, National University of Singapore, UMI MajuLab
4. Abdus Salam International Centre for Theoretical Physics, Singapore University of Technology and Design, UMI MajuLab

The calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian without explicitly preparing its eigenstates. By means of numerical simulations we show that this approach finds many of the matrix elements for the one and two qubits cases. Specifically, while in the first case, one can initialize the ansatz parameters over a broad interval, in the latter the optimization landscape can significantly slow down the speed of convergence and one should therefore be careful to restrict the initialization to a smaller range of parameters.

• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: SC0019040; SC0020312; SC0019449
• OSTI ID: 2204078
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 4 Vol. 15; ISSN 2542-4653
• Publisher: Stichting SciPostCopyright Statement
• Country of Publication: Netherlands
• Language: English