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Simulated Annealing Replica Exchange #377

@djelovina

Description

@djelovina

What it does

runs a multi-replica Metropolis-style simulation (with optional parallel-tempering swaps) using a provided sweep function. For each sweep step it:
Randomizes the order of replicas each sweep (permutation).
Calls the supplied sweep function for each replica to perform one Metropolis sweep and accumulates the returned delta energy into the replica's energy.
Tracks and stores the best state and energy seen per replica.
Optionally performs a parallel-tempering (PT) swap pass between neighboring temperatures using pt(...).

Outputs

returns best found energy and best found state

Intended purpose / typical use

Run a population of replicas at different temperatures to explore rugged energy landscapes.
Combine per-replica sweeps (user-supplied sweep) with periodic PT swaps to improve mixing and to find low-energy solutions.
Useful for QUBO/Ising optimization experiments and comparisons between different sweep implementations.

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