Pauli Measurement

In the field of quantum machine learning, Pauli measurements are commonly used to obtain the expectation value of a quantum circuit.

Creating isQ Code

Create a new .isq file named pauli_measurement.isq, and place it in the same directory. This file should define a quantum circuit that includes the necessary operations for performing measurements in the Pauli basis.

import std;

qbit q[1];
int pauli_inx[] = [2]; // this means Z0

// using arrays for pauli measurement
// X:0, Y:1, Z:2, I:3
// examples:
// int pauli_inx[] = {2, 2} -> Z0Z1
// int pauli_inx[] = {0, 1, 2, 3} -> X0Y1Z2I3
// int pauli_inx[] = {1} -> Y0

unit pauli(int puali_idx[], qbit q[]) {
    for i in 0:puali_idx.length {
        if (puali_idx[i] == 0) {
            H(q[i]);
            M(q[i]);
        }
        if (puali_idx[i] == 1) {
            X2P(q[i]);
            M(q[i]);
        }
        if (puali_idx[i] == 2) {
            M(q[i]);
        }
        if (puali_idx[i] == 3) {
            continue;
        }
    }
}

unit main() {
    Ry(1.0, q[0]);
    pauli(pauli_inx, q);
    // Z0 measure
}

We use tempfileto simulate here.

FILE_CONTENT = """\
import std;

qbit q[1];
int pauli_inx[] = [2]; // this means Z0

// using arrays for pauli measurement
// X:0, Y:1, Z:2, I:3
// examples:
// int pauli_inx[] = {2, 2} -> Z0Z1
// int pauli_inx[] = {0, 1, 2, 3} -> X0Y1Z2I3
// int pauli_inx[] = {1} -> Y0

unit pauli(int puali_idx[], qbit q[]) {
    for i in 0:puali_idx.length {
        if (puali_idx[i] == 0) {
            H(q[i]);
            M(q[i]);
        }
        if (puali_idx[i] == 1) {
            X2P(q[i]);
            M(q[i]);
        }
        if (puali_idx[i] == 2) {
            M(q[i]);
        }
        if (puali_idx[i] == 3) {
            continue;
        }
    }
}

unit main() {
    Ry(1.0, q[0]);
    pauli(pauli_inx, q);
    // Z0 measure
}"""

Pauli Measurement

The file pauli_measurement.isq provides an example of how to perform Pauli measurements. Please refer carefully to the comments in the .isq file for detailed explanations.

After creating an instance of IsqCircuit (e.g., qc), you can perform a Pauli measurement by calling qc.pauli_measure(). This function returns the result of the Pauli measurement, with the output value ranging from −1 to 1.

import tempfile
from pathlib import Path

from isqtools import IsqCircuit
from isqtools.backend import NumpyBackend
from isqtools.draw import Drawer

with tempfile.TemporaryDirectory() as temp_dir:
    temp_dir_path = Path(temp_dir)
    temp_file_path = temp_dir_path / "pauli_measurement.isq"
    with open(temp_file_path, "w") as temp_file:
        temp_file.write(FILE_CONTENT)
    backend = NumpyBackend()
    qc = IsqCircuit(
        file=str(temp_file_path),
        backend=backend,
        sample=False,
    )

    print(qc.pauli_measure())
    dr = Drawer()
    dr.plot(qc.qcis)

0.5403023058681398

Environment Information

The following versions of software and libraries are used in this tutorial:

import platform
import subprocess
from importlib.metadata import version

print(f"Python version used in this tutorial: {platform.python_version()}")
print(f"Execution environment: {platform.system()} {platform.release()}\n")


isqc_version = subprocess.check_output(
    ["isqc", "-V"], stderr=subprocess.STDOUT, text=True
).strip()
print(f"isqc version: {isqc_version}")

isqtools_version = version("isqtools")
print(f"isqtools version: {isqtools_version}")

numpy_version = version("numpy")
print(f"NumPy version: {numpy_version}")

Python version used in this tutorial: 3.13.5
Execution environment: Linux 6.12.41

isqc version: isQ Compiler 0.2.5
isqtools version: 1.3.0
NumPy version: 2.3.1