quantum

Short visualizations of related concepts (github)

• The vectors inscribing a regular n-gon inscribed on the unit circle sum to zero
• Conjugacy classes of the Symmetric Group S3
• Cosets of Z12 for the subgroup generated by <4>, intuitions for “Hidden Subgroup”
• Matrix multiplication mechanics via linear map composition
• Make homomorphism injective by taking quotient group with respect to kernel

Reference materials

• Introduction to Quantum Information (Coursera), Instructor: Joonwoo Bae
• Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang
• Abstract Algebra by I. N. Herstein
• Linear Algebra Done Right by Sheldon Axler

import numpy as np

# Pauli matrices
Z = np.array([[1,0],[0,-1]])
X = np.array([[0,1],[1,0]])

# Computational Basis
one = np.array([[0],[1]])
zero = np.array([[1],[0]])

# EPR State phi-
phi = 1. / np.sqrt(2) * (np.kron(zero, one) - np.kron(one, zero))

# Show that one of the terms from the Bell inequality has
# expected observable of 1/sqrt(2), killing "local realism"
QS = np.kron(Z, 1/np.sqrt(2) * (-1 * Z - X))
print(np.inner(phi.conj().T, np.inner(QS,phi.T).T))