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ExcitationSolve - A fast gradient-free optimizer for excitations in fixed and adaptive VQEs

Jäger, Jonas, Kaldenbach, Thierry Nicolas, Haas, Max, Schultheis, Erik

Published Jan 1, 2024• 0 citations
OpenAlex

Abstract

In recent years, the variational quantum eigensolver (VQE)[1] has carried the hope of the quantum computing community for achieving quantum utility. It aims to find the ground state and corresponding energy of a molecular hamiltonian by classically optimizing the parameters $\theta_j$ of a variational quantum circuit. In order to guarantee the conservation of qunatities such as particle number or spin, physically inspired ansätze such as the UCCSD ansatz are most promising. ExcitationSolve provides a quantum-aware optimizer for such physically inspired ansätze, making best use of prior knowlege about the operators used in the ansatz.

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Fast gradient-free optimization of excitations in variational quantum eigensolvers

Jonas Jäger, Thierry N. Kaldenbach, Max Haas +1 more

Abstract Finding molecular ground states and energies with variational quantum eigensolvers is central to chemistry applications on quantum computers. Physically motivated ansätze based on excitation operators respect physical symmetries, but existing quantum-aware optimizers, such as Rotosolve, have been limited to simpler operator types. To fill this gap, we introduce ExcitationSolve, a fast quantum-aware optimizer that is globally-informed, gradient-free, and hyperparameter-free. ExcitationSolve extends these optimizers to parameterized unitaries with generators G of the form G 3 = G exhibited by excitation operators in approaches such as unitary coupled cluster. ExcitationSolve determines the global optimum along each variational parameter using the same quantum resources that gradient-based optimizers require for one update step. We provide optimization strategies for both fixed and adaptive variational ansätze, along with generalizations for simultaneously selecting and optimizing multiple excitations. On molecular ground state energy benchmarks, ExcitationSolve outperforms state-of-the-art optimizers by converging faster, achieving chemical accuracy for equilibrium geometries in a single parameter sweep, yielding shallower adaptive ansätze and remaining robust to real hardware noise. By uniting physical insight with efficient optimization, ExcitationSolve paves the way for scalable quantum chemistry calculations.

arXiv:2409.05939•Communications Physics•Oct 30, 2025•7 citations

ExcitationSolve- A fast gradient-free optimizer for excitations in fixed and adaptive VQEs

Haas, Max, Jäger, Jonas, Kaldenbach, Thierry +3 more

I presented our optimizer ExcitationSolve, the fundamental workings of it and some results for both fixed and adaptive ansätze

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Molecular excited state VQE simulations with iteratively constructed qubit-excitation-based ans\"atze

Yordan S. Yordanov, C. H. W. Barnes, David R. M. Arvidsson-Shukur

Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ansatze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. In this paper, we introduce the ``excited iterative qubit-excitation-based variational quantum eigensolver'' (e-IQEB-VQE) protocol to calculate molecular excited state energies. The e-IQEB-VQE constructs efficient problem-tailored ansatze by iteratively appending evolutions of qubit excitation operators. The e-IQEB-VQE is an adaptation of the IQEB-VQE protocol, designed to be less dependent on the choice of an initial reference state. We perform classical numerical simulations for LiH and BeH$_2$ to benchmark the performance of the IQEB-VQE. We demonstrate that the e-IQEB-VQE can construct highly accurate ansatze that require at least an order of magnitude fewer $CNOT$s than standard fixed UCC ansatze, such as the UCCSD and the GUCCSD.

•Jun 11, 2021•1 citation

Molecular-excited-state calculations with the qubit-excitation-based adaptive variational quantum eigensolver protocol

Yordan S. Yordanov, C. H. W. Barnes, David R. M. Arvidsson-Shukur

Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate-scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ans\"atze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. We introduce the excited qubit-excitation-based adaptive (e-QEB-ADAPT)-VQE protocol to calculate molecular-excited-state energies. The e-QEB-ADAPT-VQE constructs efficient problem-tailored ans\"atze by iteratively appending evolutions of qubit excitation operators. The e-QEB-ADAPT-VQE also improves on previous ADAPT-VQE protocol in that it is designed to be independent on the choice of initial reference state. We perform classical numerical simulations for LiH and ${\mathrm{BeH}}_{2}$ to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ans\"atze that require at least an order of magnitude fewer cnot gates than standard fixed unitary coupled-cluster ans\"atze, such as the UCCSD and the GUCCSD. We also show that the e-QEB-ADAPT-VQE is more successful in constructing ans\"atze for excited molecular states than other ADAPT-VQE protocols.

Physical Review A•Sep 29, 2022•17 citations

Gradient-Based Excitation Filter for Molecular Ground-State Simulation

Run-Hong He, Qingjie Chai, Xin Hong +4 more

Molecular system simulation is one of the most promising areas for demonstrating practical quantum advantage with near-term quantum computers. The Variational Quantum Eigensolver (VQE) is a leading algorithm for studying molecular energy levels, yet it still faces significant challenges due to excessive circuit depth. This paper introduces a method to efficiently simplify the Unitary Coupled-Cluster with Single and Double Excitations (UCCSD) ansatz in classical computer. We propose to estimate the correlation energy contributions of excitations using their gradients at Hartree-Fock state, supported by theoretical proof. By projecting the system's full Hamiltonian and Hartree-Fock state onto the subspace of excitation operators, these gradients can be computed efficiently and parallelly on classical computers with complexity only equivalent to $16\times16$ matrix multiplication. Leveling these gradients, the simplified ansatz can be readily constructed through the ordering and truncation of the corresponding excitations. Furthermore, we introduce a strategy that utilizes free parameters to indirectly identify critical excitations, reducing gradient computations by $\thicksim$60\% by exploiting the constraints of spin adaptation. Numerical experiments on prototype molecular systems (H\textsubscript{4}, HF, H\textsubscript{2}O, BeH\textsubscript{2} and NH\textsubscript{3}) demonstrate that our primary results and ablative studies achieve parameter reductions up to 46\% and 69\%, respectively, compared to state-of-the-art benchmarks (ADAPT-VQE and SymUCCSD), enabling significantly more compact quantum circuits with enhanced near-term feasibility.

arXiv:2506.20398•Jun 25, 2025•0 citations

Hamiltonian-Aware ADAPT Variational Quantum Eigensolver for Molecular Ground-State Simulation

Runhong He, Chao Liu, Xin Hong +5 more

Designing compact ansätze in Variational Quantum Eigensolver (VQE) is crucial for solving energetic problems of practical molecules on near-term quantum devices. However, existing Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansätze face two challenges: improper operator selection and accumulation of degraded operators. In this paper, we propose the Hamiltonian-Aware (HA) ADAPT-VQE algorithm to address these issues. First, we establish a novel excitation operator selection criterion. It breaks the local constraint of existing criteria by incorporating Hamiltonian information, prioritizes physically meaningful excitation operators, and incurs no extra classical or quantum computational overhead. Furthermore, we develop a problem-adaptive method for discriminating and pruning redundant excitation operators stemming from improper selection and inevitable degradation. This method balances redundant operator pruning and convergence guarantee, and is applicable to ansätze with arbitrary scales. Systematic numerical experiments on typical strongly correlated molecular systems demonstrate that our HA-ADAPT-VQE avoids energy plateaus and outperforms baseline algorithms in terms of energy error, ansatz size, and measurement cost. This work offers an efficient, robust ansatz construction paradigm, facilitating the development and practical deployment of large-scale VQE in quantum chemistry.

quant-pharXiv:2606.13118•Journal of Chemical Theory and Computation•Jun 12, 2026•0 citations
In recent years, the variational quantum eigensolver (VQE)[1] has carried the hope of the quantum computing community for achieving quantum utility. It aims to find the ground state and corresponding energy of a molecular hamiltonian by classically optimizing the parameters θj\theta_jθj​ of a variational quantum circuit. In order to guarantee the conservation of qunatities such as particle number or spin, physically inspired ansätze such as the UCCSD ansatz are most promising. ExcitationSolve provides a quantum-aware optimizer for such physically inspired ansätze, making best use of prior knowlege about the operators used in the ansatz.
Abstract Finding molecular ground states and energies with variational quantum eigensolvers is central to chemistry applications on quantum computers. Physically motivated ansätze based on excitation operators respect physical symmetries, but existing quantum-aware optimizers, such as Rotosolve, have been limited to simpler operator types. To fill this gap, we introduce ExcitationSolve, a fast quantum-aware optimizer that is globally-informed, gradient-free, and hyperparameter-free. ExcitationSolve extends these optimizers to parameterized unitaries with generators G of the form G 3 = G exhibited by excitation operators in approaches such as unitary coupled cluster. ExcitationSolve determines the global optimum along each variational parameter using the same quantum resources that gradient-based optimizers require for one update step. We provide optimization strategies for both fixed and adaptive variational ansätze, along with generalizations for simultaneously selecting and optimizing multiple excitations. On molecular ground state energy benchmarks, ExcitationSolve outperforms state-of-the-art optimizers by converging faster, achieving chemical accuracy for equilibrium geometries in a single parameter sweep, yielding shallower adaptive ansätze and remaining robust to real hardware noise. By uniting physical insight with efficient optimization, ExcitationSolve paves the way for scalable quantum chemistry calculations.
Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ansatze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. In this paper, we introduce the ``excited iterative qubit-excitation-based variational quantum eigensolver'' (e-IQEB-VQE) protocol to calculate molecular excited state energies. The e-IQEB-VQE constructs efficient problem-tailored ansatze by iteratively appending evolutions of qubit excitation operators. The e-IQEB-VQE is an adaptation of the IQEB-VQE protocol, designed to be less dependent on the choice of an initial reference state. We perform classical numerical simulations for LiH and BeH2_22​ to benchmark the performance of the IQEB-VQE. We demonstrate that the e-IQEB-VQE can construct highly accurate ansatze that require at least an order of magnitude fewer CNOTCNOTCNOTs than standard fixed UCC ansatze, such as the UCCSD and the GUCCSD.
Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate-scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ans\"atze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. We introduce the excited qubit-excitation-based adaptive (e-QEB-ADAPT)-VQE protocol to calculate molecular-excited-state energies. The e-QEB-ADAPT-VQE constructs efficient problem-tailored ans\"atze by iteratively appending evolutions of qubit excitation operators. The e-QEB-ADAPT-VQE also improves on previous ADAPT-VQE protocol in that it is designed to be independent on the choice of initial reference state. We perform classical numerical simulations for LiH and BeH2{\mathrm{BeH}}_{2}BeH2​ to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ans\"atze that require at least an order of magnitude fewer cnot gates than standard fixed unitary coupled-cluster ans\"atze, such as the UCCSD and the GUCCSD. We also show that the e-QEB-ADAPT-VQE is more successful in constructing ans\"atze for excited molecular states than other ADAPT-VQE protocols.
Molecular system simulation is one of the most promising areas for demonstrating practical quantum advantage with near-term quantum computers. The Variational Quantum Eigensolver (VQE) is a leading algorithm for studying molecular energy levels, yet it still faces significant challenges due to excessive circuit depth. This paper introduces a method to efficiently simplify the Unitary Coupled-Cluster with Single and Double Excitations (UCCSD) ansatz in classical computer. We propose to estimate the correlation energy contributions of excitations using their gradients at Hartree-Fock state, supported by theoretical proof. By projecting the system's full Hamiltonian and Hartree-Fock state onto the subspace of excitation operators, these gradients can be computed efficiently and parallelly on classical computers with complexity only equivalent to 16×1616\times1616×16 matrix multiplication. Leveling these gradients, the simplified ansatz can be readily constructed through the ordering and truncation of the corresponding excitations. Furthermore, we introduce a strategy that utilizes free parameters to indirectly identify critical excitations, reducing gradient computations by $\thicksim$60\% by exploiting the constraints of spin adaptation. Numerical experiments on prototype molecular systems (H\textsubscript{4}, HF, H\textsubscript{2}O, BeH\textsubscript{2} and NH\textsubscript{3}) demonstrate that our primary results and ablative studies achieve parameter reductions up to 46\% and 69\%, respectively, compared to state-of-the-art benchmarks (ADAPT-VQE and SymUCCSD), enabling significantly more compact quantum circuits with enhanced near-term feasibility.
Designing compact ansätze in Variational Quantum Eigensolver (VQE) is crucial for solving energetic problems of practical molecules on near-term quantum devices. However, existing Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansätze face two challenges: improper operator selection and accumulation of degraded operators. In this paper, we propose the Hamiltonian-Aware (HA) ADAPT-VQE algorithm to address these issues. First, we establish a novel excitation operator selection criterion. It breaks the local constraint of existing criteria by incorporating Hamiltonian information, prioritizes physically meaningful excitation operators, and incurs no extra classical or quantum computational overhead. Furthermore, we develop a problem-adaptive method for discriminating and pruning redundant excitation operators stemming from improper selection and inevitable degradation. This method balances redundant operator pruning and convergence guarantee, and is applicable to ansätze with arbitrary scales. Systematic numerical experiments on typical strongly correlated molecular systems demonstrate that our HA-ADAPT-VQE avoids energy plateaus and outperforms baseline algorithms in terms of energy error, ansatz size, and measurement cost. This work offers an efficient, robust ansatz construction paradigm, facilitating the development and practical deployment of large-scale VQE in quantum chemistry.