Sample-based quantum diagonalization for electronic structure on quantum-centric supercomputers
Abstract
Electronic structure (ES) calculations are an anticipated application for quantum computers, offering both practical and challenging use cases around the 100-qubit scale. With quantum processors now having more than 150 qubits, this appears promising. However, until recently, ES calculations on quantum computers were confined to low qubit and gate counts, limiting their applicability to current-generation devices. The emergence of quantum-centric supercomputing (QCSC) architectures [1], which integrate quantum and classical computing as co-processors, has recently extended the scale of ES calculations on present-day quantum devices to 77 qubits and 3,590 two-qubit gates [2].
This talk presents the sample-based quantum diagonalization (SQD) method, which has made larger-scale simulations possible. SQD is a form of selected configuration interaction in which a quantum circuit is used to read out Slater determinants [2-4]. An error mitigation at the level of individual samples ensures the conservation of molecular symmetries, and the Schrödinger equation is projected onto the subspace spanned by the readout and mitigated determinants before being solved classically. We will (i) introduce SQD in the context of ES methods for classical and quantum computers, (ii) describe the quantum circuits used to read out determinants, (iii) discuss the error mitigation approach, and (iv) present results on the dissociation of N2 and the ground state of [2Fe–2S] and [4Fe–4S] clusters [5], obtained using an IBM Heron device in conjunction with the Fugaku supercomputer.
This study expands the reach of quantum computation for ES, to active spaces with more electrons and orbitals than exact diagonalization can tackle. It offers new insights and opportunities into using QCSC algorithms and architectures to study more challenging and practical ES use cases.
[1] Y. Alexeev et al, Fut. Gen. Comp. Sys 160, 666-710 (2024) [2] J. Robledo Moreno et al, arXiv:2405.05068 (2024) [3] K. Kanno et al, arXiv:2302.11320 (2023) [4] J. Yu et al, arXiv:2501.09702 (2025) [5] S. Sharma et al, Nat. Chem 6, 927-933 (2014)