qutip

name	qutip
description	Compute quantum state expectation values for Pauli matrices from Bloch sphere coordinates. Use when working with quantum state analysis, Bloch sphere representation, or Pauli matrix expectation values.

QuTiP: Quantum State Expectation Values from Bloch Sphere

Overview

Given Bloch sphere coordinates (theta, phi), compute the expectation values of the three Pauli matrices (σx, σy, σz).

Creating Quantum State from Bloch Coordinates

from qutip import spin_coherent, expect, sigmax, sigmay, sigmaz
import numpy as np

# Read theta and phi in degrees
theta_deg, phi_deg = map(float, open("/root/input.txt").read().split())
theta = np.radians(theta_deg)  # Convert to radians
phi = np.radians(phi_deg)

# Create quantum state on Bloch sphere
# spin_coherent(s, theta, phi) where s=1/2 for qubit
psi = spin_coherent(1/2, theta, phi)

# Compute expectation values
sx = expect(sigmax(), psi)
sy = expect(sigmay(), psi)
sz = expect(sigmaz(), psi)

# Print results with 3 decimal places
print(f"Sigma X: {sx:+.3f}")
print(f"Sigma Y: {sy:+.3f}")
print(f"Sigma Z: {sz:+.3f}")

Key Functions

spin_coherent(s, theta, phi)

Creates a coherent spin state on the Bloch sphere.

• s: spin quantum number (use 1/2 for qubit)
• theta: polar angle in radians (0 to π)
• phi: azimuthal angle in radians (0 to 2π)

expect(op, state)

Computes expectation value ⟨ψ|O|ψ⟩ of an operator.

• op: operator (e.g., sigmax(), sigmaz())
• state: quantum state (ket or density matrix)

Pauli Matrices

sigmax()   # σx
sigmay()   # σy
sigmaz()   # σz

Example: theta=90°, phi=0° (Bloch sphere +X state)

theta = np.radians(90)
phi = np.radians(0)
psi = spin_coherent(1/2, theta, phi)
# Should give: <σx>≈1, <σy>≈0, <σz>≈0

Key Reference

• spin_coherent(1/2, theta, phi) — Create qubit state from Bloch angles
• expect(operator, state) — Compute expectation value
• sigmax(), sigmay(), sigmaz() — Pauli matrices
• np.radians() — Convert degrees to radians