Classical algorithms for many-body quantum systems at finite energies

Abstract

We investigate quantum inspired algorithms to compute physical observables of quantum many-body systems at finite energies. They are based on the quantum algorithms proposed in [Lu et al. PRX Quantum 2, 020321 (2021)], which use the quantum simulation of the dynamics of such systems, as well as classical filtering and sampling techniques. Here, we replace the quantum simulation by standard classical methods based on matrix product states and operators. As a result, we can address significantly larger systems than those reachable by exact diagonalization or by other algorithms. We demonstrate the performance with spin chains up to 80 sites.

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Cited by in corpus (12)

• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics
• Simulating prethermalization using near-term quantum computers
• Microcanonical windows on quantum operators
• 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
• Microcanonical Free Cumulants in lattice systems
• Matrix product state approximations to quantum states of low energy variance
• Efficient Quantum Algorithm for Filtering Product States
• Dilution of error in digital Hamiltonian simulation
• Simulating Floquet scrambling circuits on trapped-ion quantum computers
• Probing Off-diagonal Eigenstate Thermalization with Tensor Networks