observable

Measurements in Pauli basis

Since R2024b

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

Description

An observable object represents a set of measurements in the Pauli basis, which corresponds to X, Y, and Z on the Bloch sphere. You can use an observable object to calculate the expected value of a quantum circuit or state in the specified basis.

For more information about observables, see Observable.

Creation

Syntax

o = observable(paulis,weights)

o = observable(hermitian)

Description

o = observable(paulis,weights) creates a set of measurements in the specified Pauli basis with the corresponding weights.

o = observable(hermitian) computes the equivalent Pauli basis and corresponding weights from the specified Hermitian matrix and the uses the basis and weights to create a set of measurements.

Input Arguments

paulis — Pauli basis measurements

string vector | character matrix

Pauli basis measurements, specified as a string vector or character matrix. Specify the elements of paulis as combinations of "X", "Y", "Z", or "I", where the jth character of an element indicates the specified measurement basis on the jth qubit.

Every element of paulis must have n characters, where n is the number of qubits in the quantum circuit or gate. paulis must have the same number of elements as weights.

This argument sets the Paulis property.

weights — Weights of Pauli basis measurements

real numeric vector

Weights of the Pauli basis measurements, specified as a real numeric vector. weights must have the same number of elements as paulis.

This argument sets the Weights property.

hermitian — Hermitian matrix

square matrix

Hermitian matrix, specified as a square matrix of size $$2^n$$-by-$$2^n$$, where n is the number of qubits in the quantum circuit or state.

Output Arguments

o — Set of measurements in Pauli basis

observable object

Set of measurements in the Pauli basis, returned as an observable object.

Properties

Paulis — Pauli basis measurements

string vector

This property is read-only.

Pauli basis measurements, represented as a string vector. The elements of paulis are combinations of "X", "Y", "Z", or "I", where the jth character of an element indicates the specified measurement basis on the jth qubit.

Every element of Paulis has n elements, where n is the number of qubits in the quantum circuit or gate. The Paulis vector has the same number of elements as the Weights vector.

Weights — Weights of Pauli basis measurements

real numeric vector

This property is read-only.

Weights of the Pauli basis measurements, represented as a real numeric vector. The Weights vector has the same number of elements as the Paulis vector.

NumQubits — Number of qubits

positive integer scalar

This property is read-only.

Number of qubits in the quantum circuit or state, represented as a positive integer scalar.

Object Functions

getMatrix

Matrix representation of observable

Examples

Create Observable from Pauli Measurements

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])

o = 
  observable with properties:

       Paulis: [2×1 string]
      Weights: [2×1 double]
    NumQubits: 2

Create Observable from Hermitian Matrix

Create an observable from a 4-by-4 Hermitian matrix.

H = [-1 0 0 2;
    0 -1 2 0;
    0 2 1 0;
    2 0 0 1];
o = observable(H)

o = 
  observable with properties:

       Paulis: [2×1 string]
      Weights: [2×1 double]
    NumQubits: 2

Examine the Pauli basis measurements and weights of the observable. The $\mathit{X}$ measurement basis is observed on the first and second qubits with weight 2 and the $\mathit{Z}$ measurement basis is observed on the first qubit with weight –1.

paulis = o.Paulis

paulis = 2×1 string
    "XX"
    "ZI"

weights = o.Weights

weights = 2×1

     2
    -1

More About

Observable

An observable is defined by a Hermitian matrix whose eigenvalues correspond to the possible measurement results of a quantum circuit or state. You can decompose this matrix into a weighted sum of smaller observables expressed in the Pauli basis.

Version History

Introduced in R2024b