Present-day sample-based quantum algorithms within quantum-centric supercomputing workflows require substantial classical post-processing, large circuit depths to produce chemically relevant samples, and long QPU times to execute the many circuits needed for molecules of chemically relevant size. We introduce FMO-QVM-HCI-HSQD, a resource-efficient sample-based framework that breaks a large problem into fragments, runs the fragments in parallel on virtual regions of the QPU, and reduces circuit depth through a half-qubit ansatz whose samples seed an HCI expansion. We demonstrate the algorithm on ibm_marrakesh and ibm_boston for the water trimer and the carmofur_Mpro complex with up to 52 qubits, benchmarking against FMO-CCSD(T), FMO-CASCI and FMO-HCI. For the water trimer (14 spin orbitals for monomers, 28 for dimers), our method reduces the two-qubit depth by 39% compared to FMO-QVM-SQD and the QPU time by 82% compared to sequential FMO-SQD, and accesses 3% of the determinant subspace versus 40% for FMO-SQD, while achieving more accurate energies. For the carmofur_Mpro complex (16 and 32 spin orbitals), it reduces the two-qubit depth by 47% and the QPU time by 20% compared to FMO-QVM-SQD, and accesses 0.007% of the determinant subspace versus 40%, while remaining within chemical accuracy. Extending the carmofur_Mpro active space in the 6-31G basis to 52 and 104 spin orbitals, sampled on 26 and 52 qubits, the total energy deviates from FMO-HCI by only 1.22 mHa. These results show that combining fragmentation, virtual QPU partitioning and half-qubit sampling makes sample-based quantum simulation of chemically relevant systems feasible on current hardware.
AI Summary
The paper asks how to reduce qubit requirements, circuit depth, and QPU time in sample-based molecular simulation. Its FMO-QVM-HCI-HSQD workflow combines established FMO2 fragmentation, half-register LUCJ sampling, heat-bath selected CI seeded by reconstructed determinants, and quality-aware allocation of independent fragment circuits across a QPU. Barrier–reset–barrier sequences enable temporal reuse within one job.
Hardware tests use IBM Heron processors. For an STO-3G water trimer, with exact monomer energies and quantum-solved dimers, the workflow gives a 0.262 mHa total-energy deviation from FMO-FCI. Relative to QVM-SQD, two-qubit depth falls by 39%; QPU time falls from 16.98 s for sequential SQD to 2.99 s. The determinant subspace fraction is approximately 3%, versus 40% for SQD. For an STO-3G carmofur–protease fragment model, the deviation from FMO-CASCI is 0.487 mHa, with 47% lower two-qubit depth and 20% lower QPU time than QVM-SQD. A larger 6-31G calculation samples 104-spin-orbital dimers on 52 qubits; HCI plus semistochastic PT2 gives a total energy 1.22 mHa from a tighter-threshold FMO-HCI reference.
The paper notes that agreement between HCI-based calculations does not establish a benefit from quantum sampling. In one small-system seed comparison, quantum seeds barely change the error (0.132 to 0.130 mHa) while enlarging the selected space by 46%; classical CISD seeds perform better. Other stated limitations include approximate large-system references, unquantified fragmentation error, classical recovery of interspin correlation, hardware-limited concurrency, routing-induced depth increases, and single-run hardware results without repeatability estimates.
Little sign of AI-generated textIncrementalMissing comparisonOverclaims
Central claim may not hold: Chemical accuracy is demonstrated only relative to fragmented active-space references, with an approximate HCI reference for the largest calculation and no quantified fragmentation error.
The small-system total-energy benchmarks use exact classical monomer energies rather than the quantum-solver monomer energies.
The only seed-control experiment finds negligible energy improvement and a 45.6% larger determinant space from quantum seeds, leaving a useful quantum-sampling contribution unestablished.
The explanation of the STO-3G carmofur timing reduction incorrectly assumes fully simultaneous execution despite explicit temporal region reuse.
The claim that the small-system variational spaces cover nearly the entire determinant space contradicts the reported coverage of approximately 3% and 0.004–0.010%.
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
Present-day sample-based quantum algorithms within quantum-centric supercomputing workflows require substantial classical post-processing, large circuit depths to produce chemically relevant samples, and long QPU times to execute the many circuits needed for molecules of chemically relevant size. We introduce FMO-QVM-HCI-HSQD, a resource-efficient sample-based framework that breaks a large problem into fragments, runs the fragments in parallel on virtual regions of the QPU, and reduces circuit depth through a half-qubit ansatz whose samples seed an HCI expansion. We demonstrate the algorithm on ibm_marrakesh and ibm_boston for the water trimer and the carmofur_Mpro complex with up to 52 qubits, benchmarking against FMO-CCSD(T), FMO-CASCI and FMO-HCI. For the water trimer (14 spin orbitals for monomers, 28 for dimers), our method reduces the two-qubit depth by 39% compared to FMO-QVM-SQD and the QPU time by 82% compared to sequential FMO-SQD, and accesses 3% of the determinant subspace versus 40% for FMO-SQD, while achieving more accurate energies. For the carmofur_Mpro complex (16 and 32 spin orbitals), it reduces the two-qubit depth by 47% and the QPU time by 20% compared to FMO-QVM-SQD, and accesses 0.007% of the determinant subspace versus 40%, while remaining within chemical accuracy. Extending the carmofur_Mpro active space in the 6-31G basis to 52 and 104 spin orbitals, sampled on 26 and 52 qubits, the total energy deviates from FMO-HCI by only 1.22 mHa. These results show that combining fragmentation, virtual QPU partitioning and half-qubit sampling makes sample-based quantum simulation of chemically relevant systems feasible on current hardware.
The paper asks how to reduce qubit requirements, circuit depth, and QPU time in sample-based molecular simulation. Its FMO-QVM-HCI-HSQD workflow combines established FMO2 fragmentation, half-register LUCJ sampling, heat-bath selected CI seeded by reconstructed determinants, and quality-aware allocation of independent fragment circuits across a QPU. Barrier–reset–barrier sequences enable temporal reuse within one job.
Hardware tests use IBM Heron processors. For an STO-3G water trimer, with exact monomer energies and quantum-solved dimers, the workflow gives a 0.262 mHa total-energy deviation from FMO-FCI. Relative to QVM-SQD, two-qubit depth falls by 39%; QPU time falls from 16.98 s for sequential SQD to 2.99 s. The determinant subspace fraction is approximately 3%, versus 40% for SQD. For an STO-3G carmofur–protease fragment model, the deviation from FMO-CASCI is 0.487 mHa, with 47% lower two-qubit depth and 20% lower QPU time than QVM-SQD. A larger 6-31G calculation samples 104-spin-orbital dimers on 52 qubits; HCI plus semistochastic PT2 gives a total energy 1.22 mHa from a tighter-threshold FMO-HCI reference.
The paper notes that agreement between HCI-based calculations does not establish a benefit from quantum sampling. In one small-system seed comparison, quantum seeds barely change the error (0.132 to 0.130 mHa) while enlarging the selected space by 46%; classical CISD seeds perform better. Other stated limitations include approximate large-system references, unquantified fragmentation error, classical recovery of interspin correlation, hardware-limited concurrency, routing-induced depth increases, and single-run hardware results without repeatability estimates.
Sample-based quantum diagonalization (SQD) offers a powerful route to accurate quantum chemistry on noisy intermediate-scale quantum (NISQ) devices by combining quantum sampling with classical diagonalization. Here we introduce HSQD, a novel half-qubit SQD approach that halves the qubit requirement for simulating a chemical system and drastically reduces overall circuit depth and gate counts, suppressing hardware noise. When modeling the dissociation of the nitrogen molecule with a (10e, 26o) active space, HSQD matches the accuracy of SQD on IBM quantum hardware using only half the number of qubits and 40% fewer measurements. We further enhance HSQD with a heat-bath configuration interaction (HCI) inspired selection of the samples, forming HCI-HSQD. This yields sub-millihartree accuracy across the N2 potential energy surface and produces subspaces up to 39% smaller than those from classical HCI, showing a significant improvement in the compactness of the ground-state representation. Finally, we demonstrate the scalability of HCI-HSQD using iron-sulfur clusters, reaching active spaces of up to (54e, 36o) while using only half as many qubits as the original SQD. For these systems, HCI-HSQD reduces SQD energy errors by up to 76% for [2Fe-2S] and 26% for [4Fe-4S], while also reducing subspace sizes, halving measurement requirements, and eliminating expensive post-processing. Together, these results establish half-qubit SQD as a noise-resilient and resource-efficient pathway toward practical quantum advantage in strongly correlated chemistry.
Fragment molecular orbital (FMO) quantum chemistry offers a natural route to parallel quantum computing: large molecular calculations can be decomposed into smaller quantum subproblems that can, in principle, run concurrently. Their practical benefit on real quantum hardware, however, has remained unclear. We demonstrate parallel FMO calculations on three room-temperature diamond-based 'Quoll' quantum computers installed on-site at the Oak Ridge Leadership Computing Facility. Helium clusters (Hen, n=2,4,8,10,14) served as a testbed for total energy calculations using the Quantum Wave Function Sampler (QWFS), a selected configuration interaction (SCI) approach. We compare two execution modes: synchronous shot-parallel execution, in which quantum processors jointly sample QWFS circuits and combine their SPAM-corrected counts into a single probability distribution; and asynchronous fragment-parallel execution, in which processors independently evaluate FMO fragments using device-specific optimized circuits. Both modes increase quantum sampling throughput without systematic loss of accuracy. The three-QPU shot-parallel workflow reaches a parallel efficiency of 93.60%, while the fragment-parallel workflow achieves a measured efficiency of 75.01%, increasing to 95.17% when excluding the non-useful idle time associated with non-interruptible submitted jobs. In both cases, the assembled FMO-QWFS energies remain chemically accurate compared to the classical ideal. These results provide a proof-of-concept demonstration that parallel quantum execution can improve the practical throughput of quantum chemistry workflows on prototype hardware, motivating the development of future HPC environments with many fault-tolerant quantum processors operating as a distributed resource for molecular and materials simulation.
We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H2, LiH, BeH2, H2O, and NH3. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H2 and HeH+ using both STO-3G and 6-31G basis sets, and for LiH and BeH2 in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 × 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.
Quantum-centric supercomputing (QCSC) approaches, such as sample-based quantum diagonalization (SQD), combine quantum processors with high-performance computers (HPC), offering a promising route toward solving challenging electronic structure problems. However, implementation of QCSC approaches to large active space calculations is constrained by the associated number of qubits, deep quantum circuits, sampling cost, and large-scale Hamiltonian diagonalization. To overcome these limitations, we introduce a distributed QCSC framework that decomposes complex molecular problems into parallel sub-problems requiring fewer qubits, shallower circuits, and reduced shot budgets. A physically motivated, two-step aggregation scheme then reconstructs the global solution: first, a computational bit assignment strategy optimizes a cost function to appropriately map local bit indices to global ones, yielding a mapped tensor product state (MTPS); second, an inter-fragment correlation recovery module restores missing cross-fragment interactions. Herein, we employ a multi-layered generative machine learning architecture, starting with utilizing the recently proposed physics-informed generative SQD (PIGen-SQD) as a distributed QCSC solver, followed by a secondary generative module to model configuration distributions and identify dominant sectors of the global Hilbert space. For water and formamide dimers, our method achieves up to 95% reduction in the diagonalization dimension while enhancing energy accuracy by an order of magnitude over conventional SQD. Furthermore, application to the water hexamer ((H2O)6) cage successfully decomposes a 120-qubit problem into six 20-qubit monomeric subsystems, and stitches the monomers under a dimeric approximation, demonstrating excellent agreement with the reference classical methods.
We develop a workflow decomposing a molecule into fragments via quantum embedding and simulating them with a heterogeneous quantum-classical (HQC) method. We sample fragment electronic configurations on two 156-qubit quantum processors (ibm_cleveland, ibm_kobe), using up to 94 qubits, running 21,006 circuits for over 239 hours, collecting 3.0⋅109 measurement outcomes -- the most resource-intensive HQC computation for quantum chemistry to date. We compute fragment wavefunctions via optimized subspace diagonalization on supercomputers Fugaku, Miyabi-G, and ROQUO, achieving 72.5% parallel efficiency with scalable distributed linear algebra kernels. We simulate two protein-ligand complexes spanning dispersion- and electrostatics-dominated regimes (11,608, 12,635 atoms), demonstrate >40× increase in system size and up to 210× improvement in accuracy over previous state-of-the-art, with HQC matching coupled-cluster (CCSD) accuracy in fragment energies. We present the first HQC protein-ligand binding prediction using a mixed-basis set and an automated end-to-end workflow enabling practical HQC calculations of large protein systems.
Quantum computers offer significant potential for complex system analysis, yet their application in large systems is hindered by limitations such as qubit availability and quantum hardware noise. While the variational quantum eigensolver (VQE) was proposed to address these issues, its scalability remains limited. Many efforts, including new ansätze and Hamiltonian modifications, have been made to overcome these challenges. In this work, we introduced the novel Fragment Molecular Orbital/Variational Quantum Eigensolver (FMO/VQE) algorithm. This method combines the fragment molecular orbital (FMO) approach with VQE and efficiently utilizes qubits for quantum chemistry simulations. Employing the UCCSD ansatz, the FMO/VQE achieved an absolute error of just 0.053 mHa with 8 qubits in a [Formula: see text] system using the STO-3G basis set, and an error of 1.376 mHa with 16 qubits in a [Formula: see text] system with the 6-31G basis set. These results indicated a significant advancement in scalability over conventional VQE, maintaining accuracy with fewer qubits. Therefore, our FMO/VQE method exemplifies how integrating fragment-based quantum chemistry with quantum algorithms can enhance scalability, facilitating more complex molecular simulations and aligning with quantum computing advancements.