qubo2ising

Convert QUBO problem to Ising observable

Since R2024b

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

Syntax

o = qubo2ising(qprob)

Description

o = qubo2ising(qprob) converts the QUBO problem to an equivalent Ising observable.

Examples

Convert QUBO to Ising Observable

Create a QUBO problem for the quadratic matrix Q, linear vector c, and constant term d, where

$$\begin{array}{l}\mathit{Q}=\left[\begin{array}{ccc}0& -1& 2\\ -1& 0& 4\\ 2& 4& 0\end{array}\right]\\ \mathit{c}=\left[\begin{array}{ccc}-5& 6& -4\end{array}\right]\\ \mathit{d}=12.\end{array}$$

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

qprob = 
  qubo with properties:

    QuadraticTerm: [3×3 double]
       LinearTerm: [3×1 double]
     ConstantTerm: 12
     NumVariables: 3

Convert the QUBO problem to an Ising observable.

o = qubo2ising(qprob)

o = 
  observable with properties:

       Paulis: [7×1 string]
      Weights: [7×1 double]
    NumQubits: 3

Evaluate the QUBO and calculate the expected value of the Ising observable at the point [0;1;0]. The Ising observable is an equivalent representation of the QUBO problem, so the values are the same.

x = [0;1;0];
s = quantum.gate.QuantumState("010");
objective = evaluateObjective(qprob,x)

objective = 
18

ev = observe(s,o)

ev = 
18

Input Arguments

qprob — QUBO problem

qubo object | matrix

QUBO problem, specified as a qubo object or matrix that represents the QUBO problem.

Output Arguments

o — Ising observable

observable object

Ising observable, returned as an observable object. The Pauli measurements are a combination of I and Z basis measurements.

More About

Ising Problem

The Ising problem has the same formulation as a QUBO problem but uses a linear transformation that converts the binary variables 0 and 1 to –1 and 1. These values corresponds to the eigenvalues of the Pauli Z measurement operator. For more information, see What Is a QUBO Problem?

Version History

Introduced in R2024b