Projection algorithm for state preparation on quantum computers

Journal Article · 28 September 2023 · Physical Review. C

DOI: https://doi.org/10.1103/physrevc.108.l031306 · OSTI ID:2007360

Stetcu, I.  ^[1]; Baroni, A. ^[2]; Carlson, J. ^[1]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
2. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences (NCCS)

We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one additional auxiliary qubit. The total time evolved for an accurate solution is proportional to the ratio of the spectrum range of the trial state to the gap to the lowest excited state, a substantial improvement over other projection algorithms, and the accuracy increases exponentially with the time evolved. Isolating the quantum numbers is efficient because of the known eigenvalues and increases the gap thus shortening the propagation time required. The success rate of the algorithm, or the probability of producing the desired state, is a simple function of measurement times and phases and is dominated by the square overlap of the original state to the desired state. We present examples from the nuclear shell model and the Heisenberg model. In conclusion, we compare this algorithm to previous algorithms for short evolution times and discuss potential further improvements.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: 89233218CNA000001; AC05-00OR22725
• OSTI ID: 2007360
• Alternate ID(s): OSTI ID: 2217741
• Report Number(s): LA-UR--22-30149
• Journal Information: Physical Review. C, Journal Name: Physical Review. C Journal Issue: 3 Vol. 108; ISSN 2469-9985
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English