sf.decompositions

Warning

Unless you are a Strawberry Fields developer, you likely do not need to use these functions directly.

See the decomposition operations for details on embedding states, graphs, and unitaries within a photonic quantum circuit.

This module implements common shared matrix decompositions that are used to perform gate decompositions.

Functions

M(n, sigma, delta, m)

The symmetric Mach Zehnder interferometer matrix.

P(j, phi, m)

The phase shifter matrix.

T(m, n, theta, phi, nmax)

The Clements T matrix from Eq 1 of the paper

Ti(m, n, theta, phi, nmax)

The inverse Clements T matrix

bipartite_graph_embed(A[, …])

Embed a bipartite graph into a Gaussian state.

bloch_messiah(S[, tol, rounding])

Bloch-Messiah decomposition of a symplectic matrix.

covmat_to_hamil(V[, tol])

Converts a covariance matrix to a Hamiltonian.

graph_embed(A[, mean_photon_per_mode, …])

Embed a graph into a Gaussian state.

graph_embed_deprecated(A[, max_mean_photon, …])

Embed a graph into a Gaussian state.

hamil_to_covmat(H[, tol])

Converts a Hamiltonian matrix to a covariance matrix.

mach_zehnder(m, n, internal_phase, …)

A two-mode Mach-Zehnder interferometer section.

mach_zehnder_inv(m, n, phi_int, phi_ext, nmax)

The inverse of the Mach-Zehnder unitary matrix.

nullMZ(n, m, U)

Nullifies element n,m of U using mach_zehnder.

nullMZi(m, n, U)

Nullifies element m,n of U using mach_zehnder_inv.

nullT(n, m, U)

Nullifies element n,m of U using T

nullTi(m, n, U)

Nullifies element m,n of U using Ti

rectangular(V[, tol])

Rectangular decomposition of a unitary matrix, with local phase shifts applied between two interferometers.

rectangular_MZ(V[, tol])

Rectangular decomposition of a unitary matrix, with local phase shifts applied between two interferometers.

rectangular_compact(U[, rtol, atol])

Rectangular decomposition of a unitary with sMZIs and phase-shifters, as given in FIG.

rectangular_phase_end(V[, tol])

Rectangular decomposition of a unitary matrix, with all local phase shifts placed after the interferometers.

rectangular_symmetric(V[, tol])

Decomposition of a unitary into an array of symmetric beamsplitters.

takagi(N[, tol, rounding])

Autonne-Takagi decomposition of a complex symmetric (not Hermitian!) matrix.

triangular(V[, tol])

Triangular decomposition of a unitary matrix due to Reck et al.

triangular_compact(U[, rtol, atol])

Triangular decomposition of a unitary matrix with sMZIs and phase-shifters, as given in FIG.

williamson(V[, tol])

Williamson decomposition of positive-definite (real) symmetric matrix.