Near-Term Quantum Algorithms

11:30 am – 2:30 pm, Tuesday March 18 // Session MAR-G34 //Anaheim Convention Center, 256A (Level 2)

Chair:: Kostyantyn Kechedzhi, Google LLC
Topics:
Sponsored by: DQI

Rapid initial state preparation for the quantum simulation of strongly correlated molecules

12:42 pm – 1:18 pm

Presenter: Dominic W Berry (Macquarie University)

Authors: Yu Tong (Caltech), Tanuj Khattar (Google), Alec White (Quantum Simulation Technologies Inc), Tae In Kim (Seoul National University), Guang Hao Low (Google), Sergio Boixo (Google LLC), Lin Lin (University of California, Berkeley), Seunghoon Lee (Seoul National University), Garnet Chan (Caltech), Ryan Babbush (Google LLC), Nicholas Rubin (Google)

Much research in quantum simulation has focused on the estimation of ground state energies, but assuming that the ground state has been prepared. In reality, it is a major challenge to prepare the approximate ground state, and to perform the energy estimation in a way that accounts for the imperfect preparation. In this work we solve that problem, showing how to prepare and sample these initial states in a way that only modestly increases the overall complexity. We do this in three ways.

First, we develop a new way of preparing matrix product states (MPS). We derive a method of implementing general unitary operations with a cost about 7 times less than that in prior work. This method of implementing unitary operations is then used to derive a scheme for preparing MPSs, by using a sequence of unitary operations, with a substantial speedup over prior work.

Second, we provide methods to effectively sample from the output of phase estimation seeded with low and high overlap initial states. Ideally one would perform many samples, and take the lowest sample as the estimate of the ground state energy. That can yield large error, because any sample with large error could incorrectly be taken as the estimate. To solve this problem, we use the theory of window functions to minimise the error and thereby provide the best complexity. In the case where there is low overlap between the prepared state and the ground state, we show how to provide even better performance by a binary search approach.

Third, we use extrapolation to perform numerical estimates of the overlap provided by MPS approximations to the ground state for Fe-S cluster systems that are challenging to compute classically. We show that a large overlap ~0.9 can be obtained with bond dimension 4000. As a result, the MPS preparation cost is a modest contribution to the overall complexity, and the high overlap means that only two samples are needed with our techniques. The overall complexity is then comparable to that obtained with the assumption of a perfect initial state.

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