Rapid Initial-State Preparation for the Quantum Simulation of Strongly Correlated Molecules

<p> Studies on quantum algorithms for ground-state energy estimation often assume perfect ground-state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here, we address that problem in two ways: by faster preparation of matrix-product-state (MPS) approximations and by more efficient filtering of the prepared state to find the ground-state energy. We show how to achieve unitary synthesis with a Toffoli complexity about <math display='inline'> <mn>7</mn> <mo>×</mo> </math> lower than that in prior work and use that to derive a more efficient MPS-preparation method. For filtering, we present two different approaches: sampling and binary search. For both, we use the theory of window functions to avoid large phase errors and minimize the complexity. We find that the binary-search approach provides better scaling with the overlap at the cost of a larger constant factor, such that it will be preferred for overlaps less than about <math display='inline'> <mn>0.003</mn> </math> . Finally, we estimate the total resources to perform ground-state energy estimation of <math display='inline'> <mi>Fe</mi> </math> - <math display='inline'> <mrow> <mrow> <mi mathvariant='normal'>S</mi> </mrow> </mrow> </math> cluster systems, including the <math display='inline'> <mrow> <mi>Fe</mi> <mi>Mo</mi> </mrow> </math> cofactor by estimating the overlap of different MPS initial states with potential ground states of the <math display='inline'> <mrow> <mi>Fe</mi> <mi>Mo</mi> </mrow> </math> cofactor using an extrapolation procedure. With a modest MPS bond dimension of <math display='inline'> <mn>4000</mn> </math> , our procedure produces an estimate of approximately <math display='inline'> <mn>0.9</mn> </math> overlap squared with a candidate ground state of the <math display='inline'> <mrow> <mi>Fe</mi> <mi>Mo</mi> </mrow> </math> cofactor, producing a total resource estimate of <math. Authors: Berry, Dominic W. (ORCID:0000000334461449); Tong, Yu (ORCID:0000000275559373); Khattar, Tanuj (ORCID:0009000355453066); White, Alec (ORCID:0000000297431469); Kim, Tae In (ORCID:0000000236911688)