Distinguishing thermal versus quantum annealing using probability-flux signatures across interaction networks

• URL: http://arxiv.org/abs/2511.16457v1
• Date: Thu, 20 Nov 2025 15:23:53 GMT
• Title: Distinguishing thermal versus quantum annealing using probability-flux signatures across interaction networks
• Abstract summary: We show that thermal and quantum fluctuations navigate a system toward the ground state in simulated annealing.<n>These insights may improve mappings of optimization problems to Ising spin systems, yielding more accurate solutions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Simulated annealing provides a heuristic solution to combinatorial optimization problems. The cost function of a problem is mapped to the energy function of a physical many-body system, and, using thermal or quantum fluctuations, the system explores the state space to find the ground state, which may correspond to the optimal solution of the problem. Studies have highlighted both the similarities and differences between thermal and quantum fluctuations. Nevertheless, fundamental understanding of thermal and quantum annealing remains incomplete, making it difficult to design problem instances that fairly compare the two methods. Here, we investigate the many-body dynamics of thermal and quantum annealing by examining all possible interaction networks of $\pm J$ Ising spin systems up to seven spins. Our comprehensive investigation reveals that differences between thermal and quantum annealing emerge for particular interaction networks, indicating that the structure of the energy landscape distinguishes the two dynamics. We identify the microscopic origin of these differences through probability fluxes in state space, finding that the two dynamics are broadly similar but that quantum tunnelling produces qualitative differences. Our results provide insight into how thermal and quantum fluctuations navigate a system toward the ground state in simulated annealing, and are experimentally verifiable in atomic, molecular, and optical systems. Furthermore, these insights may improve mappings of optimization problems to Ising spin systems, yielding more accurate solutions in faster simulated annealing and thus benefiting real-world applications in industry. Our comprehensive survey of interaction networks and visualization of probability flux can help to understand, predict, and control quantum advantage in quantum annealing.

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