getMatrix

Matrix representation of observable

Since R2024b

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

Syntax

H = getMatrix(o)

Description

H = getMatrix(o) returns the sparse Hermitian matrix representation of the specified observable. For more information, see Matrix Representation of Observable.

Examples

Matrix Representation of Observable

Create an observable from a two-qubit Pauli basis measurement where the $\mathit{X}$ measurement basis is observed on the first and second qubits with weight 2.4 and the $\mathit{Z}$ measurement basis is observed on the first qubit with weight –1.2.

o = observable(["XX" "ZI"],[2.4 -1.2]);

Get the sparse Hermitian matrix representation of the observable.

H = getMatrix(o)

H = 4×4 sparse double matrix (8 nonzeros)
   (1,1)      -1.2000
   (4,1)       2.4000
   (2,2)      -1.2000
   (3,2)       2.4000
   (2,3)       2.4000
   (3,3)       1.2000
   (1,4)       2.4000
   (4,4)       1.2000

Input Arguments

o — Observable

observable object

Observable, specified as an observable object.

Output Arguments

H — Matrix representation of observable

sparse Hermitian matrix

Matrix representation of the observable, returned as a sparse Hermitian matrix. The size of the matrix is $$2^n$$-by-$$2^n$$, where n is the number of qubits in the quantum circuit or state.

Limitations

• As the number of qubits n increases, the size of the matrix grows exponentially as $$2^n$$-by-$$2^n$$. So, using getMatrix is practical only when n is less than about 15.

More About

Matrix Representation of Observable

The matrix representation of an observable is calculated as a linear combination of the Kronecker products of the specified Pauli basis measurements. For example, the matrix representation of an observable with Pauli basis measurements ["XX" "ZI"] and corresponding weights [2.4 -1.2] is calculated as

$$2.4(X\otimes X)-1.2(Z\otimes I)=2.4\left[\begin{array}{cccc}0& 0& 0& 1\\ 0& 0& 1& 0\\ 0& 1& 0& 0\\ 1& 0& 0& 0\end{array}\right]-1.2\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& -1\end{array}\right]=\left[\begin{array}{cccc}-1.2& 0& 0& 2.4\\ 0& -1.2& 2.4& 0\\ 0& 2.4& 1.2& 0\\ 2.4& 0& 0& 1.2\end{array}\right].$$

Version History

Introduced in R2024b