Symplectics¶

`cxgate_symplectic`	The symplectic matrix of a controlled X gate.
`czgate_symplectic`	The symplectic matrix of a controlled Z gate.
`interferometer_symplectic`	The symplectic matrix of an N-mode interferometer parametrized by an NxN unitary matrix.
`mzgate_symplectic`	The symplectic matrix of a Mach-Zehnder gate.
`pgate_symplectic`	The symplectic matrix of a quadratic phase gate.
`realinterferometer_symplectic`	The symplectic matrix of an N-mode interferometer parametrized by an NxN orthogonal matrix.

cxgate_symplectic¶

mrmustard.physics.symplectics.cxgate_symplectic(s)[source]¶

The symplectic matrix of a controlled X gate.

Parameters:: s (float | Sequence[float]) – The control parameter.
Returns:: The symplectic matrix of a CX gate.
Return type:: Matrix

czgate_symplectic¶

mrmustard.physics.symplectics.czgate_symplectic(s)[source]¶

The symplectic matrix of a controlled Z gate.

Parameters:: s (float | Sequence[float]) – The control parameter.
Returns:: The symplectic matrix of a CZ gate.
Return type:: Matrix

interferometer_symplectic¶

mrmustard.physics.symplectics.interferometer_symplectic(unitary)[source]¶

The symplectic matrix of an N-mode interferometer parametrized by an NxN unitary matrix.

Parameters:: unitary (Matrix) – A unitary matrix. For N modes it must have shape (N,N).
Returns:: The symplectic matrix of an N-mode interferometer.
Return type:: Matrix

mzgate_symplectic¶

mrmustard.physics.symplectics.mzgate_symplectic(phi_a, phi_b, internal)[source]¶

The symplectic matrix of a Mach-Zehnder gate.

It supports two conventions:

if internal=True, both phases act inside the interferometer: phi_a on the upper arm, phi_b on the lower arm;
if internal = False, both phases act on the upper arm: phi_a before the first BS, phi_b after the first BS.

Parameters:

phi_a (float | Sequence[float]) – The phase in the upper arm of the MZ interferometer
phi_b (float | Sequence[float]) – The phase in the lower arm or external of the MZ interferometer
internal (bool) – Whether phases are both in the internal arms.

Returns:

The symplectic matrix of a Mach-Zehnder gate.

Return type:

Matrix

pgate_symplectic¶

mrmustard.physics.symplectics.pgate_symplectic(n_modes, shearing)[source]¶

The symplectic matrix of a quadratic phase gate.

Parameters:

n_modes (int) – The number of modes.
shearing (float | Sequence[float]) – The shearing parameter.

Returns:

The symplectic matrix of a phase gate.

Return type:

Matrix

realinterferometer_symplectic¶

mrmustard.physics.symplectics.realinterferometer_symplectic(orthogonal)[source]¶

The symplectic matrix of an N-mode interferometer parametrized by an NxN orthogonal matrix.

Parameters:: orthogonal (Matrix) – A real orthogonal matrix. For N modes it must have shape (N,N).
Returns:: The symplectic matrix of an N-mode interferometer.
Return type:: Matrix

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