sf.ops.Interferometer

class Interferometer(U, mesh='rectangular', drop_identity=True, tol=1e-06)

Bases: strawberryfields.ops.Decomposition

Apply a linear interferometer to the specified qumodes.

This operation uses either the rectangular decomposition or triangular decomposition to decompose a linear interferometer into a sequence of beamsplitters and rotation gates.

By specifying the keyword argument mesh, the scheme used to implement the interferometer may be adjusted:

• mesh='rectangular' (default): uses the scheme described in [23], resulting in a rectangular array of \(M(M-1)/2\) beamsplitters:

  

  Local phase shifts appear in the middle of the beamsplitter array. Use mesh='rectangular_phase_end to instead commute all local phase shifts to the end of the beamsplitter array.

  By default, the interferometers are decomposed into BSgate operations. To instead decompose the interferometer using the MZgate, use mesh='rectangular_symmetric'.

  To use the compact rectangular decomposition of Bell and Walmsley (arXiv:2104.0756), use mesh='rectangular_compact'.

• mesh='triangular': uses the scheme described in [26], resulting in a triangular array of \(M(M-1)/2\) beamsplitters:

  

  To use the compact triangular decomposition, use mesh='triangular_compact'.

  Local phase shifts appear at the end of the beamsplitter array.

Parameters

• U (array[complex]) – an \(N\times N\) unitary matrix

• mesh (str) –

  the scheme used to implement the interferometer. Options include:

  • 'rectangular' - rectangular mesh, with local phase shifts applied between interferometers

  • 'rectangular_phase_end' - rectangular mesh, with local phase shifts placed after all interferometers

  • 'rectangular_symmetric' - rectangular mesh, with local phase shifts placed after all interferometers, and all beamsplitters decomposed into pairs of symmetric beamsplitters and phase shifters

  • rectangular_compact' - rectangular mesh, with two independant phase shifts placed inside each MZI, extra phase shifts on edges and at the input and output.

  • 'triangular' - triangular mesh

  • 'triangular_compact' - triangular mesh, with two independant phase shifts placed inside each MZI.

• drop_identity (bool) – If True, decomposed gates with trivial parameters, such that they correspond to an identity operation, are removed.

• tol (float) – the tolerance used when checking if the input matrix is unitary: \(|U-U^\dagger| <\) tol

Details and Conventions

The rectangular decomposition allows any passive Gaussian transformation to be decomposed into a series of beamsplitters and rotation gates.

Definition

For every real orthogonal symplectic matrix

\[\begin{split}O=\begin{bmatrix}X&-Y\\ Y&X\end{bmatrix}\in\mathbb{R}^{2N\times 2N},\end{split}\]

the corresponding unitary matrix \(U=X+iY\in\mathbb{C}^{N\times N}\) representing a multiport interferometer can be decomposed into a set of \(N(N-1)/2\) beamsplitters and single mode rotations with circuit depth of \(N\).

For more details, see [23].

Note

The rectangular decomposition as formulated by Clements [23] uses a different beamsplitter convention to Strawberry Fields:

\[BS_{clements}(\theta, \phi) = BS(\theta, 0) R(\phi)\]

Attributes

measurement_deps	Extra dependencies due to parameters that depend on measurements.
ns

measurement_deps

Extra dependencies due to parameters that depend on measurements.

Returns

dependencies

Return type

set[RegRef]

ns = None

Methods

apply(reg, backend, **kwargs)	Ask a local backend to execute the operation on the current register state right away.
decompose(reg, **kwargs)	Decompose the operation into elementary operations supported by the backend API.
merge(other)	Merge the operation with another (acting on the exact same set of subsystems).

apply(reg, backend, **kwargs)

Ask a local backend to execute the operation on the current register state right away.

Takes care of parameter evaluations and any pending formal transformations (like dagger) and then calls Operation._apply().

Parameters

• reg (Sequence[RegRef]) – subsystem(s) the operation is acting on

• backend (BaseBackend) – backend to execute the operation

Returns

the result of self._apply

Return type

Any

decompose(reg, **kwargs)

Decompose the operation into elementary operations supported by the backend API.

See strawberryfields.backends.base.

Parameters

reg (Sequence[RegRef]) – subsystems the operation is acting on

Returns

decomposition as a list of operations acting on specific subsystems

Return type

list[Command]

merge(other)

Merge the operation with another (acting on the exact same set of subsystems).

Note

For subclass overrides: merge may return a newly created object, or self, or other, but it must never modify self or other because the same Operation objects may be also used elsewhere.

Parameters

other (Operation) – operation to merge this one with

Returns

other * self. The return value None represents the identity gate (doing nothing).

Return type

Operation, None

Raises

MergeFailure – if the two operations cannot be merged

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