Exponential quantum speedups in quantum chemistry with linear depth

• URL: http://arxiv.org/abs/2503.21041v1
• Date: Wed, 26 Mar 2025 23:15:32 GMT
• Title: Exponential quantum speedups in quantum chemistry with linear depth
• Authors: Oskar Leimkuhler, K. Birgitta Whaley,
• Abstract summary: We prove a connection to particle number conserving matchgate circuits with fermionic magic state inputs.<n>We apply this result to quantum multi-reference methods designed for near-term quantum hardware.<n>We discuss the implications for achieving exponential quantum advantage in quantum chemistry on near-term hardware.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove classical simulation hardness, under the generalized $\mathsf{P}\neq\mathsf{NP}$ 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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