Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
arXiv:2312.04105 · doi:10.1103/PhysRevResearch.6.023110
Abstract
Predicting the properties of strongly correlated materials is a significant challenge in condensed matter theory. The widely used dynamical mean-field theory faces difficulty in solving quantum impurity models numerically. Hybrid quantum--classical algorithms such as variational quantum eigensolver emerge as a potential solution for quantum impurity models. A common challenge in these algorithms is the rapid growth of the number of variational parameters with the number of spin-orbitals in the impurity. In our approach to this problem, we develop compact ansatzes using a combination of two different strategies. First, we employ compact physics-inspired ansatz, -unitary cluster Jastrow ansatz, developed in the field of quantum chemistry. Second, we eliminate largely redundant variational parameters of physics-inspired ansatzes associated with bath sites based on physical intuition. This is based on the fact that a quantum impurity model with a star-like geometry has no direct hopping between bath sites. We benchmark the accuracy of these ansatzes for both ground-state energy and dynamic quantities by solving typical quantum impurity models with/without shot noise. The results suggest that we can maintain the accuracy of ground-state energy while we drop the number of variational parameters associated with bath sites. Furthermore, we demonstrate that a moment expansion, when combined with the proposed ansatzes, can calculate the imaginary-time Green's functions under the influence of shot noise. This study demonstrates the potential for addressing complex impurity models in large-scale quantum simulations with fewer variational parameters without sacrificing accuracy.
References in corpus (53)
- Quantum Computing in the NISQ era and beyond
- A variational eigenvalue solver on a quantum processor
- Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
- Machine learning and the physical sciences
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Continuous-time Monte Carlo methods for quantum impurity models
- Adiabatic Quantum Computing
- Simulated Quantum Computation of Molecular Energies
- The Variational Quantum Eigensolver: a review of methods and best practices
- Fermionic quantum computation
- Scalable Quantum Simulation of Molecular Energies
- Density matrix embedding: A simple alternative to dynamical mean-field theory
- The Bravyi-Kitaev transformation for quantum computation of electronic structure
- Variational ansatz-based quantum simulation of imaginary time evolution
- Practical Quantum Error Mitigation for Near-Future Applications
- Variational Quantum Computation of Excited States
- Theory of variational quantum simulation
- Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
- Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
- Qulacs: a fast and versatile quantum circuit simulator for research purpose
- Even more efficient quantum computations of chemistry through tensor hypercontraction
- Variational quantum algorithms for discovering Hamiltonian spectra
- Hybrid quantum-classical approach to correlated materials
- Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
- Sequential minimal optimization for quantum-classical hybrid algorithms
- Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
- Orbital optimized unitary coupled cluster theory for quantum computer
- A Jastrow-type decomposition in quantum chemistry for low-depth quantum circuits
- How to discretize a quantum bath for real-time evolution
- Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver
- Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation
- Calculation of the Green's function on near-term quantum computers
- Complexity of quantum impurity problems
- Quantum Filter Diagonalization with Double-Factorized Hamiltonians
- Imaginary-time matrix product state impurity solver for dynamical mean-field theory
- Calculating transition amplitudes by variational quantum deflation
- Adaptive variational quantum eigensolvers for highly excited states
- Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in SrRuO
- Minimum Hardware Requirements for Hybrid Quantum-Classical DMFT
- Efficient hybridization fitting for dynamical mean-field theory via semi-definite relaxation
- Gutzwiller Hybrid Quantum-Classical Computing Approach for Correlated Materials
- Fully Algebraic and Self-consistent Effective Dynamics in a Static Quantum Embedding
- A 'moment-conserving' reformulation of GW theory
- Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
- Extending Density Matrix Embedding: A Static Two-Particle Theory
- Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models
- Sparse modeling of large-scale quantum impurity models with low symmetries
- DCore: Integrated DMFT software for correlated electrons
- Efficient Compression Of The Environment Of An Open Quantum System
- Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach
- Dynamical mean-field theory for the Hubbard-Holstein model on a quantum device
- Unitary Coupled Cluster: Seizing the Quantum Moment
- Constructing `full-frequency' spectra via moment constraints for coupled cluster Green's functions