Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits

Abstract

The Jordan-Wigner transformation maps a one-dimensional spin-1/2 system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with XX and ZZ couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the ZZ interaction arises due to an inductive coupling and the XX interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators.

5+5 pages, 9 figures

References in corpus (7)

• Charge insensitive qubit design derived from the Cooper pair box
• Digital quantum simulation of fermionic models with a superconducting circuit
• Quantum Simulation of the Hubbard Model with Dopant Atoms in Silicon
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment
• Fermionic Models with Superconducting Circuits
• Distortion of a reduced equilibrium density matrix: influence on quantum emulation

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