Distortion of a reduced equilibrium density matrix: Influence on quantum emulation

Abstract

We study a system coupled to external degrees of freedom, called bath, where we assume that the total system consisting of system and bath is in equilibrium. An expansion in the coupling between system and bath leads to a general form of the reduced density matrix of the system as a function of the bath self energy. The coupling to the bath results in a renormalization of the energies of the system and in a change of the eigenbasis. This theory is applicable to quantum emulators in thermal equilibrium. Undesired external degrees of freedom can affect their reliability. We study the influence of bosonic degrees of freedom on the state of a six qubit system.

Reconstructing the ideal results of a perturbed analog quantum simulator

“…The total system described by H is in thermal equilibrium. It should be emphasized that if coupling to the thermal bath is not infinitely weak it cannot be assumed that the only result of this coupling is the creation of equilibrium [54][55][56]. In the main part of this paper we focus on the situation at zero temperature and in Sec.…”

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

“…But we estimate that qubit designs are available with sufficient quality to simulate the quantum state evolution on interesting, long time scales before decoherence dominates the dynamics. The effects of a bath coupled to a quantum emulator have been investigated in part [24] but need to be explored further. For a first estimate we have to compare the microscopic time scales with the decoherence time, or inversely, the coupling energies with the decoherence rate.…”

Detector Readout of Analog Quantum Simulators

“…Note that in our treatment, the system-bath coupling is weak with its only effect being to thermalize the system to equilibrium. The influences of strong simulator-bath coupling and structured spectrum have been studied in [41][42][43][44][45].…”