Exposing a Fatal Flaw in Sample-based Quantum Diagonalization Methods

• URL: http://arxiv.org/abs/2501.07231v2
• Date: Fri, 21 Feb 2025 08:32:41 GMT
• Title: Exposing a Fatal Flaw in Sample-based Quantum Diagonalization Methods
• Authors: Peter Reinholdt, Karl Michael Ziems, Erik Rosendahl Kjellgren, Sonia Coriani, Stephan P. A. Sauer, Jacob Kongsted,
• Abstract summary: We show that QSCI methods face fundamental limitations that severely hinder their practical applicability in chemistry.<n>We demonstrate that while QSCI can, in principle, yield high-quality CI expansions, the method struggles with inefficiencies in finding new determinants.<n>This ultimately hinders utility in quantum chemistry applications as QSCI falls behind more efficient classical counterparts.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Schr\"odinger equation with quantum computers. In this work, we show that QSCI methods face fundamental 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 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 fatal flaw in QSCI methods 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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