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Critical limitations in quantum-selected configuration interaction methods

Critical limitations in quantum-selected configuration interaction methods
Critical limitations in quantum-selected configuration interaction methods

Quantum Selected Configuration Interaction (QSCI) methods (also known as Sample-based Quantum Diagonalization, SQD) have emerged as promising near-term approaches to solving the electronic Schrödinger equation with quantum computers. In this work, we perform numerical analysis to show that QSCI methods face critical limitations that severely hinder their practical applicability in chemistry. Using the nitrogen molecule and the iron-sulfur cluster [2Fe-2S] as examples, we demonstrate that while QSCI can, in principle, yield high-quality configuration interaction (CI) expansions similar to classical SCI heuristics in some cases, the method struggles with inefficiencies in finding new determinants as sampling repeatedly selects already seen configurations. This inefficiency becomes especially pronounced when targeting high-accuracy results or sampling from an approximate ansatz. In cases where the sampling problem is not present, the resulting CI expansions are less compact than those generated from classical heuristics, rendering QSCI an overall more expensive method. Our findings suggest a significant drawback in QSCI methods when sampling from the ground-state distribution as the inescapable trade-off between finding sufficiently many determinants and generating compact, accurate CI expansions. This ultimately hinders utility in quantum chemistry applications, as QSCI falls behind more efficient classical counterparts.

1549-9618
6811-6822
Reinholdt, Peter
ddb08ed1-8804-437d-816d-d9e7ee558022
Ziems, Karl Michael
6d346238-2471-47c7-b89f-590059caf037
Kjellgren, Erik Rosendahl
c05eb9d4-e87e-43da-800a-1828d8d7f95f
Coriani, Sonia
a1d68d22-6db5-4c02-9971-097ff3f7bc71
Sauer, Stephan P.A.
7a0e1312-165e-4670-ac1c-a0f3541e4181
Kongsted, Jacob
460ce016-8491-4084-8934-a439c16105c5
Reinholdt, Peter
ddb08ed1-8804-437d-816d-d9e7ee558022
Ziems, Karl Michael
6d346238-2471-47c7-b89f-590059caf037
Kjellgren, Erik Rosendahl
c05eb9d4-e87e-43da-800a-1828d8d7f95f
Coriani, Sonia
a1d68d22-6db5-4c02-9971-097ff3f7bc71
Sauer, Stephan P.A.
7a0e1312-165e-4670-ac1c-a0f3541e4181
Kongsted, Jacob
460ce016-8491-4084-8934-a439c16105c5

Reinholdt, Peter, Ziems, Karl Michael, Kjellgren, Erik Rosendahl, Coriani, Sonia, Sauer, Stephan P.A. and Kongsted, Jacob (2025) Critical limitations in quantum-selected configuration interaction methods. Journal of Chemical Theory and Computation, 21 (14), 6811-6822. (doi:10.1021/acs.jctc.5c00375).

Record type: Article

Abstract

Quantum Selected Configuration Interaction (QSCI) methods (also known as Sample-based Quantum Diagonalization, SQD) have emerged as promising near-term approaches to solving the electronic Schrödinger equation with quantum computers. In this work, we perform numerical analysis to show that QSCI methods face critical limitations that severely hinder their practical applicability in chemistry. Using the nitrogen molecule and the iron-sulfur cluster [2Fe-2S] as examples, we demonstrate that while QSCI can, in principle, yield high-quality configuration interaction (CI) expansions similar to classical SCI heuristics in some cases, the method struggles with inefficiencies in finding new determinants as sampling repeatedly selects already seen configurations. This inefficiency becomes especially pronounced when targeting high-accuracy results or sampling from an approximate ansatz. In cases where the sampling problem is not present, the resulting CI expansions are less compact than those generated from classical heuristics, rendering QSCI an overall more expensive method. Our findings suggest a significant drawback in QSCI methods when sampling from the ground-state distribution as the inescapable trade-off between finding sufficiently many determinants and generating compact, accurate CI expansions. This ultimately hinders utility in quantum chemistry applications, as QSCI falls behind more efficient classical counterparts.

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QSCI_paper - Accepted Manuscript
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More information

Accepted/In Press date: 16 June 2025
e-pub ahead of print date: 30 June 2025
Published date: 22 July 2025

Identifiers

Local EPrints ID: 504166
URI: http://eprints.soton.ac.uk/id/eprint/504166
ISSN: 1549-9618
PURE UUID: ee223420-29d5-4780-9231-c169f945f4ff
ORCID for Karl Michael Ziems: ORCID iD orcid.org/0000-0001-5369-7778

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Date deposited: 28 Aug 2025 16:40
Last modified: 29 Aug 2025 02:18

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Contributors

Author: Peter Reinholdt
Author: Karl Michael Ziems ORCID iD
Author: Erik Rosendahl Kjellgren
Author: Sonia Coriani
Author: Stephan P.A. Sauer
Author: Jacob Kongsted

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