Introduces the eigenwalk problem and proves a linear-diameter support-localization theorem for sparse eigenvectors, yielding poly(n)-time classical exact diagonalization for O(1)-sparse extremal eigenvectors of poly(n)-sparse 2^n-dimensional Hamiltonians.
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Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers
32 Pith papers cite this work, alongside 15 external citations. Polarity classification is still indexing.
32
Pith papers citing it
15
external citations · Pith
abstract
We propose quantum-selected configuration interaction (QSCI), a class of hybrid quantum-classical algorithms for calculating the ground- and excited-state energies of many-electron Hamiltonians on noisy quantum devices. Suppose that an approximate ground state can be prepared on a quantum computer either by variational quantum eigensolver or by some other method. Then, by sampling the state in the computational basis, which is hard for classical computation in general, one can identify the electron configurations that are important for reproducing the ground state. The Hamiltonian in the subspace spanned by those important configurations is diagonalized on classical computers to output the ground-state energy and the corresponding eigenvector. The excited-state energies can be obtained similarly. The result is robust against statistical and physical errors because the noisy quantum devices are used only to define the subspace, and the resulting ground-state energy strictly satisfies the variational principle even in the presence of such errors. The expectation values of various other operators can also be estimated for obtained eigenstates with no additional quantum cost, since the explicit eigenvectors in the subspaces are known. We verified our proposal by numerical simulations, and demonstrated it on a quantum device for an 8-qubit molecular Hamiltonian. The proposed algorithms are potentially feasible to tackle some challenging molecules by exploiting quantum devices with several tens of qubits, assisted by high-performance classical computing resources for diagonalization.
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GQKAE uses quantum-inspired Kolmogorov-Arnold networks to reduce parameters by 66% in generative quantum eigensolvers while achieving chemical accuracy on H4, N2, LiH, and other molecules.
Divide-and-conquer QAOA samples and Hamming-weight-conditioned neural network surrogates accelerate MCMC mixing for constrained Ising problems by average factors of 20.3 and 7.6 over classical pair-flip baselines.
CSQD improves SQD energy estimates in strongly correlated systems by replacing a global reference occupancy vector with cluster-specific ones, lowering energies by up to 15.95 mHa for stretched N2 and 57.82 mHa for [2Fe-2S].
EXASP prepares the lowest bright excited state of a fermionic Hamiltonian by adiabatically evolving a ground-state-plus-photon system, demonstrated on Hubbard chains, methylene, and a two-qubit IBM chip.
Hybrid QSCI method with LCNot-UCCSD ansatz and RBM-based configuration recovery enables NISQ-era molecular simulations, demonstrated on small molecules and DMET-embedded protein-ligand systems.
HI-NQS uses a dual-channel autoregressive Transformer NQS inside an iterative sample-diagonalize-update loop to reach chemical accuracy on small molecules and nitrogen active spaces with better determinant scaling than CIPSI.
QC-AFQMC per-step scaling reduced from O(N^5.5) to O(N^4.5) via Aitken's block transformation for singular Pfaffians and algorithmic differentiation for force bias, with demonstrations on H8 from real quantum data and Li2O4.
Filter-assisted SQD uses a quantum filter to engineer sparser ground-state wavefunctions, yielding orders-of-magnitude lower energy errors and reduced sampling overhead versus standard SQD on the transverse-longitudinal Ising model.
An ancilla-free method projects many-electron states onto point-group irreps via orbital rotations derived from representation-matrix eigenvectors and demonstrates it on benzene and ferrocene with a 32-qubit IBM hardware run.
COO co-optimizes orbitals with TrimCI to absorb many-body correlations into the basis, cutting determinant count by orders of magnitude for iron-sulfur clusters versus localized bases or DMRG.
A tree tensor network renormalization decomposes matrix product states into log-depth quantum circuits with a fidelity-depth trade-off parameter, extended to matrix product operators for ancilla-free overlap verification circuits.
SQD-AA reduces total query complexity by more than 100x on model distributions and achieves the lowest T-gate counts with 3-4 orders shallower circuits than iQPE for molecular examples.
A divide-and-conquer framework using QAOA and neural network surrogates accelerates constrained MCMC by factors of 7.6 to 20.3 over classical methods.
A Transformer policy optimizes quantum circuit ansatzes for QSCI, yielding up to 98% reduction in two-qubit gates while reaching chemical accuracy on N2 and competitive compactness with classical methods.
Tensor-network compression of nearest-neighbor circuits plus four-type measurements yields 0.4-4.7% error on 8-qubit Hubbard energy gaps and enables QPE-type runs on IBM devices up to 52 qubits with over 4000 two-qubit gates.
Quantum computed moments method on IBM hardware estimates water dipole moment to 0.03 debye of FCI, outperforming VQE by factor of two in error.
A QSCI variant using stochastic quantum time evolution selects compact configuration subspaces for SiH4 energies, achieving over 200x reduction versus conventional SCI at large separations while matching Heatbath CI compactness.
NuQuLib maps realistic nuclear Hamiltonians to qubit Hamiltonians and compares T-gate costs of QPE, QKrylov, and ODMD across valence and no-core model spaces.
A DFT-embedded quantum-selected configuration interaction framework combines quantum and classical methods to achieve ~1 kcal/mol accuracy on large-scale chemical systems using a subset of qubits from a 144-qubit quantum computer.
NLCE+QA on trapped-ion QPU computes TFIM thermodynamic-limit energies and dispersions using ASP, VQE, and a new CX-test.
ffsim is a new open-source library that accelerates fermionic quantum circuit simulation by using particle number and spin symmetries to cut memory and runtime, outperforming FQE on benchmarks up to 64 qubits.
SQD needs an exponentially increasing number of computational-basis configurations to approximate ground-state energies of Heisenberg and Hubbard models within fixed accuracy, even when configurations are chosen optimally by probability.
The authors present Pilot-Quantum, a middleware for adaptive resource management in hybrid quantum-HPC systems, along with execution motifs and a performance modeling toolkit called Q-Dreamer.
citing papers explorer
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Polynomial-time exact diagonalization via sparse guided eigenwalks
Introduces the eigenwalk problem and proves a linear-diameter support-localization theorem for sparse eigenvectors, yielding poly(n)-time classical exact diagonalization for O(1)-sparse extremal eigenvectors of poly(n)-sparse 2^n-dimensional Hamiltonians.
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Generative Quantum-inspired Kolmogorov-Arnold Eigensolver
GQKAE uses quantum-inspired Kolmogorov-Arnold networks to reduce parameters by 66% in generative quantum eigensolvers while achieving chemical accuracy on H4, N2, LiH, and other molecules.
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Divide-and-Conquer Neural Network Surrogates for Quantum Sampling: Accelerating Markov Chain Monte Carlo in Large-Scale Constrained Optimization Problems
Divide-and-conquer QAOA samples and Hamming-weight-conditioned neural network surrogates accelerate MCMC mixing for constrained Ising problems by average factors of 20.3 and 7.6 over classical pair-flip baselines.
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Cluster-Adaptive Sample-Based Quantum Diagonalization for Strongly Correlated Systems
CSQD improves SQD energy estimates in strongly correlated systems by replacing a global reference occupancy vector with cluster-specific ones, lowering energies by up to 15.95 mHa for stretched N2 and 57.82 mHa for [2Fe-2S].
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Excited state preparation on a quantum computer through adiabatic light-matter coupling
EXASP prepares the lowest bright excited state of a fermionic Hamiltonian by adiabatically evolving a ground-state-plus-photon system, demonstrated on Hubbard chains, methylene, and a two-qubit IBM chip.
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Bridging the NISQ and Fault-Tolerant Regimes: Generative-ML-Assisted Quantum Selected CI for Molecular Simulations
Hybrid QSCI method with LCNot-UCCSD ansatz and RBM-based configuration recovery enables NISQ-era molecular simulations, demonstrated on small molecules and DMET-embedded protein-ligand systems.
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An Iterative Dual-Channel Neural Quantum State Algorithm for Selected Configuration Interaction
HI-NQS uses a dual-channel autoregressive Transformer NQS inside an iterative sample-diagonalize-update loop to reach chemical accuracy on small molecules and nitrogen active spaces with better determinant scaling than CIPSI.
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Quantum-Classical Auxiliary-Field Quantum Monte Carlo at the Edge of Practicability
QC-AFQMC per-step scaling reduced from O(N^5.5) to O(N^4.5) via Aitken's block transformation for singular Pfaffians and algorithmic differentiation for force bias, with demonstrations on H8 from real quantum data and Li2O4.
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Filter-assisted quantum subspace diagonalization via wavefunction sparsity engineering
Filter-assisted SQD uses a quantum filter to engineer sparser ground-state wavefunctions, yielding orders-of-magnitude lower energy errors and reduced sampling overhead versus standard SQD on the transverse-longitudinal Ising model.
-
Point-group symmetry analysis of many-electron wavefunctions on a quantum computer
An ancilla-free method projects many-electron states onto point-group irreps via orbital rotations derived from representation-matrix eigenvectors and demonstrates it on benzene and ferrocene with a 32-qubit IBM hardware run.
-
Absorbing Many-Body Correlations into Core-Optimized Orbitals
COO co-optimizes orbitals with TrimCI to absorb many-body correlations into the basis, cutting determinant count by orders of magnitude for iron-sulfur clusters versus localized bases or DMRG.
-
Practical Log-Depth Quantum State Preparation and Circuit Verification via Tree Tensor Network Compilation
A tree tensor network renormalization decomposes matrix product states into log-depth quantum circuits with a fidelity-depth trade-off parameter, extended to matrix product operators for ancilla-free overlap verification circuits.
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Sample-Based Quantum Diagonalization with Amplitude Amplification
SQD-AA reduces total query complexity by more than 100x on model distributions and achieves the lowest T-gate counts with 3-4 orders shallower circuits than iQPE for molecular examples.
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Forecasts of CMB $E$-mode anomalies for AliCPT-1
A divide-and-conquer framework using QAOA and neural network surrogates accelerates constrained MCMC by factors of 7.6 to 20.3 over classical methods.
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Generative Circuit Design for Quantum-Selected Configuration Interaction
A Transformer policy optimizes quantum circuit ansatzes for QSCI, yielding up to 98% reduction in two-qubit gates while reaching chemical accuracy on N2 and competitive compactness with classical methods.
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Tensor-based phase difference estimation on time series analysis
Tensor-network compression of nearest-neighbor circuits plus four-type measurements yields 0.4-4.7% error on 8-qubit Hubbard energy gaps and enables QPE-type runs on IBM devices up to 52 qubits with over 4000 two-qubit gates.
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Moments-based quantum computation of the electric dipole moment of molecular systems
Quantum computed moments method on IBM hardware estimates water dipole moment to 0.03 debye of FCI, outperforming VQE by factor of two in error.
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Towards Compact Wavefunctions from Quantum-Selected Configuration Interaction
A QSCI variant using stochastic quantum time evolution selects compact configuration subspaces for SiH4 energies, achieving over 200x reduction versus conventional SCI at large separations while matching Heatbath CI compactness.
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Nuclear Many-Body Systems as Benchmarks for Quantum Computing
NuQuLib maps realistic nuclear Hamiltonians to qubit Hamiltonians and compares T-gate costs of QPE, QKrylov, and ODMD across valence and no-core model spaces.
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Quantum computing for accurate large-scale electronic-structure calculations: DFT-embedded, post-processed quantum-selected configuration interaction
A DFT-embedded quantum-selected configuration interaction framework combines quantum and classical methods to achieve ~1 kcal/mol accuracy on large-scale chemical systems using a subset of qubits from a 144-qubit quantum computer.
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Thermodynamic-limit dispersion relations on trapped-ion quantum hardware
NLCE+QA on trapped-ion QPU computes TFIM thermodynamic-limit energies and dispersions using ASP, VQE, and a new CX-test.
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ffsim: Faster simulation of fermionic quantum circuits
ffsim is a new open-source library that accelerates fermionic quantum circuit simulation by using particle number and spin symmetries to cut memory and runtime, outperforming FQE on benchmarks up to 64 qubits.
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A Critical Assessment of the Sample-Based Quantum Diagonalization for Heisenberg and Hubbard Models
SQD needs an exponentially increasing number of computational-basis configurations to approximate ground-state energies of Heisenberg and Hubbard models within fixed accuracy, even when configurations are chosen optimally by probability.
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Hybrid Quantum-HPC Middleware Systems for Adaptive Resource, Workload and Task Management
The authors present Pilot-Quantum, a middleware for adaptive resource management in hybrid quantum-HPC systems, along with execution motifs and a performance modeling toolkit called Q-Dreamer.
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Quantum-centric simulation of hydrogen abstraction by sample-based quantum diagonalization and entanglement forging
Demonstrates combined entanglement forging and sample-based quantum diagonalization on superconducting hardware to calculate energies for hydrogen abstraction in 2,2-diphenyldipropane across active spaces up to 39 electrons and 39 orbitals.
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Quantum-Classical Embedding via Ghost Gutzwiller Approximation for Enhanced Simulations of Correlated Electron Systems
Introduces ghost Gutzwiller quantum embedding for ground-state and spectral simulations of correlated electrons on quantum devices, tested on the infinite-dimensional Hubbard model with error mitigation.
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Interaction geometry and ground-state properties of sparse quantum lattice models
Symmetry and frustration in power-of-p and Fibonacci graphs drive distinct ground-state phase behaviors in sparse long-range quantum models, unified by an effective-geometry principle.
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Additive binding energies in asphalt on a quantum processor via quantum-selected configuration interaction (QSCI)
Hybrid quantum workflow on IQM Emerald processor computes -3.52 kcal/mol binding energy for pyridine-phenol complex via QSCI in (10e,10o) space, matching CASCI but underbinding relative to CCSD(T) benchmark of -8.5 to -9.5 kcal/mol.
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Noise and Configuration Recovery Impact on Quantum Selected Configuration Interaction
Noise in LUCJ sampling for QSCI on N2 expands the configuration space beyond the ideal ansatz and, when paired with recovery, produces more accurate CI energies than noiseless sampling.
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Practical HPCQC Integration with QDMI: A Real-Hardware Case Study with IQM Systems
A QDMI-based adapter for IQM quantum hardware enables reusable integration with Slurm and Qiskit in HPC centers, with open-source code provided.
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Quantum Simulation of Ligand-like Molecules through Sample-based Quantum Diagonalization in Density Matrix Embedding Framework
Using DMET to fragment molecules and SQD to solve the fragments on IBM hardware, the authors report ground-state energies for eight ligand-like molecules that agree with DMET-FCI to within about 10⁻⁶ Hartree.
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Accelerating Quantum Eigensolver Algorithms With Machine Learning
XGBoost models trained on ≤16-qubit data predict eigensolver hyperparameters and reduce error by 0.12% on 28-qubit systems.