Simulating a ring-like Hubbard system with a quantum computer

Abstract

We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a product state to an intrinsically interacting ground state as hopping amplitudes are changed. We locate this transition and solve for the ground state energy with high quantitative accuracy using a variational quantum algorithm executed on an IBM quantum computer. Our results are enabled by a variational ansatz that takes full advantage of the maximal set of commuting ${\mathbb{Z}}_2$ symmetries of the problem and a Lanczos-inspired error mitigation algorithm. They are a benchmark on the way to exploiting near term quantum simulators for quantum many-body problems.

References in corpus (34)

• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Quantum machine learning in feature Hilbert spaces
• Superconducting Qubits: Current State of Play
• Error mitigation for short-depth quantum circuits
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Extending the computational reach of a noisy superconducting quantum processor
• Scalable Quantum Simulation of Molecular Energies
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Quantum optimization using variational algorithms on near-term quantum devices
• Implementation of a Quantum Search Algorithm on a Nuclear Magnetic Resonance Quantum Computer
• Robust determination of molecular spectra on a quantum processor
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Solving strongly correlated electron models on a quantum computer
• Quantum Risk Analysis
• Simulating quantum many-body dynamics on a current digital quantum computer
• Option Pricing using Quantum Computers
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Challenges and Opportunities of Near-Term Quantum Computing Systems
• Verifying Multipartite Entangled GHZ States via Multiple Quantum Coherences
• Reducing qubit requirements for quantum simulation using molecular point group symmetries
• Identification of symmetry-protected topological states on noisy quantum computers
• Many-body physics in the NISQ era: quantum programming a discrete time crystal
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Fragile Mott Insulators
• Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems
• Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors
• Algorithmic Error Mitigation Scheme for Current Quantum Processors
• Probing many-body localization on a noisy quantum computer
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• Möbius molecules and fragile Mott insulators

Cited by in corpus (8)

• Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer
• Using Differential Evolution to avoid local minima in Variational Quantum Algorithms
• Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation
• A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems
• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models
• Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study
• Recursive relations and quantum eigensolver algorithms within modified Schrieffer--Wolff transformations for the Hubbard dimer