Excited States from ADAPT-VQE convergence path in Many-Body Problems: application to nuclear pairing problem and H₄ molecule dissociation

2025/06/27 by Zhang, Jing, Lacroix, Denis · 7 citations
#FOS: Physical sciences #Nuclear Theory (nucl-th) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2506.22275

Abstract

A quantum computing algorithm is proposed to obtain low-lying excited states in many-body interacting systems. The approximate eigenstates are obtained by using a quantum space diagonalization method in a subspace of states selected from the convergence path of the ADAPT-VQE (adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver) towards the ground state of the many-body problem. This method is shown to be accurate with only a small overhead in terms of quantum resources required to get the ground state. We also show that the quantum algorithm might be used to facilitate the convergence of the ADAPT-VQE method itself. Successful applications of the technique are made to like-particle pairing as well as neutron-proton pairing. Finally, the H₄ molecule's dissociation also illustrates the technique, demonstrating its accuracy and versatility.

Citations

• Variational simulation of the Lipkin-Meshkov-Glick model on a neutral atom quantum computer
• A Quantum Annealing Protocol to Solve the Nuclear Shell Model
• Challenging Excited States from Adaptive Quantum Eigensolvers: Subspace Expansions vs. State-Averaged Strategies
• Quantum computing for extracting nuclear resonances
• Quantum computing for extracting nuclear resonances
• Neutron-proton pairing correlations described on quantum computers
• Variance Minimisation of the Lipkin-Meshkov-Glick Model on a Quantum Computer
• Shell-model study of ⁵⁸Ni using quantum computing algorithm
• Exploiting symmetries in nuclear Hamiltonians for ground state preparation
• Solving the Lipkin model using quantum computers with two qubits only with a hybrid quantum-classical technique based on the Generator Coordinate Method
• Subspace methods for electronic structure simulations on quantum computers
• Restoring symmetries in quantum computing using Classical Shadows
• Quantum benefit of the quantum equation of motion for the strongly coupled many-body problem
• Electronic Excited States from a Variance-Based Contracted Quantum Eigensolver
• Quantum computing with and for many-body physics
• Radiative processes on a quantum computer
• Variational quantum algorithms
• Recent developments in the PySCF program package
• Practical Quantum Computation of Chemical and Nuclear Energy Levels\n Using Quantum Imaginary Time Evolution and Lanczos Algorithms
• A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons
• Cloud Quantum Computing of an Atomic Nucleus
• Self-consistent mean-field models for nuclear structure

Cited by

• Exploring fixed points and eigenstates of quantum systems with reinforcement learning
• Purified phase estimation samples spectra efficiently
• Bridging Quantum Computing and Nuclear Structure: Atomic Nuclei on a Trapped-Ion Quantum Computer
• Single-step Quantum Simulation of Two Nucleons
• Quasiparticle pairing encoding of atomic nuclei for quantum annealing
• Comparison of variational quantum eigensolvers in light nuclei
• Quantum Simulation of Nuclear Shell Model Using GCM-Based Methods on NISQ Devices

Related

• Challenging Excited States from Adaptive Quantum Eigensolvers: Subspace Expansions vs. State-Averaged Strategies
• Single-step Quantum Simulation of Two Nucleons
• A qubit-ADAPT Implementation for H₂ Molecules using an Explicitly Correlated Basis
• Molecular excited state calculations with the QEB-ADAPT-VQE
• A penalty-free quantum algorithm to find energy eigenstates