Awesome-QSCI
This repository contains a curated list of Quantum Selected Configuration Interaction (QSCI) resources — the original framework often referred to as Sample-based Quantum Diagonalization (SQD) in recent literature. This list is maintained by QunaSys Inc.
If you find this repository useful, please consider citing.
Feel free to share this list with others!
Overview
Abstract
In recent years, the field of quantum computing has been shifting from the era of noisy intermediate-scale quantum (NISQ) devices to the early-FTQC era. This new stage is characterized by the emergence of devices with hundreds of qubits. While such devices are insufficient for fully error-corrected quantum computation, they nevertheless have the potential to perform computations that are difficult for classical computers to simulate. Variational quantum algorithms have been proposed as key applications that make use of NISQ devices. In particular, the Variational Quantum Eigensolver (VQE) is expected to find applications in quantum chemistry, such as ground-state energy calculations. However, it is well known that VQE requires a large number of shots and optimization steps to suppress statistical errors and achieve sufficient accuracy. Moreover, due to statistical noise, experimental results obtained on current hardware are not strictly variational, and with today’s device performance, the impact of noise remains substantial.
Against this background, we have proposed the Quantum Selected Configuration Interaction (QSCI) algorithm [1]. QSCI enables more accurate energy calculations by restricting the role of quantum hardware to sampling tasks. The QSCI algorithm consists of the following steps:
- Prepare a reasonably optimized input state for the quantum computer.
- Perform measurements on the quantum computer using the input state.
- From the measurement results, select important electronic configurations.
- Finally, perform classical diagonalization within the subspace spanned by the selected electronic configurations.
The overall workflow is summarized in Fig. 1. In light of the challenges faced by VQE, QSCI offers several improvements. First, unlike VQE, QSCI does not require an iterative parameter-optimization loop: we prepare a fixed input state and only sample it on the computational basis, which reduces the cumulative number of shots. Second, QSCI guarantees that the estimated ground-state energy always satisfies the variational principle, even under statistical or hardware-induced errors. Consequently, unlike VQE—where noise can both break the variational property and hinder the convergence of parameter optimization—QSCI naturally reduces the impact of noise. Finally, by limiting the role of quantum hardware to sampling, it further mitigates the effect of device imperfections.
[1] K. Kanno, M. Kohda, R. Imai, S. Koh, K. Mitarai, W. Mizukami, Y. O. Nakagawa, arXiv: 2302.11320.
Citing
If you find this repository useful, please consider citing the original paper:
@ARTICLE{Kanno2023-kc,
title = "Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers",
author = "Kanno, Keita and Kohda, Masaya and Imai, Ryosuke and Koh, Sho and Mitarai, Kosuke and Mizukami, Wataru and Nakagawa, Yuya O",
journal = "arXiv [quant-ph]",
month = feb,
year = 2023,
archivePrefix = "arXiv",
primaryClass = "quant-ph",
eprint = "2302.11320"
}
Papers
A list of papers for Quantum Selected Configuration Interaction method.
Foundational Work
| Year | Paper Title | Note |
|---|---|---|
| 2023 | Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers | The original paper of QSCI. |
Methodological extensions
| Year | Paper Title | Note |
|---|---|---|
| 2023 | ADAPT-QSCI: Adaptive Construction of an Input State for Quantum-Selected Configuration Interaction | An extended study that introduces a framework for the adaptive construction of input states in QSCI. |
| 2024 | Chemistry Beyond Exact Solutions on a Quantum-Centric Supercomputer | An extended QSCI study that introduces configuration-recovery as a post-selection technique to reconstruct configurations from noisy quantum samples, named sample-based quantum diagonalization (SQD), demonstrating large-scale chemical simulations—including N₂ bond dissociation and [2Fe–2S]/[4Fe–4S] clusters. |
| 2024 | Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer | An extended QSCI study, named Hamiltonian simulation-based QSCI (HSB-QSCI), that first introduces the use of time-evolved quantum states generated by the target Hamiltonian as input states, and demonstrates this approach by performing quantum-chemical calculations of oligoacenes on quantum hardware. |
| 2024 | Quantum-selected configuration interaction with time-evolved state | An extended QSCI study, named Time-Evolved QSCI (TE-QSCI), that introduces the use of time-evolved quantum states generated by the target Hamiltonian as input states. They focus on providing an optimization-free framework for input-state preparation. |
| 2025 | Quantum-Centric Algorithm for Sample-Based Krylov Diagonalization | A study contemporaneous with TE-QSCI that frames the time-evolved-state approach within the Krylov subspace formalism, named sample-based Krylov quantum diagonalizeation (SKQD), and demonstrates large-scale calculations on impurity models for impurity models using a quantum-centric supercomputing platform. |
| 2025 | Implicit solvent sample-based quantum diagonalization | A QSCI-related study that integrates an implicit solvent model (IEF-PCM) into the QSCI with configuration recovery workflow, applying it to polar molecules (methanol, methylamine, ethanol, water) in aqueous solution with 27-52 qubit devices, thereby demonstrating scalability of quantum-centric simulations including solvent effects. |
| 2025 | Auxiliary-field quantum Monte Carlo method with quantum selected configuration interaction | A QSCI-related study that uses a QSCI-derived trial wave function within an auxiliary-field quantum Monte Carlo framework (QSCI-AFQMC), enabling a hybrid treatment of static correlation on quantum hardware and dynamical correlation via classical Monte Carlo, and demonstrating its potential on molecular systems such as H2O and linear H4. |
| 2025 | Enhancing Accuracy of Quantum-Selected Configuration Interaction Calculations using Multireference Perturbation Theory: Application to Aromatic Molecules | A study that augments the original QSCI framework with a classical multireference perturbation treatment (GMC-QDPT), forming the QSCI-PT scheme to recover dynamical correlation, and demonstrates improved accuracy for the ground and excited states of aromatic molecules (naphthalene and tetracene), with further gains via systematic expansion of the QSCI-selected configuration space. |
| 2025 | Sampling-based Quantum Optimization Algorithm with Quantum Relaxation | A sampling-based quantum optimization study inspired by the QSCI framework, introducing the Sampling-based Quantum Optimization Algorithm (SQOA) with Quantum Relaxation encoding and parameter transferability from small to larger instances, and demonstrating its performance on MaxCut problems up to 40 nodes on quantum hardware. |
| 2025 | Neural Network Assisted Fermionic Compression Encoding: A Lossy-QSCI Framework for Scalable Quantum Chemistry Simulations | A study proposing Lossy-QSCI, an extension of the QSCI framework that enhances resource efficiency through two complementary components: Chemical-RLE, which compresses fermionic state encoding for systems with $N$ electrons and $M$ orbitals to achieve $O(N \log M)$ qubit scaling, and NN-FED, a neural-network-assisted decoder that reconstructs fermionic expectation values from compressed measurements. |
| 2025 | Coupled cluster method tailored by quantum selected configuration interaction | A study introducing the QSCI-TCC hybrid scheme, which tailors conventional coupled-cluster theory with a QSCI-derived active-space wave function to embed static correlation from quantum sampling and subsequently recover dynamical correlation, demonstrating chemically accurate results ($\le$ 1kcal/mol) for the dissociation of H2O and N2 with a modest number of measurement shots. |
| 2025 | Quantum Assisted Ghost Gutzwiller Ansatz | A study that integrates QSCI-based sampling into the ghost Gutzwiller embedding framework (gGut), using quantum-selected configuration interaction and circuit-cutting techniques on quantum hardware (up to 24 qubits) to build a highly sparse CI basis (~1% of full) and accurately capture the metal-to-insulator transition in a Hubbard-type model. |
| 2025 | Quantum chemistry with provable convergence via randomized sample-based quantum diagonalization | A QSCI-related study that introduces SqDRIFT, combining sample-based Krylov quantum diagonalization with qDRIFT randomized compilation to achieve provable convergence and reduced circuit depth, and demonstrates its applicability to utility-scale molecular Hamiltonians beyond the reach of exact diagonalization. |
| 2025 | Adaptive-basis sample-based neural diagonalization for quantum many-body systems | A QSCI-related study that introduces sample-based neural diagonalization with an adaptive basis, combining autoregressive neural sampling and learnable basis transformations to extend the applicability of sample-based diagonalization to quantum many-body systems with delocalized ground states. |
| 2025 | Towards Compact Wavefunctions from Quantum-Selected Configuration Interaction | A QSCI-related study that investigates how wavefunctions obtained from quantum-selected configuration interaction can be systematically compressed, demonstrating that a small subset of selected configurations is sufficient to faithfully reproduce both the energy and the structure of the original QSCI wavefunction. |
| 2025 | Size-consistent implementation of Hamiltonian simulation-based quantum-selected configuration interaction method for the supramolecular approach | A QSCI-related methodological study that introduces a size-consistent implementation of Hamiltonian simulation-based QSCI, enabling accurate supramolecular interaction energy calculations by systematically restoring the product-state structure required for size consistency. |
| 2025 | Classically Prepared, Quantumly Evolved: Hybrid Algorithm for Molecular Spectra | A QSCI-inspired methodological study that computes molecular excitation spectra by combining classical preparation of perturbed ground states with short-time quantum evolution to identify dynamically relevant subspaces, enabling efficient classical reconstruction of long-time dynamics and spectral functions. |
| 2025 | Enhancing Chemistry on Quantum Computers with Fermionic Linear Optical Simulation | A QSCI-related methodological study that introduces ExtraFerm, a fermionic linear-optics–based classical simulator for estimating Born-rule probabilities of chemistry-inspired quantum circuits, and demonstrates its integration with sample-based quantum diagonalization to significantly improve accuracy and variance with minimal overhead. |
| 2025 | Improved parameter initialization for the (local) unitary cluster Jastrow ansatz | A methodological study that improves the performance of QSCI and SQD with the (local) unitary cluster Jastrow ansatz by introducing compressed double factorization and tensor-network–based surrogate optimization for parameter initialization, highlighting the distinct ansatz requirements of sample-based quantum algorithms. |
| 2025 | Physics Informed Generative Machine Learning for Accelerated Quantum-centric Supercomputing | A methodological extension of sample-based quantum diagonalization that introduces physics-informed generative machine learning for configuration recovery, combining perturbative screening with RBM-based guided sampling to achieve chemically accurate energies with substantially reduced diagonalization cost on quantum hardware. |
Applications
| Year | Paper Title | Note |
|---|---|---|
| 2024 | Solving an Industrially Relevant Quantum Chemistry Problem on Quantum Hardware | A QSCI-related study that performs ground-state energy calculations of the Fe(III)-NTA complex on a trapped-ion quantum processor, employing QSCI with a self-consistent configuration-recovery method as a post-selection technique and achieving chemical accuracy by incorporating molecular symmetry in the recovery process. |
| 2024 | Accurate quantum-centric simulations of supramolecular interactions | A QSCI-related study that incorporates configuration recovery in post-selection to improve sampling quality and applies this framework to non-covalent molecular interactions, demonstrating quantum-centric simulations with chemical-level accuracy. |
| 2024 | Quantum-centric computation of molecular excited states with extended sample-based quantum diagonalization | A QSCI study incorporating configuration recovery and extended by subspace expansion to compute low-lying molecular excited states, demonstrating its application to the nitrogen molecule and a [2Fe–2S] cluster. |
| 2024 | Quantum-Centric Study of Methylene Singlet and Triplet States | A QSCI study incorporating configuration recovery and extending the framework to open-shell molecular systems, further demonstrating ground- and excited-state calculations of methylene (CH2) on a 52-qubit processor and validating the applicability of QSCI to radical systems. |
| 2024 | Towards quantum-centric simulations of extended molecules: sample-based quantum diagonalization enhanced with density matrix embedding theory | A QSCI-related study that integrates density-matrix embedding theory to partition large molecular systems into tractable active regions, applies QSCI and configuration-recovery within those regions, and demonstrates its capability on an 18-hydrogen ring and conformers of cyclohexane. |
| 2025 | Efficient Quantum Chemistry Calculations on Noisy Quantum Hardware | |
| 2025 | Enhancing the accuracy and efficiency of sample-based quantum diagonalization with phaseless auxiliary-field quantum Monte Carlo | A QSCI-related study that systematically integrates phaseless AFQMC with QSCI trial wavefunctions, focusing on improving correlation-energy recovery and sampling efficiency, and demonstrating quantitative analyses of truncation thresholds (up to 99.5%) for N2 and [2Fe–2S] systems. |
| 2025 | Computing band gaps of periodic materials via sample-based quantum diagonalization | A study applying the QSCI framework to periodic crystalline materials, where a DFT-derived extended Hubbard Hamiltonian is solved via configuration sampling from a LUCJ quantum circuit on 38–46 qubits to predict electronic band gaps. |
| 2025 | Surface Reaction Simulations for Battery Materials through Sample-Based Quantum Diagonalization and Local Embedding | A materials-oriented hybrid quantum-classical study that builds upon the QSCI framework with configuration recovery, further introducing excitation operators in an extended variant referred to as Ext-SQD, and applying it within a local embedding scheme to simulate Li-O2 surface reactions, where this extended approach achieves higher accuracy than CCSD for electrode surface chemistry. |
| 2025 | Quantum computation of a quasiparticle band structure with the quantum-selected configuration interaction | A study applying the QSCI framework combined with QSE to compute quasiparticle band structures of a silicon material using a 16-qubit IBM quantum processor, aiming to reduce the VQE-optimization overhead and improve scalability for materials applications. |
| 2025 | Symmetry-adapted sample-based quantum diagonalization: Application to lattice model | A study extending the QSCI with configuration-recovery framework by incorporating lattice and spin symmetries into the sampled configuration subspace—termed symmetry-adapted SQD—and applying it to a two-leg Hubbard ladder model, where superconducting correlation functions and spin correlations are evaluated, showing faster convergence and improved wave-function compactness compared to the non-symmetry-adapted formulation. |
| 2025 | Quantum-Centric Alchemical Free Energy Calculations | A study introducing a quantum-centric alchemical free-energy workflow that integrates the QSCI framework into the book-ending correction method for QM/MM calculations. |
| 2025 | Quantum-centric simulation of hydrogen abstraction by sample-based quantum diagonalization and entanglement forging | A QSCI-related study that performs quantum-centric simulations of a hydrogen abstraction reaction by combining sample-based quantum diagonalization with entanglement forging, reducing qubit requirements and computing activation and reaction energies on a superconducting quantum processor with accuracy assessed across multiple active spaces. |
| 2025 | Sample-based Quantum Diagonalization Methods for Modeling the Photochemistry of Diazirine and Diazo Compounds | A QSCI-related application study that employs sample-based quantum diagonalization and its extended variant to model ground- and excited-state potential energy surfaces of diazirine and diazo compounds, demonstrating chemically accurate photochemical energetics for systems requiring large active spaces on superconducting quantum hardware. |
| 2025 | Quantum simulation of carbon capture in periodic metal-organic frameworks | A QSCI-related application study that applies sample-based quantum diagonalization to periodic metal–organic frameworks, combining plane-wave electronic structure with localized active-space selection to compute CO2 adsorption energies in strongly correlated MOF materials. |
| 2025 | Closed-loop calculations of electronic structure on a quantum processor and a classical supercomputer at full scale | A large-scale QSCI application study that demonstrates a closed-loop quantum–classical workflow, combining sample-based quantum diagonalization on superconducting quantum processors with massive distributed diagonalization on a classical supercomputer to tackle strongly correlated iron–sulfur clusters beyond the reach of exact methods. |
| 2025 | Quantum Simulation of Ligand-like Molecules through Sample-based Quantum Diagonalization in Density Matrix Embedding Framework | An application study that integrates sample-based quantum diagonalization as a high-level impurity solver within the density matrix embedding theory framework, demonstrating chemically accurate ground-state energies for ligand-like molecules using superconducting quantum hardware. |
Evaluations / Benchmarks
| Year | Paper Title | Note |
|---|---|---|
| 2025 | Critical Limitations in Quantum-Selected Configuration Interaction Methods | A related study that provides a critical assessment of QSCI, identifying repeated sampling of already-selected configurations as a key factor that degrades its sampling efficiency, and analyzing the resulting scalability challenges through numerical benchmarks on molecular systems. |
| 2025 | From Promise to Practice: Benchmarking Quantum Chemistry on Quantum Hardware | A large-scale benchmark study that systematically evaluates sample-based quantum diagonalization on real quantum hardware across the W4-11 thermochemistry dataset, revealing when SQD reaches CCSD-level accuracy via energy-variance extrapolation and identifying chemical regimes where it fails. |
| 2025 | Simulating and Sampling from Quantum Circuits with 2D Tensor Networks | A benchmark study that classically simulates and samples QSCI-relevant quantum circuits using geometry-matched 2D tensor networks, demonstrating that LUCJ circuits on heavy-hex architectures can be efficiently and accurately sampled and highlighting the critical role of device topology in assessing quantum advantage. |
| 2025 | Convergence of sample-based quantum diagonalization on a variable-length cuprate chain | A benchmark study that systematically analyzes the convergence of sample-based quantum diagonalization on strongly correlated cuprate chains of increasing length, identifying sampling plateaus, their dependence on ansatz design, operator expansion order, and orbital basis, and revealing that hardware noise can unexpectedly aid convergence. |
Others
| Year | Paper Title | Note |
|---|---|---|
| 2025 | HIVQE: Handover Iterative Variational Quantum Eigensolver for Efficient Quantum Chemistry Calculations | |
| 2025 | Tensor-Product Bitstring Selected Configuration Interaction | A study introducing Tensor-Product Bitstring Selected Configuration Interaction (TBSCI), which uses a tensor-product bitstring representation and distributed CI-vector storage to handle trillions of determinants on classical HPC, significantly improving the scalability of SCI methods. |
| 2025 | Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques | A conceptual framework paper proposing the integration of the QSCI methodology with projection-based embedding and classical molecular-dynamics techniques to form a multiscale hybrid workflow, outlining how QSCI can serve as an active-region quantum solver to extend applications toward realistic chemical systems. |
| 2025 | Cyclic Variational Quantum Eigensolver: Escaping Barren Plateaus through Staircase Descent | A VQE-based study that introduces a cyclic optimization scheme with measurement-driven reference-state expansion, incorporating configuration-selection ideas conceptually related to QSCI to mitigate barren plateaus in strongly correlated molecular systems. |
| 2025 | From VQE To SQD: Modern Quantum Algorithms For The Electronic Structure Problem | A review-style perspective that surveys modern quantum algorithms for electronic structure, comparing variational quantum eigensolvers and sample-based quantum diagonalization, and clarifying their shared variational foundations and complementary strengths. |
| 2025 | From Random Determinants to the Ground State | A classical selected-configuration-interaction study that demonstrates how compact ground-state subspaces can be discovered starting from random Slater determinants, providing a purely classical analogue of the subspace-selection principles underlying QSCI and SQD. |
| 2025 | Observability Architecture for Quantum-Centric Supercomputing Workflows | A workflow- and infrastructure-focused study that introduces an application-level observability architecture for quantum-centric supercomputing and demonstrates how domain-level telemetry enables systematic analysis of solver behavior and performance in closed-loop SQD workflows. |
Contirbution
Contributions are welcome.
Suggestions for missing or relevant papers, as well as improvements to existing summaries or classifications, are appreciated. Please feel free to open an issue or submit a pull request.