# Annealing Approach to Quantum Tomography

## TL;DR

This paper proposes a novel quantum tomography method using annealing, formulating it as an optimization problem on classical parameters based on maximum entropy, and suggests it can be physically implemented via effective Hamiltonians.

## Contribution

It introduces a new annealing-based approach to quantum tomography by framing it as an optimization problem on classical parameters derived from maximum entropy principles.

## Key findings

- Formulates quantum tomography as a classical parameter optimization problem.
- Shows the objective function can be physically implemented as an effective Hamiltonian.
- Proposes quantum annealing to find the optimal parameters via ground state search.

## Abstract

Annealing approach to quantum tomography is theoretically proposed. First, based on the maximum entropy principle, we introduce classical parameters to combine "quantum models (or quantum states)" given a prior for potentially representing the unknown target state. Then, we formulate the quantum tomography as an optimization problem on the classical parameters, by employing relative entropy of the parametrized state with the target state as the objective function to be minimized. We show that the objective function is physically implementable, in a theoretical sense at least, as an effective Hamiltonian to be induced by physical interactions of the system with environment systems being prepared in the target state. Corollary, applying quantum annealing to the effective Hamiltonian, we can execute quantum tomography by obtaining the ground state that gives the optimal parameters.