Kavli Affiliate: Birgitta Whaley
| First 5 Authors: Oskar Leimkuhler, K. Birgitta Whaley, , ,
| Summary:
We prove classical simulation hardness, under the generalized
$mathsf{P}neqmathsf{NP}$ conjecture, for quantum circuit families with
applications in near-term quantum chemical ground state estimation. The proof
exploits a connection to particle number conserving matchgate circuits with
fermionic magic state inputs, which are shown to be universal for quantum
computation under post-selection, and are therefore not classically simulable
in the worst case, in either the strong (multiplicative) or weak (sampling)
sense. We apply this result to quantum multi-reference methods designed for
near-term quantum hardware by ruling out certain dequantization strategies for
computing the off-diagonal matrix elements. We demonstrate these quantum
speedups for two choices of reference state that incorporate both static and
dynamic correlations to model the electronic eigenstates of molecular systems:
orbital-rotated matrix product states, which are preparable in linear depth,
and unitary coupled-cluster with single and double excitations. In each case we
discuss the implications for achieving exponential quantum advantage in quantum
chemistry on near-term hardware.
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