/singleshot-bayesian-estimation

Code repository for "Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations"

Primary LanguageMATLABGNU General Public License v3.0GPL-3.0

Code to accompany: Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations

Jessica Bavaresco, Patryk Lipka-Bartosik, Pavel Sekatski, and Mohammad Mehboudi

This is a repository for the code used in the article "Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations, Jessica Bavaresco, Patryk Lipka-Bartosik, Pavel Sekatski, and Mohammad Mehboudi, Phys. Rev. Research 6, 023305 (2024), arXiv:2311.01513 [quant-ph]".

All code is written in MATLAB and requires:

  • Yalmip - a free MATLAB toolbox for rapid prototyping of optimization problems
  • SeDuMi - a linear/quadratic/semidefinite solver for Matlab and Octave
  • QETLAB - a free MATLAB toolbox for quantum entanglement theory

This repository consists of the following:

CODE

  • SDP_scoreoptimization.m: SDP that solves the optimization in Eq. (18). That is, that given a set of operators { $X(\hat{\theta}_i)$ }, maximizes or minimizes (depending on the reward/cost function) the score $\mathcal{S}$ over testers $T=$ { $T_i$ }.

  • tester2realization.m: Function that computes a quantum state and measurement that compose a quantum realization of a given tester, according to Eqs. (12) and (13) of the paper.

  • script_phaseestimation.m: Script for the metrology problem presented in Sec. V.A. Example 1: Paradigmatic example – Local phase estimation It evaluates methods 1, 2, and 3 for the parameters of this example, outlined in the paper.

  • script_thermometry.m: Script for the metrology problem presented in Sec. V.B. Example 2: Non-unitary evolution – Thermometry. It evaluates methods 1, 2, and 3 for the parameters of this example, outlined in the paper.

  • script_su2estimation.m: Script for the metrology problem presented in Sec. V.C. Example 3: Multi-parameter estimation – SU(2) gates. It evaluates methods 1, 2, and 3 for the parameters of this example, outlined in the paper.

DATA

  • data_phaseestimation.mat: Output data obtained from script_phaseestimation.m containing the optimal scores, testers, states and measurements found by our methods for the metrology problem presented in Sec. V.A. Example 1: Paradigmatic example – Local phase estimation.

  • data_thermometry_scores&testers.mat: Output data obtained from script_thermometry.m containing the optimal scores and testers found by our methods for the metrology problem presented in Sec. V.B. Example 2: Non-unitary evolution – Thermometry.

  • data_thermometry_states.mat: Output data obtained from script_thermometry.m containing the optimal states found by our methods for the metrology problem presented in Sec. V.B. Example 2: Non-unitary evolution – Thermometry.

  • data_thermometry_measurements.mat: Output data obtained from script_thermometry.m containing the measurements found by our methods for the metrology problem presented in Sec. V.B. Example 2: Non-unitary evolution – Thermometry.

  • data_su2estimation.mat: Output data obtained from script_su2estimation.m containing the optimal scores, testers, states and measurements found by our methods for the metrology problem presented in Sec. V.C. Example 3: Multi-parameter estimation – SU(2) gates.