Abstract
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. We compare this algorithm to previous algorithms for short evolution times and discuss potential further improvements.
| Original language | English |
|---|---|
| Article number | L031306 |
| Journal | Physical Review C |
| Volume | 108 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2023 |
Funding
We thank C. W. Johnson and R. Weiss for the feedback on the manuscript. A.B. thanks Y. Subasi, A. Roggero, E. Dumitrescu, Y. Wang, T. Morris for discussions regarding the LCU-like algorithms for state preparation. This work was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. 89233218CNA000001, and Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. I.S. and J.C. gratefully acknowledge partial support by the Advanced Simulation and Computing (ASC) Program. A.B.'s work is supported by the U.S. Department of Energy, Office of Science, Nuclear Physics Quantum Horizons initiative. This work was partially funded by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Program Office under FWP ERKJ382. J.C. and A.B. also acknowledge the Quantum Science Center for partial support of their work on this project.