Closed-loop calculations of electronic structure on a quantum processor and a classical supercomputer at full scale

TL;DR

This work demonstrates a scalable quantum-classical approach to electronic-structure calculations by integrating a pre-fault-tolerant quantum processor with a classical supercomputer in a closed-loop workflow (SQD). A differential-evolution–driven optimization of LUCJ circuits, combined with a classical subspace diagonalization (Davidson) and a fermionic Gaussian unitary dressing, enables tackling 50e/36o and 54e/36o active spaces mapped to 72 qubits. On [2Fe-2S] and [4Fe-4S] iron-sulfur clusters, the method yields energies surpassing CCSD and approaching DMRG, with zero-variance extrapolations within ~0.12 Eh of DMRG, and demonstrates scalable resource management up to tens of thousands of classical nodes. This work highlights the viability and value of quantum-classical co-design at scale and outlines how improved quantum error rates could reduce classical resource demands while expanding applicability to challenging chemical problems.

Abstract

Quantum computers must operate in concert with classical computers to deliver on the promise of quantum advantage for practical problems. To achieve that, it is important to understand how quantum and classical computing can interact together, and how one can characterize the scalability and efficiency of hybrid quantum-classical workflows. So far, early experiments with quantum-centric supercomputing workflows have been limited in scale and complexity. Here, we use a Heron quantum processor deployed on premises with the entire supercomputer Fugaku to perform the largest computation of electronic structure involving quantum and classical high-performance computing. We design a closed-loop workflow between the quantum processors and 152,064 classical nodes of Fugaku, to approximate the electronic structure of chemistry models beyond the reach of exact diagonalization, with accuracy comparable to some all-classical approximation methods. Our work pushes the limits of the integration of quantum and classical high-performance computing, showcasing computational resource orchestration at the largest scale possible for current classical supercomputers.

Figures (8)

• Figure 1: Geometries of the [2Fe-2S] (top) and [4Fe-4S] (bottom) clusters considered in this study.
• Figure 2: Depiction of the workflow used to optimize the quantum energies.(a) High-level overview of the workflow to update the circuit parameters. The update of circuit parameters relies in a differential evolution algorithm with two populations of walkers, for a total of four walkers. The purple blocks labeled "QC" correspond to the execution of four quantum circuits associated to the walkers. The green blocks depict the SQD energy estimation for each of the walkers, which are executed in parallel in a HPC environment. Each of the green blocks executes three iterations of configuration recovery (R) with their corresponding projections (P) and diagonalizations (D). Purple arrows represent the loading of quantum circuits into the quantum processor. Green arrows represent the transfer of quantum measurement outcomes to the classical component. The dotted green lines denote the carryover of a fraction of configurations ${\bf{x}}$ with the largest SQD wave function component. (b) Top: The classical component of the workflow includes the configuration recovery step and projection and diagonalization in the subspace $\mathcal{S}^{(i)}$. The diagonalization step, achieved with a Davidson eigensolver. The red inset shows the distribution of the matrix-vector multiplication required by the Davidson eigensolver, where the application of each row of the matrix is distributed across a number of nodes of the supercomputer Fugaku. The massive parallelization allows to perform diagonalizations on $10^9$-dimensional subspaces in under 10 mins. (b) Bottom: Depiction of the LUCJ quantum circuit considered in this study, executed on Heron quantum processors, and the corresponding circuit layout.
• Figure 3: Schematic of the Kobe quantum processor. Out of the full chip, 77 qubits are employed in the experiment, with 72 primary qubits highlighted in green and 5 ancillary qubits in orange; the remaining qubits are shown in gray.
• Figure 4: (a)Electronic structure calculations using Heron quantum processors and the supercomputer Fugaku. Quantum energies (markers) as a function of the optimization step (a) for the [2Fe–2S] cluster, and (b) for the [4Fe–4S] cluster. The calculations for the [4Fe–4S] cluster with $10^8$ and $10^9$ determinants were performed on IBM Marrakesh, whereas the $10^{10}$ case and all [2Fe–2S] calculations were carried out on IBM Kobe. For reference, we also show the previous state-of-the-art (SOTA) quantum energy robledo2024chemistry, as well as the energies obtained from Hartree–Fock (HF), configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles (CCSD). (c) Quantum ( Heron processor) and classical ( Fugaku supercomputer) resource usage as a function of elapsed wall time. The orchestration of quantum and classical resources aims at minimizing idle (white) time. The data is from the $10^8$ determinants subspace from (b).
• Figure 5: Wall time profile of QPU and CPU usage. Computations for population 0 (p0) and population 1 (p1) are alternately executed on the classical processor. Here throw is the processing to prepare and send instructions to the quantum computer, retrieve receives output from the quantum computer; pre-processing prepares the list of configurations for diagonalization, and diagonalization performs projection and diagonalization to obtain molecular energies.