A note on large-scale quantum chemistry on quantum computers: the case of a molecule with half-Möbius topology
Samuele Piccinelli, Stefano Barison, Alberto Baiardi, Francesco Tacchino, Jascha Repp, Igor Rončević, Florian Albrecht, Harry L. Anderson, Leo Gross, Alessandro Curioni, Ivano Tavernelli
We report quantum chemistry calculations performed on superconducting quantum processors for a molecule exhibiting the half-Möbius electronic topology originally introduced by Rončević et al. Using SqDRIFT, a randomized sample-based Krylov quantum diagonalization algorithm, we achieve reliable quantum simulations on active spaces corresponding to 36 orbitals (72 qubits) and extend previous studies up to 50 orbitals (100 qubits). We demonstrate that a systematic increase of active space sizes, which has a concrete impact on the accuracy of the electronic structure description, is achievable with state-of-the-art quantum processors, thus offering a promising path towards practically relevant quantum-assisted electronic-structure calculations.
We report quantum chemistry calculations performed on superconducting quantum processors for a molecule exhibiting the half-Möbius electronic topology originally introduced by Rončević et al. Using SqDRIFT, a randomized sample-based Krylov quantum diagonalization algorithm, we achieve reliable quantum simulations on active spaces corresponding to 36 orbitals (72 qubits) and extend previous studies up to 50 orbitals (100 qubits). We demonstrate that a systematic increase of active space sizes, which has a concrete impact on the accuracy of the electronic structure description, is achievable with state-of-the-art quantum processors, thus offering a promising path towards practically relevant quantum-assisted electronic-structure calculations.
We report quantum chemistry calculations performed on superconducting quantum processors for a molecule exhibiting the half-Möbius electronic topology originally introduced by Rončević et al. Using SqDRIFT, a randomized sample-based Krylov quantum diagonalization algorithm, we achieve reliable quantum simulations on active spaces corresponding to 36 orbitals (72 qubits) and extend previous studies up to 50 orbitals (100 qubits). We demonstrate that a systematic increase of active space sizes, which has a concrete impact on the accuracy of the electronic structure description, is achievable with state-of-the-art quantum processors, thus offering a promising path towards practically relevant quantum-assisted electronic-structure calculations.
Quantum algorithms based on classical processing of individual samples have recently emerged as a promising route to perform large-scale quantum-chemical calculations on pre-fault-tolerant and early-fault-tolerant quantum devices. In these algorithms, the quantum computer acts as a sampling engine that generates the subspace in which the Hamiltonian is classically diagonalized. The recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) uses quantum Krylov states as circuits from which samples are collected. Convergence guarantees can be derived for SKQD under assumptions similar to those of quantum phase estimation -- namely, a sufficiently large overlap between the reference and the target ground state -- with the additional requirement that the ground-state wave function be well approximated by a polynomial subset of the full Hilbert space. However, implementations of SKQD for complex many-body Hamiltonians, such as quantum chemistry ones, are limited by the depths of time-evolution circuits needed to generate Krylov vectors. In this work, we introduce a method that combines SKQD with a qDRIFT randomized compilation of the Hamiltonian propagator. The resulting algorithm, termed SqDRIFT, enables executing quantum chemistry experiments on present-day quantum processors while retaining provable convergence guarantees, which we extend to account for the error of the randomized compilation and of finite sampling. We demonstrate its viability by applying SqDRIFT to calculate the electronic ground-state energy of several polycyclic aromatic hydrocarbons, up to system sizes beyond the reach of exact diagonalization.
Accurately capturing electron correlation in large-scale molecular systems remains one of the foremost challenges in quantum chemistry and a primary driver for the development of quantum algorithms. Classical configuration-interaction methods, while rigorous, suffer from exponential scaling, rendering them impractical for large or strongly correlated systems. Overcoming this limitation is central to realizing the promise of quantum computing in chemistry. Here, we investigate the pyridine-Li ion complex using three quantum algorithms: the variational quantum eigensolver (VQE), the subspace quantum diagonalization (SQD) method, and the recently introduced handover iterative VQE (HI-VQE). Our results demonstrate how new generations of hybrid quantum-classical frameworks overcome the scalability and noise sensitivity that constrain conventional VQE approaches. SQD and HI-VQE achieve ground-state energy calculations for problem sizes inaccessible to classical computation, marking a clear advance toward quantum advantage. In particular, HI-VQE enables calculations within active spaces as large as (24e,22o), requiring 44 qubits-well beyond the reach of classical CASCI and VQE. This capability provides a systematic pathway for incorporating increasing numbers of electrons into quantum treatment, thereby approaching exact molecular energies. Importantly, both SQD and HI-VQE exhibit robustness against hardware noise, a critical improvement over earlier approaches. By enabling quantum simulations of molecular systems previously deemed intractable, SQD and HI-VQE offer a realistic route toward practical quantum advantage in computational chemistry. The comparison between HI-VQE and SQD shows that optimizing circuit parameters is crucial for accurate simulation.
A universal quantum computer can simulate diverse quantum systems, with electronic structure for chemistry offering challenging problems for practical use cases around the hundred-qubit mark. Although current quantum processors have reached this size, deep circuits and a large number of measurements lead to prohibitive runtimes for quantum computers in isolation. Here, we demonstrate the use of classical distributed computing to offload all but an intrinsically quantum component of a workflow for electronic structure simulations. Using a Heron superconducting processor and the supercomputer Fugaku, we simulate the ground-state dissociation of N 2 and the ground state properties of [2Fe-2S] and [4Fe-4S] clusters, with circuits up to 77 qubits and 10,570 gates. The proposed algorithm processes quantum samples to produce upper bounds for the ground-state energy and sparse approximations to the ground-state wave functions. Our results suggest that, for current error rates, a quantum-centric supercomputing architecture can tackle challenging chemistry problems beyond sizes amenable to exact diagonalization.
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.
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology. This requires a truncated representation of the electronic structure Hamiltonian using a finite number of orbitals. While it is, in principle, obvious how to improve on the representation by including more orbitals, this is usually unfeasible in practice (e.g., because of the limited number of qubits available) and severely compromises the accuracy of the obtained results. Here, we propose a quantum algorithm that improves on the representation of the physical problem by virtue of second-order perturbation theory. In particular, our quantum algorithm evaluates the second-order energy correction through a series of time-evolution steps under the unperturbed Hamiltonian. An important application is to go beyond the active-space approximation, allowing to include corrections of virtual orbitals, known as multireference perturbation theory. Here, we exploit the fact that the unperturbed Hamiltonian is diagonal for virtual orbitals and show that the number of qubits is independent of the number of virtual orbitals. This gives rise to more accurate energy estimates without increasing the number of qubits. Moreover, we demonstrate numerically for realistic chemical systems that the total runtime has highly favorable scaling in the number of virtual orbitals compared to previous studies. Numerical calculations confirm the necessity of the multireference perturbation theory energy corrections to reach accurate ground-state energy estimates. Our perturbation theory quantum algorithm can also be applied to symmetry-adapted perturbation theory. As such, we demonstrate that perturbation theory can help to reduce the quantum hardware requirements for quantum chemistry. Published by the American Physical Society 2024