Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer

Abstract

Calculating the equilibrium properties of condensed matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude $⟨\psi |e^{-i\hat{H}t}|\psi ⟩$ from initial states $|\psi ⟩$ and a time evolution under the Hamiltonian $\hat{H}$ up to short times $t$. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a $16$-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm.

18 pages, 12 figures

References in corpus (31)

• Thermalization and its mechanism for generic isolated quantum systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Demonstration of the trapped-ion quantum-CCD computer architecture
• A Race Track Trapped-Ion Quantum Processor
• Time-evolving a matrix product state with long-ranged interactions
• Quantum Simulation for High Energy Physics
• Spectral functions in one-dimensional quantum systems at T>0
• Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• Toolbox for entanglement detection and fidelity estimation
• Mott insulating states with competing orders in the triangular lattice Hubbard model
• Algorithms for quantum simulation at finite energies
• A Compact Fermion to Qubit Mapping
• Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer
• Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation
• Classically optimized Hamiltonian simulation
• Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
• Classical simulation of short-time quantum dynamics
• Optimal compression of quantum many-body time evolution operators into brickwall circuits
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics
• Simulating prethermalization using near-term quantum computers
• Classical algorithms for many-body quantum systems at finite energies
• Phase-Sensitive Quantum Measurement without Controlled Operations
• Time Evolution of Uniform Sequential Circuits
• Calculating the many-body density of states on a digital quantum computer
• Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers
• Energy-filtered random-phase states as microcanonical thermal pure quantum states
• Random insights into the complexity of two-dimensional tensor network calculations

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• Experimental Demonstration of Break-Even for the Compact Fermionic Encoding
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• Energy-filtered quantum states and the emergence of non-local correlations
• Lindblad engineering for quantum Gibbs state preparation under the eigenstate thermalization hypothesis
• Experimental demonstration of optimal measurement for unambiguously discriminating asymmetric qudit states
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• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Extracting the spin excitation spectrum of a fermionic system using a quantum processor
• Probabilistic imaginary-time evolution in state-vector-based and shot-based simulations and on quantum devices
• Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model