Berry Phase Estimation in Gate-Based Adiabatic Quantum Simulation

Abstract

Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate the Berry phase and use it to classify the topological order of both single-particle and interacting models, highlighting the differences between the two. This algorithm is immediately extensible to any interacting topological system. Our results evidence the potential of near-term quantum hardware for the topological classification of quantum matter.

Main text: 4 pages, 3 figures; Supplemental material: 9 pages, 9 figures

References in corpus (28)

• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Adiabatic Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• Quantum Algorithms Revisited
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Towards Quantum Chemistry on a Quantum Computer
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• Synthesis of Quantum Logic Circuits
• The Zak phase and the existence of edge states in graphene
• Digitized adiabatic quantum computing with a superconducting circuit
• Cloud Quantum Computing of an Atomic Nucleus
• Topological Phases in Graphene Nanoribbons: Junction States, Spin Centers and Quantum Spin Chains
• Solving strongly correlated electron models on a quantum computer
• Destructive quantum interference in spin tunneling problems
• Error-mitigated digital quantum simulation
• Observation of topological transitions in interacting quantum circuits
• Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark
• Measuring a topological transition in an artificial spin 1/2 system
• Quantized Berry Phases as Local Order Parameters of Quantum Liquids
• Observing Topological Invariants Using Quantum Walk in Superconducting Circuits
• Dynamical Quantum Hall Effect in the Parameter Space
• Observation of topological Uhlmann phases with superconducting qubits
• Digital Quantum Simulation of the Statistical Mechanics of a Frustrated Magnet
• Realizing and detecting a topological insulator in the AIII symmetry class

Cited by in corpus (10)

• Simulating Quantum Materials with Digital Quantum Computers
• Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates
• Digital Simulation of Topological Matter on Programmable Quantum Processors
• Calculating nonadiabatic couplings and Berry's phase by variational quantum eigensolvers
• Robust measurement of wave function topology on NISQ quantum computers
• A hybrid quantum algorithm to detect conical intersections
• Cavity-QED of a quantum metamaterial with tunable disorder
• Quantum computing topological invariants of two-dimensional quantum matter
• Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach