Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2309.01676 · The Journal of Physical Chemistry Letters

Quantum Information-Assisted Complete Active Space Optimization (QICAS)

Lexin Ding, Stefan Knecht, Christian Schilling

Published Dec 4, 2023• 28 citations
arXivHTMLPDF

Abstract

We propose an effective quantum information-assisted complete active space optimization scheme (QICAS). What sets QICAS apart from other correlation-based selection schemes is (i) the use of unique measures from quantum information that assess the correlation in electronic structures in an unambiguous and predictive manner and (ii) an orbital optimization step that minimizes the correlation discarded by the active space approximation. Equipped with these features, QICAS yields, for smaller correlated molecule, sets of optimized orbitals with respect to which the complete active space configuration interaction energy reaches the corresponding complete active space self-consistent field (CASSCF) energy within chemical accuracy. For more challenging systems such as the chromium dimer, QICAS offers an excellent starting point for CASSCF by greatly reducing the number of iterations required for numerical convergence. Accordingly, our study validates a profound empirical conjecture: the energetically optimal nonactive spaces are predominantly those that contain the least entanglement.

DOI
10.1021/acs.jpclett.3c02536

Related papers

Complete Active Space Methods for NISQ Devices: The Importance of Canonical Orbital Optimization for Accuracy and Noise Resilience

Juan Ángel de Gracia Triviño, Mickaël G. Delcey, Goran P. Wendin

To avoid the scaling of the number of qubits with the size of the basis set, one can divide the molecular space into active and inactive regions, which is also known as complete active space methods. However, selecting the active space alone is not enough to accurately describe quantum mechanical effects such as correlation. This study emphasizes the importance of optimizing the active space orbitals to describe correlation and improve the basis-dependent Hartree-Fock energies. We will explore classical and quantum computation methods for orbital optimization and compare the chemically inspired ansatz, UCCSD, with the classical full CI approach for describing the active space in both weakly and strongly correlated molecules. Finally, we will investigate the practical implementation of a quantum CASSCF, where hardware-efficient circuits must be used and noise can interfere with accuracy and convergence. Additionally, we will examine the impact of using canonical and noncanonical active orbitals on the convergence of the quantum CASSCF routine in the presence of noise.

Journal of Chemical Theory and Computation•Apr 27, 2023•28 citations

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive

Aaron Fitzpatrick, Anton Nykänen, N. Walter Talarico +4 more

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C 5 H 5 ) 2 ], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

arXiv:2212.11405•The Journal of Physical Chemistry A•Mar 28, 2024•22 citations

Automated Identification of Relevant Frontier Orbitals for Chemical Compounds and Processes

Christopher Johannes Stein, Markus Reiher

Quantum-chemical multi-configurational methods are required for a proper description of static electron correlation, a phenomenon inherent to the electronic structure of molecules with multiple (near-)degenerate frontier orbitals. Here, we review how a property of these frontier orbitals, namely the entanglement entropy is related to static electron correlation. A subset of orbitals, the so-called active orbital space is an essential ingredient for all multi-configurational methods. We proposed an automated selection of this active orbital space, that would otherwise be a tedious and error prone manual procedure, based on entanglement measures. Here, we extend this scheme to demonstrate its capability for the selection of consistent active spaces for several excited states and along reaction coordinates.

arXiv:1702.00450•CHIMIA International Journal for Chemistry•Apr 26, 2017•81 citations

Supramolecular approach-based intermolecular interaction energy calculations using quantum phase estimation algorithm

Yuhei Tachi, Akihiko Arakawa, Taisei Osawa +2 more

Accurate computation of non-covalent, intermolecular interaction energies is important to understand various chemical phenomena, and quantum computers are anticipated to accelerate it. Although the state-of-the-art quantum computers are still noisy and intermediate-scale ones, development of theoretical frameworks those are expected to work on a fault-tolerant quantum computer is an urgent issue. In this work, we explore resource-efficient implementation of the quantum phase estimation-based complete active space configuration interaction (QPE-CASCI) calculations, with the aid of the second-order Møller--Plesset perturbation theory (MP2)-based active space selection with Boys localized orbitals. We performed numerical simulations of QPE for the supramolecular approach-based intermolecular interaction energy calculations of the hydrogen-bonded water dimer, using 6 system and 6 ancilla qubits. With the aid of algorithmic error mitigation, the QPE-CASCI simulations achieved interaction energy predictions with an error of 0.02 kcal mol$^{-1}$ relative to the CASCI result, demonstrating the accuracy and efficiency of the proposed methodology. Preliminary results on quantum circuit compression for QPE are also presented to reduce the number of two-qubit gates and depth.

quant-pharXiv:2512.04587•Dec 5, 2025•0 citations

Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems

Pavlo Golub, Andrej Antalík, Libor Veis +1 more

Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)-porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.

Journal of Chemical Theory and Computation•Sep 27, 2021•37 citations

Quantum Slater-exponent optimization for electronic-structure calculations on simulated noisy intermediate-scale quantum computers

Difa Farhani Hakim, Teguh Budi Prayitno, Pak Shen Choong +2 more

In resource-efficient near-term quantum computers, development on the variational quantum eigensolver (VQE) algorithm that improves the accuracy of electronic structure calculations while maintaining low-requirement quantum gate counts is indispensable. We integrate Slater-type orbitals within the VQE framework, where the ground-state energy minimization with respect to the Slater exponents is shown as a second-order dependence on these parameters, enhancing accuracy compared with the standard methods while maintaining the same number of qubits. Using the full configuration interaction energy as the cost function, optimized parameters for first- and second-row elements are reported and related to the shielding constant, indicating a need to revise the previously established Slater rules. The active space is improved by substantially contracting the orbital exponents of extended basis sets relative to minimal ones, hence capturing additional electron-correlation effects. By considering the geometric structure of the parameter space, quantum Slater-exponent optimization (Q-SEO) demonstrates accelerated convergence to the target ground state, characterized by distinct parameter trajectories. The integration of a decision tree with Q-SEO effectively mitigates error in noisy environments.

Physical Review A•Jan 15, 2026•3 citations
We propose an effective quantum information-assisted complete active space optimization scheme (QICAS). What sets QICAS apart from other correlation-based selection schemes is (i) the use of unique measures from quantum information that assess the correlation in electronic structures in an unambiguous and predictive manner and (ii) an orbital optimization step that minimizes the correlation discarded by the active space approximation. Equipped with these features, QICAS yields, for smaller correlated molecule, sets of optimized orbitals with respect to which the complete active space configuration interaction energy reaches the corresponding complete active space self-consistent field (CASSCF) energy within chemical accuracy. For more challenging systems such as the chromium dimer, QICAS offers an excellent starting point for CASSCF by greatly reducing the number of iterations required for numerical convergence. Accordingly, our study validates a profound empirical conjecture: the energetically optimal nonactive spaces are predominantly those that contain the least entanglement.
To avoid the scaling of the number of qubits with the size of the basis set, one can divide the molecular space into active and inactive regions, which is also known as complete active space methods. However, selecting the active space alone is not enough to accurately describe quantum mechanical effects such as correlation. This study emphasizes the importance of optimizing the active space orbitals to describe correlation and improve the basis-dependent Hartree-Fock energies. We will explore classical and quantum computation methods for orbital optimization and compare the chemically inspired ansatz, UCCSD, with the classical full CI approach for describing the active space in both weakly and strongly correlated molecules. Finally, we will investigate the practical implementation of a quantum CASSCF, where hardware-efficient circuits must be used and noise can interfere with accuracy and convergence. Additionally, we will examine the impact of using canonical and noncanonical active orbitals on the convergence of the quantum CASSCF routine in the presence of noise.
We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C 5 H 5 ) 2 ], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.
Quantum-chemical multi-configurational methods are required for a proper description of static electron correlation, a phenomenon inherent to the electronic structure of molecules with multiple (near-)degenerate frontier orbitals. Here, we review how a property of these frontier orbitals, namely the entanglement entropy is related to static electron correlation. A subset of orbitals, the so-called active orbital space is an essential ingredient for all multi-configurational methods. We proposed an automated selection of this active orbital space, that would otherwise be a tedious and error prone manual procedure, based on entanglement measures. Here, we extend this scheme to demonstrate its capability for the selection of consistent active spaces for several excited states and along reaction coordinates.
Accurate computation of non-covalent, intermolecular interaction energies is important to understand various chemical phenomena, and quantum computers are anticipated to accelerate it. Although the state-of-the-art quantum computers are still noisy and intermediate-scale ones, development of theoretical frameworks those are expected to work on a fault-tolerant quantum computer is an urgent issue. In this work, we explore resource-efficient implementation of the quantum phase estimation-based complete active space configuration interaction (QPE-CASCI) calculations, with the aid of the second-order Møller--Plesset perturbation theory (MP2)-based active space selection with Boys localized orbitals. We performed numerical simulations of QPE for the supramolecular approach-based intermolecular interaction energy calculations of the hydrogen-bonded water dimer, using 6 system and 6 ancilla qubits. With the aid of algorithmic error mitigation, the QPE-CASCI simulations achieved interaction energy predictions with an error of 0.02 kcal mol−1^{-1}−1 relative to the CASCI result, demonstrating the accuracy and efficiency of the proposed methodology. Preliminary results on quantum circuit compression for QPE are also presented to reduce the number of two-qubit gates and depth.
Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe(II)-porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.
In resource-efficient near-term quantum computers, development on the variational quantum eigensolver (VQE) algorithm that improves the accuracy of electronic structure calculations while maintaining low-requirement quantum gate counts is indispensable. We integrate Slater-type orbitals within the VQE framework, where the ground-state energy minimization with respect to the Slater exponents is shown as a second-order dependence on these parameters, enhancing accuracy compared with the standard methods while maintaining the same number of qubits. Using the full configuration interaction energy as the cost function, optimized parameters for first- and second-row elements are reported and related to the shielding constant, indicating a need to revise the previously established Slater rules. The active space is improved by substantially contracting the orbital exponents of extended basis sets relative to minimal ones, hence capturing additional electron-correlation effects. By considering the geometric structure of the parameter space, quantum Slater-exponent optimization (Q-SEO) demonstrates accelerated convergence to the target ground state, characterized by distinct parameter trajectories. The integration of a decision tree with Q-SEO effectively mitigates error in noisy environments.