Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
arXiv:2506.19150 · doi:10.1063/5.0294540
Abstract
We present an adaptive variational quantum algorithm to estimate the Berry phase accumulated by a nondegenerate ground state under cyclic, adiabatic evolution of a time-dependent Hamiltonian. Our method leverages cyclic adiabatic evolution of the Hamiltonian and employs adaptive variational quantum algorithms for state preparation and evolution, optimizing circuit efficiency while maintaining high accuracy. We benchmark our approach on dimerized Fermi-Hubbard chains with four sites, demonstrating precise Berry phase simulations in both noninteracting and interacting regimes. Our results show that circuit depths reach up to 106 layers for noninteracting systems and increase to 279 layers for interacting systems due to added complexity. Additionally, we demonstrate the robustness of our scheme across a wide range of parameters governing adiabatic evolution and variational algorithm. These findings highlight the potential of adaptive variational quantum algorithms for advancing quantum simulations of topological materials and computing geometric phases in strongly correlated systems.
References in corpus (67)
- Topological Insulators
- Topological insulators and superconductors
- Quantum Computing in the NISQ era and beyond
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Berry Phase Effects on Electronic Properties
- Weyl and Dirac Semimetals in Three Dimensional Solids
- Maximally localized Wannier functions: Theory and applications
- Adiabatic Quantum Computing
- Simulated Quantum Computation of Molecular Energies
- Shortcuts to adiabaticity: concepts, methods, and applications
- Zoo of quantum-topological phases of matter
- Symmetry protection of topological order in one-dimensional quantum spin systems
- Quantum algorithms for quantum chemistry and quantum materials science
- Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
- Quantum Error Mitigation
- Toward the first quantum simulation with quantum speedup
- Theory of variational quantum simulation
- qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
- Bounds for the adiabatic approximation with applications to quantum computation
- Simulating quantum many-body dynamics on a current digital quantum computer
- Minimizing irreversible losses in quantum systems by local counter-diabatic driving
- Observation of topological transitions in interacting quantum circuits
- Detecting topological invariants in nonunitary discrete-time quantum walks
- Floquet-engineering counterdiabatic protocols in quantum many-body systems
- Qubit-excitation-based adaptive variational quantum eigensolver
- Crossing a topological phase transition with a quantum computer
- Fisher Information in Noisy Intermediate-Scale Quantum Applications
- Adaptive Variational Quantum Dynamics Simulations
- Sufficiency Criterion for the Validity of the Adiabatic Approximation
- Identification of symmetry-protected topological states on noisy quantum computers
- Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
- The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation
- Many-body topological invariants from randomized measurements
- Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation
- Efficient step-merged quantum imaginary time evolution algorithm for quantum chemistry
- Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
- Measuring the winding number in a large-scale chiral quantum walk
- Topological phases of a dimerized Fermi-Hubbard model for semiconductor nano-lattices
- Fermionic projected entangled-pair states and topological phases
- Measuring the Berry Phase in a Superconducting Phase Qubit by a Shortcut to Adiabaticity
- Digital Simulation of Topological Matter on Programmable Quantum Processors
- Gutzwiller Hybrid Quantum-Classical Computing Approach for Correlated Materials
- Entanglement Spectrum of Su-Schrieffer-Heeger-Hubbard Model
- Necessary and sufficient condition for quantum adiabatic evolution by unitary control fields
- Effective calculation of the Green's function in the time domain on near-term quantum processors
- Observation of higher-order topological states on a quantum computer
- Error Bounds for Variational Quantum Time Evolution
- Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
- Calculating nonadiabatic couplings and Berry's phase by variational quantum eigensolvers
- Path-integral Monte Carlo method for the local Z_2 Berry phase
- Berry Phase Estimation in Gate-Based Adiabatic Quantum Simulation
- Bang-bang shortcut to adiabaticity in trapped ion quantum simulators
- Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
- Berry phase in lattice QCD
- Robust measurement of wave function topology on NISQ quantum computers
- Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates
- Quantum subspace expansion in the presence of hardware noise
- Sufficient conditions for adiabaticity in open quantum systems
- Measuring Berry curvature with quantum Monte Carlo
- Quantum computing topological invariants of two-dimensional quantum matter
- Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
- Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
- Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
- Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
- Detecting quasi-degenerate ground states in topological models via variational quantum eigensolver
- Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers
- Su-Schrieffer-Heeger-Hubbard model at quarter filling: effects of magnetic field and non-local interactions