Decoherence induced deformation of the ground state in adiabatic quantum computation

TL;DR

This paper investigates how decoherence, including virtual excitations, affects the ground state fidelity in adiabatic quantum computation, providing a quantitative measure and analyzing its dependence on qubit coherence times.

Contribution

It introduces the normalized ground state fidelity as a measure of decoherence effects, including virtual excitations, and relates it to qubit relaxation and dephasing times.

Findings

Virtual excitations reduce ground state fidelity even at zero temperature.

Normalized fidelity can be calculated perturbatively at finite temperatures.

Fidelity scaling depends on qubits' relaxation and dephasing times.

Abstract

Despite more than a decade of research on adiabatic quantum computation (AQC), its decoherence properties are still poorly understood. Many theoretical works have suggested that AQC is more robust against decoherence, but a quantitative relation between its performance and the qubits' coherence properties, such as decoherence time, is still lacking. While the thermal excitations are known to be important sources of errors, they are predominantly dependent on temperature but rather insensitive to the qubits' coherence. Less understood is the role of virtual excitations, which can also reduce the ground state probability even at zero temperature. Here, we introduce normalized ground state fidelity as a measure of the decoherence-induced deformation of the ground state due to virtual transitions. We calculate the normalized fidelity perturbatively at finite temperatures and discuss its relation to the qubits' relaxation and dephasing times, as well as its projected scaling properties.