Operators

Operators are important constructs for many quantum applications. This section covers how to define and use spin operators as well as additional tools for defining more sophisticated operators.

Constructing Spin Operators

The spin_op type provides an abstraction for a general tensor product of Pauli spin operators, and their sums.

Spin operators are constructed using the spin.z(), spin.y(), spin.x(), and spin.i() functions, corresponding to the \(Z\), \(Y\), \(X\), and \(I\) Pauli operators. For example, spin.z(0) corresponds to a Pauli \(Z\) operation acting on qubit 0. The example below demonstrates how to construct the following operator \(2XYX - 3ZZY\).

import cudaq
from cudaq import spin

operator = 2 * spin.x(0) * spin.y(1) * spin.x(2) - 3 * spin.z(0) * spin.z( 1) * spin.y(2)

There are a number of convenient methods for combining, comparing, iterating through, and extracting information from spin operators and can be referenced here in the API.

Pauli Words and Exponentiating Pauli Words

The pauli_word type specifies a string of Pauli operations (e.g. ‘XYXZ’) and is convenient for applying operations based on exponentiated Pauli words. The code below demonstrates how a list of Pauli words, along with their coefficients, are provided as kernel inputs and converted into operators by the exp_pauli function.

The cell below applies the following operation: \(e^{i(0.432XZY +0.324IXX)}\)

words = ['XYZ', 'IXX']
coefficients = [0.432, 0.324]


@cudaq.kernel
def kernel(coefficients: list[float], words: list[cudaq.pauli_word]):
    q = cudaq.qvector(3)

    for i in range(len(coefficients)):
        exp_pauli(coefficients[i], q, words[i])