# sf.ops.DensityMatrix¶

class DensityMatrix(state)[source]

Bases: strawberryfields.ops.Preparation

Prepare mode(s) using the given density matrix in the Fock basis.

The prepared modes are traced out and replaced with the given state (in the Fock basis). As a result, the overall state of system will also have to be described using a density matrix.

The provided density matrices must be of size [cutoff_dim, cutoff_dim], matching the cutoff dimension used in calls to eng.run.

Warning

The Fock basis is non-Gaussian, and thus can only be used in the Fock backends, not the Gaussian backend.

Parameters

state (array or BaseFockState) –

density matrix in the Fock basis. This can be provided as either:

• a single mode two-dimensional matrix $$\rho_{ij}$$,

• a multimode tensor $$\rho_{ij,kl,\dots,mn}$$, with two indices per mode,

• a BaseFockState state object.

When working with an $$N$$-mode density matrix in the Fock basis,

$\rho = \sum_{n_1}\cdots\sum_{n_N} c_{n_1,\cdots,n_N} \ket{n_1,\cdots,n_N}\bra{n_1,\cdots,n_N}$

we use the convention that every pair of consecutive dimensions corresponds to a subsystem; i.e.,

$\rho_{\underbrace{ij}_{\text{mode}~0}~\underbrace{kl}_{\text{mode}~1} ~\underbrace{mn}_{\text{mode}~2}}$

Thus, using index notation, we can calculate the reduced density matrix for mode 2 by taking the partial trace over modes 0 and 1:

$\braketT{n}{\text{Tr}_{01}[\rho]}{m} = \sum_{i}\sum_k \rho_{iikkmn}$
 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
 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