Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors

Abstract

A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic quantum evolution under the influence of a time-dependent Hamiltonian, where the - ideally short - fixed Trotter time steps are replaced by variational parameters. The method profits substantially from quantum variational error suppression, e.g., unitary quasi-static errors are mitigated within the algorithm. We test the performance of the VHA when applied to the Hubbard model in the presence of unitary control errors on quantum computers with realistic gate fidelities.

arXiv comment5+1 pages, 2 figures, 3 tables

References in corpus (24)

• Surface codes: Towards practical large-scale quantum computation
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Error mitigation for short-depth quantum circuits
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Effective quantum spin systems with ion traps
• Quantum Error Correction for Beginners
• Towards Practical Quantum Variational Algorithms
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Robust determination of molecular spectra on a quantum processor
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
• Blueprint for a microwave trapped-ion quantum computer
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Quantum algorithms to simulate many-body physics of correlated fermions
• Quantum gas microscopy of an attractive Fermi-Hubbard system
• Direct certification of a class of quantum simulations
• Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model
• A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer
• Effects of gate errors in digital quantum simulations of fermionic systems
• Reconstructing the ideal results of a perturbed analog quantum simulator
• Estimating the error of an analog quantum simulator by additional measurements

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