qit.utils

Utilities

This module contains utility functions which do not logically fit anywhere else.

Mathematical utilities

gcd(a, b)	Greatest common divisor.
lcm(a, b)	Least common multiple.
majorize(x, y[, tol])	Majorization partial order of real vectors.

Matrix functions

comm(A, B)	Array commutator.
acomm(A, B)	Array anticommutator.
mkron(*arg)	This is how kron should work, dammit.
tensorsum(*arg)	Like kron but adding instead of multiplying.
rank(A[, tol])	Matrix rank.
orth(A[, tol, kernel, spectrum])	Construct an orthonormal basis for the range of A using SVD
nullspace(A[, tol, spectrum])	Kernel of a matrix.
nullspace_hermitian(A[, tol])	Kernel of a superoperator matrix restricted to the Hermitian subspace.
projector(v)	Projector corresponding to vector v.
eighsort(A)	Returns eigenvalues and eigenvectors of a Hermitian matrix, sorted in nonincreasing order.
expv(t, A, v[, tol, m, iteration])	Multiply a vector by an exponentiated matrix.

Random matrices

rand_hermitian(n)	Random Hermitian n*n matrix.
rand_U(n)	Random U(n) matrix.
rand_SU(n)	Random SU(n) matrix.
rand_U1(n)	Random diagonal unitary matrix.
rand_pu(n)	Random n-partition of unity.
rand_positive(n)	Random n*n positive semidefinite matrix.
rand_GL(n)	Random GL(n, C) matrix.
rand_SL(n)	Random SL(n, C) matrix.

Superoperators

vec(rho)	Flattens a matrix into a vector.
inv_vec(v[, dim])	Reshapes a vector into a matrix.
lmul(L[, q])	Superoperator equivalent for multiplying from the left.
rmul(R[, p])	Superoperator equivalent for multiplying from the right.
lrmul(L, R)	Superoperator equivalent for multiplying both from left and right.
superop_lindblad(A[, H])	Liouvillian superoperator for a set of Lindblad operators.
superop_fp(L[, tol])	Fixed point states of a Liouvillian superoperator.
superop_to_choi(L)	Convert a Liouvillian superoperator to a Choi matrix.

Physics

angular_momentum(*args)	Angular momentum matrices.
boson_ladder(*args)	Bosonic ladder operators.
fermion_ladder(*args)	Fermionic ladder operators.

Bases, decompositions

spectral_decomposition(A[, tol])	Spectral decomposition of a Hermitian matrix.
gellmann(*args)	Gell-Mann matrices.
tensorbasis(n[, d, get_locality, only_local])	Hermitian tensor-product basis for End(H).

Miscellaneous

copy_memoize(func)	Memoization decorator for functions with immutable args, returns deep copies.
op_list(G, dim)	Operator consisting of k-local terms, given as a list.
cdot(v, A)	Real dot product of a vector and a tuple of operators.
qubits(n)	Dimension vector for an all-qubit system.
R_nmr(theta, phi)	SU(2) rotation \(\theta_\phi\) (NMR notation).
Rx(theta)	SU(2) x-rotation.
Ry(theta)	SU(2) y-rotation.
Rz(theta)	SU(2) z-rotation.
trisurf(p, max_dist)	Populates a 2D triangular surface with evenly spaced points for Delaunay triangulation.

Functions

R_nmr(theta, phi)	SU(2) rotation \(\theta_\phi\) (NMR notation).
Rx(theta)	SU(2) x-rotation.
Ry(theta)	SU(2) y-rotation.
Rz(theta)	SU(2) z-rotation.
acomm(A, B)	Array anticommutator.
angular_momentum(*args)	Angular momentum matrices.
boson_ladder(*args)	Bosonic ladder operators.
cdot(v, A)	Real dot product of a vector and a tuple of operators.
comm(A, B)	Array commutator.
copy_memoize(func)	Memoization decorator for functions with immutable args, returns deep copies.
eighsort(A)	Returns eigenvalues and eigenvectors of a Hermitian matrix, sorted in nonincreasing order.
expv(t, A, v[, tol, m, iteration])	Multiply a vector by an exponentiated matrix.
fermion_ladder(*args)	Fermionic ladder operators.
gcd(a, b)	Greatest common divisor.
gellmann(*args)	Gell-Mann matrices.
inv_vec(v[, dim])	Reshapes a vector into a matrix.
lcm(a, b)	Least common multiple.
lmul(L[, q])	Superoperator equivalent for multiplying from the left.
lrmul(L, R)	Superoperator equivalent for multiplying both from left and right.
majorize(x, y[, tol])	Majorization partial order of real vectors.
mkron(*arg)	This is how kron should work, dammit.
nullspace(A[, tol, spectrum])	Kernel of a matrix.
nullspace_hermitian(A[, tol])	Kernel of a superoperator matrix restricted to the Hermitian subspace.
op_list(G, dim)	Operator consisting of k-local terms, given as a list.
orth(A[, tol, kernel, spectrum])	Construct an orthonormal basis for the range of A using SVD
projector(v)	Projector corresponding to vector v.
qubits(n)	Dimension vector for an all-qubit system.
rand_GL(n)	Random GL(n, C) matrix.
rand_SL(n)	Random SL(n, C) matrix.
rand_SU(n)	Random SU(n) matrix.
rand_U(n)	Random U(n) matrix.
rand_U1(n)	Random diagonal unitary matrix.
rand_hermitian(n)	Random Hermitian n*n matrix.
rand_positive(n)	Random n*n positive semidefinite matrix.
rand_pu(n)	Random n-partition of unity.
rank(A[, tol])	Matrix rank.
rmul(R[, p])	Superoperator equivalent for multiplying from the right.
spectral_decomposition(A[, tol])	Spectral decomposition of a Hermitian matrix.
superop_fp(L[, tol])	Fixed point states of a Liouvillian superoperator.
superop_lindblad(A[, H])	Liouvillian superoperator for a set of Lindblad operators.
superop_to_choi(L)	Convert a Liouvillian superoperator to a Choi matrix.
tensorbasis(n[, d, get_locality, only_local])	Hermitian tensor-product basis for End(H).
tensorsum(*arg)	Like kron but adding instead of multiplying.
trisurf(p, max_dist)	Populates a 2D triangular surface with evenly spaced points for Delaunay triangulation.
vec(rho)	Flattens a matrix into a vector.