From Promise to Practice: Benchmarking Quantum Chemistry on Quantum Hardware

TL;DR

This is the largest study assessing the accuracy and precision of a quantum-hybrid algorithm on a digital quantum device across a variety of molecular systems and chemical reactions, using 16.85 hours on the superconducting quantum processor ibm_rensselaer and 724.22 node hours on the supercomputer AiMOS.

Abstract

We provide a systematic evaluation of the sample-based quantum diagonalization (SQD) method for electronic structure based on the W4-11 thermochemistry dataset, comprising 124 total atomization, 83 bond dissociation, 20 isomerization, 505 heavy-atom transfer, and 13 nucleophilic substitution processes, covering diverse bonding situations and reaction mechanisms. This is the largest study assessing the accuracy and precision of a quantum-hybrid algorithm on a digital quantum device across a variety of molecular systems and chemical reactions, using 16.85 hours on the superconducting quantum processor ibm_rensselaer and 724.22 node hours on the supercomputer AiMOS. To ensure a fair comparison, our study employs commensurate resource allocation for both classical and quantum simulations. Although SQD exhibits large statistical deviations from ground-state reference energies, energy extrapolations yield CCSD-level accuracy. While bond-breaking reactions show a systematic improvement as computational resources increase, nucleophilic substitution or heavy atom transfer reactions do not. The limitations quantified in this manuscript indicate opportunities for improvement in SQD-based algorithms. This work provides a benchmark and community resource for exploring new quantum algorithms and devices, supported by an online benchmark challenge and an open-source Python library for direct comparison.

Figures (19)

• Figure 1: Computational workflow of SQD used in this work: The preprocessing stage (left, pink) comprises classical electronic-structure calculations, the construction of the corresponding quantum circuits (illustrated in the lower panel for a closed-shell configuration with $N=12$ electrons in M=9 spatial orbitals), and their subsequent transpilation. The transpiled circuits are then executed on a quantum device (middle, blue), and the resulting measurement data are analyzed during the postprocessing stage (right, pink).
• Figure 2: (a) two-qubit gate count (black "x") and depth (orange "+") of LUCJ circuits used in SQD calculations as functions of the configuration space dimension, for the molecules in the W4-11 database at STO-6G level of theory. (b) dimension of the configuration space (black "x"), dimension of the largest computed SQD wavefunctions (orange "+") for the molecules in the W4-11 database at STO-6G level of theory, compared with $10^{4}$ (blue dashed line) taken to represent a 1-minute timeout on a personal computer, the FCI limit at the time of writing ($1.3\cdot 10^{12}$, green dashed line, Ref. gao2024distributed), and $2^{64} \simeq 10^{19}$ (purple dashed line) taken to represent the exascale limit.
• Figure 3: Comparison of MP2, CISD, CCSD, SQD with different subspace sizes (SQD$_\zeta$ with $\zeta = 25\%, 50\%, 10\%, 200\%, 400\%$) and SQD extrapolated with GEV (SQD$_\mathrm{ext}$) across the W4‑11 dataset. (a) Distribution of absolute ground-state energy errors ($|\Delta E|$) (b) Average absolute reaction energy error $|\Delta \Delta E|$ for each reaction class: total atomization (TAE), bond dissociation (BDE), isomerization (ISO), heavy‑atom transfer (HAT), and nucleophilic substitution (SN) (c) Distribution of absolute reaction energy errors for TAE processes (d) Distribution of absolute reaction energy errors for SN processes
• Figure 4: (a-c) show energy-variance extrapolations for ozone, cyanogen, and tetraphosphorus. SQD and GEV variance-energy pairs are shown as brown circles and crosses, respectively. Horizontal lines indicate ground-state energies for CISD (dotted), CCSD (dot-dashed), CCSD(T) (dashed), as well as singlet excited-states from FCI (dotted orange lines). (d) Absolute energy deviations $\Delta E$ between CCSD(T) and SQD extrapolated with LMM and GEV (blue), along with the corresponding statistical uncertainties $\mathrm{CI}(\Delta E)$ across the W4-11 dataset.
• Figure 5: (a) Circuit depth for different quantum algorithms. We denote by "V", "H", "Q" and "+" the gate depth of VQE using USCC (converged to 1 m$E_h$ of reference CCSD(T) energy), HT, QPE, and LUJC ansatz, respectively. The orange and black colors describe the Jordan-Wigner and Bravyi-Kitaev mappings, respectively. (b) Gate count (black "x") circuit and depth (orange "'+') of the LUCJ ansatz for all species in the dataset.