Adiabatic quantum computation (AQC), either in its universal form, or in the form of adiabatic quantum optimization, or quantum simulations, presents a viable alternative to gate-model quantum computation (GMQC). Although a part of the original motivation for introduction of the AQC was the promise of the increased stability against decoherence due to the energy gap between the ground and excited states, the question of the role of decoherence in AQC remains an open one. This uncertainty makes it important to quantify more precisely the decoherence properties of AQC. A crucial step towards this would be to de fine a quantitative characteristic of the decoherence strength in AQC, that plays a role similar to the decoherence time for GMQC. However, in the case of AQC, decoherence has qualitatively di fferent, static e ffect on the qubits, not limiting the operation time of an algorithm. In this work, we propose the ground state fi delity, defi ned as the distance between the open and closed system reduced density matrices normalized to the Boltzmann ground state probability, as a quantitative measure of decoherence-induced deformation of the ground state in AQC, analogous to the decoherence time for GMQC. We calculate the fidelity perturbatively at nite temperatures and express it through the same environmental noise correlators that determine the decoherence times in GMQC. We discuss the relation between fidelity and the relaxation and dephasing times of the qubits, and its projected scaling properties with the number of qubits.
In summary, we have proposed using ground state - fidelity as a quantity for measuring the strength of decoherence e ects in AQC. Fidelity plays a role similar to
decoherence time in GMQC, but takes into account qualitatively di fferent eff ects of environment on the ground state relevant to AQC. The fidelity is related to the relaxation processes and is relatively insensitive to the dephasing. Our numerical calculations indicate that fidelity close to unity can be achieved with a moderate qubit quality factor, even for large numbers of qubits. Ground state fi delity should be a useful measure of the environment related quality of AQC systems in the context of further work on important topics in AQC such as quantum error correction or the threshold theorem.
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