qaoaResult

Result of solving QUBO problem using QAOA

Since R2024b

Installation Required: This functionality requires MATLAB Support Package for Quantum Computing.

Description

The properties of the qaoaResult object provide information about the QAOA solution process for solving a QUBO problem. If you solve a QUBO problem using the solve function with Algorithm set to a qaoa object, then the resulting solution is a quboResult object that contains a qaoaResult object.

Properties

BestX — Solution point with smallest objective function value

real vector

This property is read-only.

Solution point with the smallest objective function value, returned as a real vector. BestX corresponds to an entry in AllX with the smallest objective function value.

BestFunctionValue — Smallest objective function value found

real scalar

This property is read-only.

Smallest objective function value found, returned as a real scalar. BestFunctionValue is the smallest entry in AllFunctionValues.

AllX — Solutions returned when using QAOA

real matrix

This property is read-only.

Solutions returned when using QAOA, returned as a real matrix. Each column of the matrix represents one potential solution. The associated objective function value is in the corresponding entry of AllFunctionValues.

AllFunctionValues — Objective function values returned when using QAOA

real vector

This property is read-only.

Objective function values returned when using QAOA, returned as a real vector. The objective function values correspond to the columns of AllX.

AlgorithmInformation — Circuit angle optimization results

structure

This property is read-only.

Circuit angle optimization results, returned as a structure containing the fields in this table.

Field Name	Description
AllProbabilities	Vector containing the probabilities of each unique solution being sampled from the circuit using the angles returned by the optimization solver, BestCircuitAngles
BestCircuitAngles	Array of cost and mixer gate angles returned by the optimization solver
BestExpectedValue	Best expected value returned by the optimization solver
Exitflag	exitflag returned by the optimization solver
Output	output structure returned by the optimization solver
Circuit	quantumCircuit object used in the optimization with angles set to BestCircuitAngles

ClockTime — Duration that the algorithm runs in seconds

real scalar

This property is read-only.

Duration that the algorithm runs in seconds, returned as a real scalar. ClockTime is measured internally using tic and toc.

Examples

Examine QAOA Result

Create and solve a QUBO problem using QAOA.

Q = [0 -1 2; ...
    -1 0 4; ...
    2 4 0];
c = [-5 6 -4];
d = 12;
qprob = qubo(Q,c,d);
result = solve(qprob,Algorithm=qaoa)

 
Exiting: Maximum number of function evaluations has been exceeded
         - increase MaxFunEvals option.
         Current function value: -0.970000 

result = 
  quboResult with properties:

                BestX: [3×1 double]
    BestFunctionValue: 7
      AlgorithmResult: [1×1 qaoaResult]

Examine the algorithm-specific result details.

result.AlgorithmResult

ans = 
  qaoaResult with properties:

                   BestX: [3×1 double]
       BestFunctionValue: 7
                    AllX: [3×8 double]
       AllFunctionValues: [12 8 18 22 7 7 11 19]
    AlgorithmInformation: [1×1 struct]
               ClockTime: 0.7632

Examine the details of the circuit angle optimization.

result.AlgorithmResult.AlgorithmInformation

ans = struct with fields:
     AllProbabilities: [0.2279 0.1630 0.1234 0.1091 0.0105 0.1296 0.2094 0.0271]
    BestCircuitAngles: [2×1 double]
    BestExpectedValue: -0.9700
             Exitflag: 0
               Output: [1×1 struct]
              Circuit: [1×1 quantumCircuit]

Algorithms

QAOA is a quantum-classical hybrid approach to solving optimization problems. In general, a quantum circuit represents possible solutions to the problem and a classical optimizer iteratively adjusts the angles in the circuit to improve the quality of the solution. The quantum circuit uses alternating layers of cost and mixer gates to approximately solve the provided problem. For details, see Solve Max-Cut Problem Using QAOA.

References

[1] Farhi, Edward, Jeffrey Goldstone, and Sam Gutmann. “A Quantum Approximate Optimization Algorithm.” arXiv, November 14, 2014. https://doi.org/10.48550/arXiv.1411.4028.

Version History

Introduced in R2024b