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Oxford University Press eBooks

Quantum noise and dissipation

J. C. Garrison, R. Y. Chiao

Published Jun 5, 2008• 0 citations
Publisher
DOI
10.1093/acprof:oso/9780198508861.003.0015

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Abstract Gain‐dissipative Ising machines (GIMs) are a type of quantum analog equipment that can rapidly determine the optimal solution for combinatorial optimization problems. When the noise intensity is significantly lower than the fixed point of the system, the performance of a GIM is not influenced by the fluctuation of the noise intensity. However, the noise in this study is limited to Gaussian white noise. The influence of prevalent colored noise on GIMs has not been researched. In this study, the influence of common‐colored noise on the performance of GIMs is numerically investigated. The results of a domain clustering dynamics analysis reveal that red noise can better suppress the generation of the noise‐induced irregular temporary domain. Furthermore, several prevalent MAXCUT problem topologies, including the Moebius ladder, random Moebius ladder, and 2D random lattice, are adopted as test benchmarks. The results reveal that GIMs influenced by white, blue, and violet noise perform better at low‐intensity noise condition. In contrast, pink and red noise‐injected GIMs demonstrate higher performances when applied to MAXCUT topologies with both ferromagnetic and antiferromagnetic connections under larger noise intensity conditions. This indicates that the noise dispersion can be used as an additional hyperparameter to optimize the performance of GIMs.
We study the current noise spectrum of qubits under transport conditions in a dissipative bosonic environment. We combine (non-)Markovian master equations with correlation functions in Laplace space to derive a noise formula for both weak and strong coupling to the bath. The coherence-induced reduction of noise is diminished by weak dissipation and/or a large level separation (bias). For weak dissipation, we demonstrate that the dephasing and relaxation rates of the two-level systems can be extracted from noise. In the strong dissipation regime, the localization-delocalization transition becomes visible in the low-frequency noise.