I'm studing how Quantum Metropolis Algorithm (QMA) works and I think that I've understood it. Generally, the basic Metropolis step for a gave hamiltonian at the inverse temperature $\beta$ is: 1) it starts with a initial state, 2) it changes it with a local random "kick operator", 3) it uses quantum phase estimation for evaluate the energy gap beetwen the initial state and the new state, 4) it applies a controlled rotation (based on the energy gap) to rotate an ancilla qubit prepared in a computational base state, 5) and finally it mesures this state to accept/reject the proposal new state.

First of all, I ask confirms wether this vague explanation is correct or not. Then I'll ask you the main question: in many articles on QMA, authors add to the general explanation of the Algorithm also a part where they use Quantum Simulated Annealing (QSA). I understand that this procedure is useful to switch from an initial state with high temperature to a state with lower, but I can't understand why this process is necessary: this "temperature correction" has not already done by the QMA previus described?

Maybe QSA is only an explanation of why QMA actually works...

Thank you in advance!

  • $\begingroup$ The QSA step is used in all Quantum Metropolis algorithms, or just a feature of Quantum-Quantum Metropolis algorithms, any references? There was a distinction between the two, the Quantum Metropolis algorithm, and the Quantum-Quantum one. $\endgroup$ – user3483902 Jul 21 at 18:41

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