A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer
arXiv:1508.04328 · doi:10.1103/PhysRevA.93.032303
Abstract
Many phenomena of strongly correlated materials are encapsulated in the Fermi-Hubbard model whose thermodynamical properties can be computed from its grand canonical potential according to standard procedures. In general, there is no closed form solution for lattices of more than one spatial dimension, but solutions can be approximated with cluster perturbation theory. To model long-range effects such as order parameters, a powerful method to compute the cluster's Green's function consists in finding its self-energy through a variational principle of the grand canonical potential. This opens the possibility of studying various phase transitions at finite temperature in the Fermi-Hubbard model. However, a classical cluster solver quickly hits an exponential wall in the memory (or computation time) required to store the computation variables. Here it is shown theoretically that that the cluster solver can be mapped to a subroutine on a quantum computer whose quantum memory scales as the number of orbitals in the simulated cluster. A quantum computer with a few tens of qubits could therefore simulate the thermodynamical properties of complex fermionic lattices inaccessible to classical supercomputers.
19 pages, 14 figures
References in corpus (14)
- Quantum discord and the power of one qubit
- Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
- Digital quantum simulation of fermionic models with a superconducting circuit
- Boson Sampling for Molecular Vibronic Spectra
- Variational cluster approach to correlated electron systems in low dimensions
- Solving strongly correlated electron models on a quantum computer
- Digital quantum simulation of spin models with circuit quantum electrodynamics
- A Formulation of Lattice Gauge Theories for Quantum Simulations
- Variational cluster approach to the Hubbard model: Phase-separation tendency and finite-size effects
- Preparing thermal states of quantum systems by dimension reduction
- Variational cluster approach for strongly correlated lattice bosons in the superfluid phase
- Fermionic Models with Superconducting Circuits
- Variational cluster approach to s-wave pairing in heavy-fermion superconductors
- Variational Cluster Approximation to the Thermodynamics of Quantum Spin Systems
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