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:2606.07035

Solution of the Equation-of-Motion Phonon Method eigenvalue problems on the D-Wave quantum annealer

C. De Lucia, A. Martone, F. A. D'Aniello, A. Mastroianni, G. Nunziata, G. De Gregorio, R. Folprecht, F. Knapp, N. Lo Iudice, P. Vesely

nucl-thquant-phSubmitted Jun 5, 2026• Announced Jun 8, 2026• 0 citations
arXivHTMLPDF

Abstract

The solution of large-scale eigenvalue problems is crucial in nuclear many-body theory, where Hamiltonian matrices often reach extremely large dimensions. Quantum computing opens new perspectives for addressing such demanding problems. Although the Quantum Phase Estimation algorithm offers, in principle, a systematic route to matrix diagonalization, its practical deployment demands levels of coherence and error correction that current quantum hardware cannot yet support. A viable near-term strategy is instead to exploit quantum annealing, which enables the recasting of eigenvalue problems into quadratic unconstrained binary optimization formulations that can be addressed by existing annealing-based processors. Here, we propose a hybrid quantum-classical algorithm that combines quantum annealing and classical deflation to iteratively extract the full eigenspectrum of both standard and generalized eigenvalue problems. We benchmark this method on eigenvalue problems arising from the Equation of Motion Phonon Method performing calculations on real quantum hardware. Our approach illustrates the capabilities and limitations of near-term quantum devices in addressing nuclear eigenvalue problems.

Comments
16 pages, 8 figures, 1 Tables, accepted for publication on Phys. Rev. C

Related papers

Solving Standard and Generalized EMPM Eigenvalue Problems: A QUBO Approach for the D-Wave Quantum Annealer

G. De Gregorio, C. De Lucia, A. Martone +6 more

Within the Equation of Motion Phonon Method (EMPM) framework, we address the computation of the ground-state eigenpair of nuclear Hamiltonians by reformulating the eigenvalue problem as a Quadratic Unconstrained Binary Optimization (QUBO). To this end, we adopt a QUBO-based iterative steepest-descent algorithm and validate its performance using Simulated An­nealing, demonstrating its feasibility for nuclear many-body calculations. This work represents a first step toward implementations on quantum annealers and extensions to the full eigenspectrum.

•Nov 21, 2025•0 citations

Solving Standard and Generalized EMPM Eigenvalue Problems: A QUBO Approach for the D-Wave Quantum Annealer

G. De Gregorio, C. De Lucia, Angelo Martone +6 more

Within the Equation of Motion Phonon Method (EMPM) framework, we address the computation of the ground-state eigenpair of nuclear Hamiltonians by reformulating the eigenvalue problem as a Quadratic Unconstrained Binary Optimization (QUBO). To this end, we adopt a QUBO-based iterative steepest-descent algorithm and validate its performance using Simulated An­nealing, demonstrating its feasibility for nuclear many-body calculations. This work represents a first step toward implementations on quantum annealers and extensions to the full eigenspectrum.

EPJ Web of Conferences•Jan 1, 2025•0 citations

Electronic structure with direct diagonalization on a D-wave quantum annealer

Alexander Teplukhin, Brian K. Kendrick, Sergei Tretiak +1 more

Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.

arXiv:2009.01373•Scientific Reports•Nov 27, 2020•36 citations

Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion

Singleton, RL, Rogers, ML

Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry, and statistics. Traditional solution methods such as Gaussian elimination are very time consuming for large matrices, and more efficient computational methods are desired. In the twilight of Moore's Law, quantum computing is perhaps the most direct path out of the darkness. There are two complementary paradigms for quantum computing, namely, circuit-based systems and quantum annealers. In this paper, we express floating point operations, such as division and matrix inversion, in terms of a quadratic unconstrained binary optimization (QUBO) problem, a formulation that is ideal for a quantum annealer. We first address floating point division, and then move on to matrix inversion. We provide a general algorithm for any number of dimensions, and, as a proof-of-principle, we demonstrates results from the D-Wave quantum annealer for 2 × 2 and 3 × 3 general matrices. In principle, our algorithm scales to very large numbers of linear equations; however, in practice the number is limited by the connectivity and dynamic range of the machine.

•Nov 6, 2020•22 citations

Floating-Point Calculations on a Quantum Annealer: Division and Matrix Inversion

Michael L. Rogers, Robert Singleton

Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time consuming for large matrices, and more efficient computational methods are desired. In the twilight of Moore\rq{}s Law, quantum computing is perhaps the most direct path out of the darkness. There are two complementary paradigms for quantum computing, namely, gated systems and quantum annealers. In this paper, we express floating point operations such as division and matrix inversion in terms of a {\em quadratic unconstrained binary optimization} (QUBO) problem, a formulation that is ideal for a quantum annealer. We first address floating point division, and then move on to matrix inversion. We provide a general algorithm for any number of dimensions, but we provide results from the D-Wave quantum anneler for 2x2 and 3x3 general matrices. Our algorithm scales to very large numbers of linear equations. We should also mention that our algorithm provides the full solution the the matrix problem, while HHL provides only an expectation value.

arXiv:1901.06526•Frontiers in Physics•Nov 6, 2020•3 citations

Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances

Alexander Teplukhin, Brian K. Kendrick, Dmitri Babikov

Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only. For many physics and chemistry problems, the diagonalization of complex matrices is required. For example, the calculation of quantum scattering resonances can be formulated as a complex eigenvalue problem where the real part of the eigenvalue is the resonance energy and the imaginary part is proportional to the resonance width. In the present work, we generalize the QAE to treat complex matrices: first complex Hermitian matrices and then complex symmetric matrices. These generalizations are then used to compute a quantum scattering resonance state in a 1D model potential for O + O collisions. These calculations are performed using both a software (classical) annealer and hardware annealer (the D-Wave 2000Q). The results of the complex QAE are also benchmarked against a standard linear algebra library (LAPACK). This work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device.

Physical Chemistry Chemical Physics•Jan 1, 2020•28 citations
The solution of large-scale eigenvalue problems is crucial in nuclear many-body theory, where Hamiltonian matrices often reach extremely large dimensions. Quantum computing opens new perspectives for addressing such demanding problems. Although the Quantum Phase Estimation algorithm offers, in principle, a systematic route to matrix diagonalization, its practical deployment demands levels of coherence and error correction that current quantum hardware cannot yet support. A viable near-term strategy is instead to exploit quantum annealing, which enables the recasting of eigenvalue problems into quadratic unconstrained binary optimization formulations that can be addressed by existing annealing-based processors. Here, we propose a hybrid quantum-classical algorithm that combines quantum annealing and classical deflation to iteratively extract the full eigenspectrum of both standard and generalized eigenvalue problems. We benchmark this method on eigenvalue problems arising from the Equation of Motion Phonon Method performing calculations on real quantum hardware. Our approach illustrates the capabilities and limitations of near-term quantum devices in addressing nuclear eigenvalue problems.
Within the Equation of Motion Phonon Method (EMPM) framework, we address the computation of the ground-state eigenpair of nuclear Hamiltonians by reformulating the eigenvalue problem as a Quadratic Unconstrained Binary Optimization (QUBO). To this end, we adopt a QUBO-based iterative steepest-descent algorithm and validate its performance using Simulated An­nealing, demonstrating its feasibility for nuclear many-body calculations. This work represents a first step toward implementations on quantum annealers and extensions to the full eigenspectrum.
Within the Equation of Motion Phonon Method (EMPM) framework, we address the computation of the ground-state eigenpair of nuclear Hamiltonians by reformulating the eigenvalue problem as a Quadratic Unconstrained Binary Optimization (QUBO). To this end, we adopt a QUBO-based iterative steepest-descent algorithm and validate its performance using Simulated An­nealing, demonstrating its feasibility for nuclear many-body calculations. This work represents a first step toward implementations on quantum annealers and extensions to the full eigenspectrum.
Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to solve quantum chemistry problems on near-term gate-based quantum computers and quantum annealers by developing the appropriate algorithm and software base. This work implements the general Quantum Annealer Eigensolver (QAE) algorithm to solve the molecular electronic Hamiltonian eigenvalue-eigenvector problem on a D-Wave 2000Q quantum annealer. The approach is based on the matrix formulation, efficiently uses qubit resources based on a power-of-two encoding scheme and is hardware-dominant relying on only one classically optimized parameter. We demonstrate the use of D-Wave hardware for obtaining ground and excited electronic states across a variety of small molecular systems. The approach can be adapted for use by a vast majority of electronic structure methods currently implemented in conventional quantum-chemical packages. The results of this work will encourage further development of software such as qbsolv which has promising applications in emerging quantum information processing hardware and has expectation to address large and complex optimization problems intractable for classical computers.
Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry, and statistics. Traditional solution methods such as Gaussian elimination are very time consuming for large matrices, and more efficient computational methods are desired. In the twilight of Moore's Law, quantum computing is perhaps the most direct path out of the darkness. There are two complementary paradigms for quantum computing, namely, circuit-based systems and quantum annealers. In this paper, we express floating point operations, such as division and matrix inversion, in terms of a quadratic unconstrained binary optimization (QUBO) problem, a formulation that is ideal for a quantum annealer. We first address floating point division, and then move on to matrix inversion. We provide a general algorithm for any number of dimensions, and, as a proof-of-principle, we demonstrates results from the D-Wave quantum annealer for 2 × 2 and 3 × 3 general matrices. In principle, our algorithm scales to very large numbers of linear equations; however, in practice the number is limited by the connectivity and dynamic range of the machine.
Systems of linear equations are employed almost universally across a wide range of disciplines, from physics and engineering to biology, chemistry and statistics. Traditional solution methods such as Gaussian elimination become very time consuming for large matrices, and more efficient computational methods are desired. In the twilight of Moore\rq{}s Law, quantum computing is perhaps the most direct path out of the darkness. There are two complementary paradigms for quantum computing, namely, gated systems and quantum annealers. In this paper, we express floating point operations such as division and matrix inversion in terms of a {\em quadratic unconstrained binary optimization} (QUBO) problem, a formulation that is ideal for a quantum annealer. We first address floating point division, and then move on to matrix inversion. We provide a general algorithm for any number of dimensions, but we provide results from the D-Wave quantum anneler for 2x2 and 3x3 general matrices. Our algorithm scales to very large numbers of linear equations. We should also mention that our algorithm provides the full solution the the matrix problem, while HHL provides only an expectation value.
Quantum computing is a new and rapidly evolving paradigm for solving chemistry problems. In previous work, we developed the Quantum Annealer Eigensolver (QAE) and applied it to the calculation of the vibrational spectrum of a molecule on the D-Wave quantum annealer. However, the original QAE methodology was applicable to real symmetric matrices only. For many physics and chemistry problems, the diagonalization of complex matrices is required. For example, the calculation of quantum scattering resonances can be formulated as a complex eigenvalue problem where the real part of the eigenvalue is the resonance energy and the imaginary part is proportional to the resonance width. In the present work, we generalize the QAE to treat complex matrices: first complex Hermitian matrices and then complex symmetric matrices. These generalizations are then used to compute a quantum scattering resonance state in a 1D model potential for O + O collisions. These calculations are performed using both a software (classical) annealer and hardware annealer (the D-Wave 2000Q). The results of the complex QAE are also benchmarked against a standard linear algebra library (LAPACK). This work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device.