Southwest Quantum Information and Technology

When is better ground state preparation worthwhile on a quantum computer?When is better ground state preparation worthwhile on a quantum computer?

Presenting Author: Shivesh Pathak, Sandia National Laboratories
Contributing Author(s): Antonio Russo, Stefan Seritan, Andrew Baczewski

An important application for quantum simulation is the accurate and efficient evaluation of ground state energies. One approach is to construct an approximate ground state wave function, and then repeatedly apply quantum phase estimation (QPE) to sample from the energy eigenspectrum of the associated Hamiltonian. The number of repetitions required to observe the ground state eigenvalue will be inversely proportional to the overlap with the exact ground state. As such, higher quality ground state approximations will require fewer applications of QPE. This suggests a tradeoff between improving state preparation and simply repeating QPE. So, when is it worthwhile to invest in better state preparation to increase the efficiency of computing ground state energies? To answer this question, we provide resource estimates for accurately computing ground state energies with and without a layer of sophisticated state preparation. To this end, we analyze the filter-based state preparation technique proposed in Lin and Tong’s “Near-optimal ground state preparation,” providing a new error analysis and additional implementation details. Our asymptotic analysis, as well as explicit T-counts for the transverse field Ising and first-quantized electronic structure Hamiltonians, indicate that state preparation yields a consistent near-quadratic improvement for large system sizes and high target accuracies. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

(Session 5 : Thursday from 5:00 pm - 7:00 pm)