Simulating excited states of the Lipkin model on a quantum computer

Abstract

We simulate the excited states of the Lipkin model using the recently proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM on classical computers and gives access to collective excitations based on quasi-boson operators ${\hat{O}}_n^{†}(\alpha )$ of increasing configuration complexity $\alpha$. We show, in particular, that the accuracy strongly depends on the fermion to qubit encoding. Standard encoding leads to large errors, but the use of symmetries and the Gray code reduces the quantum resources and improves significantly the results on current noisy quantum devices. With this encoding scheme, we use IBM quantum machines to compute the energy spectrum for a system of $N=2,3$ and $4$ particles and compare the accuracy against the exact solution. We found that the results of the approach with $\alpha =2$, an analog of the second random phase approximation (SRPA), are, in principle, more accurate than with $\alpha =1$, which corresponds to the random phase approximation (RPA), but the SRPA is more amenable to noise for large coupling strengths. Thus, the proposed scheme shows potential for achieving higher spectroscopic accuracy by implementations with higher configuration complexity, if a proper error mitigation method is applied.

Article: 20 pages, 10 figures

References in corpus (16)

• Theory of Core-Collapse Supernovae
• Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Entanglement Rearrangement in Self-Consistent Nuclear Structure Calculations
• Improving Hamiltonian encodings with the Gray code
• Fragmentation and systematics of the Pygmy Dipole Resonance in the stable N=82 isotones
• Preparation of excited states for nuclear dynamics on a quantum computer
• Lipkin model on a quantum computer
• Symmetry assisted preparation of entangled many-body states on a quantum computer
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
• Toward an accurate strongly-coupled many-body theory within the equation of motion framework
• Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches
• Selected topics of quantum computing for nuclear physics
• A digital quantum simulation of the Agassi model
• Effective shell-model interaction for nuclei southeast of ${}^{100}$Sn
• Many-body approach to superfluid nuclei in axial geometry

Cited by in corpus (17)

• Quantum computing of the ${}^6$Li nucleus via ordered unitary coupled clusters
• Quantum Simulations in Effective Model Spaces (I): Hamiltonian Learning-VQE using Digital Quantum Computers and Application to the Lipkin-Meshkov-Glick Model
• Multi-Body Entanglement and Information Rearrangement in Nuclear Many-Body Systems
• Finite-size criticality in fully connected spin models on superconducting quantum hardware
• Quantum Simulations of SO(5) Many-Fermion Systems using Qudits
• Quantum computation of nuclear observables involving linear combination of unitary operators
• A quantum-classical co-processing protocol towards simulating nuclear reactions on contemporary quantum hardware
• Scattering phase shifts from a quantum computer
• Accurate and precise quantum computation of valence two-neutron systems
• A Quantum Simulation Approach to Implementing Nuclear Density Functional Theory via Imaginary Time Evolution
• Variational simulation of the Lipkin-Meshkov-Glick model on a neutral atom quantum computer
• Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics
• Quantum techniques for eigenvalue problems
• Quantum computing of the pairing Hamiltonian at finite temperatures
• Emulating generator coordinate method with extended eigenvector continuation: Lipkin-Meshkov-Glick model
• Toward scalable quantum computations of atomic nuclei
• Exploring fixed points and eigenstates of quantum systems with reinforcement learning