# sf.backends.tfbackend.states.FockStateTF¶

class FockStateTF(state_data, num_modes, pure, cutoff_dim, graph, batched=False, mode_names=None, eval=True)[source]

Bases: strawberryfields.backends.states.BaseFockState

Class for the representation of quantum states in the Fock basis using the TFBackend.

Parameters
• state_data (array) – the state representation in the Fock basis

• num_modes (int) – the number of modes in the state

• pure (bool) – True if the state is a pure state, false if the state is mixed

• cutoff_dim (int) – the Fock basis truncation size

• mode_names (Sequence) – (optional) this argument contains a list providing mode names for each mode in the state.

• eval (bool) – indicates the default return behaviour for the class instance (symbolic when eval=False, numerical when eval=True)

 EQ_TOLERANCE batched The number of batches. cutoff_dim The numerical truncation of the Fock space used by the underlying state. data Returns the underlying numerical (or symbolic) representation of the state. graph The computational graph. hbar Returns the value of $$\hbar$$ used in the generation of the state. is_pure Checks whether the state is a pure state. mode_indices Returns a dictionary mapping the mode names to mode indices. mode_names Returns a dictionary mapping the mode index to mode names. num_modes Gets the number of modes that the state represents.
EQ_TOLERANCE = 1e-10
batched

The number of batches.

cutoff_dim

The numerical truncation of the Fock space used by the underlying state. Note that a cutoff of D corresponds to the Fock states $$\{|0\rangle,\dots,|D-1\rangle\}$$

Returns

the cutoff dimension

Return type

int

data

Returns the underlying numerical (or symbolic) representation of the state. The form of this data differs for different backends.

graph

The computational graph.

hbar

Returns the value of $$\hbar$$ used in the generation of the state.

The value of $$\hbar$$ is a convention chosen in the definition of $$\x$$ and $$\p$$. See Operators for more details.

Returns

$$\hbar$$ value.

Return type

float

is_pure

Checks whether the state is a pure state.

Returns

True if and only if the state is pure.

Return type

bool

mode_indices

Returns a dictionary mapping the mode names to mode indices.

The mode names are determined from the initialization argument mode_names. If these were not supplied, the names are generated automatically based on the mode indices.

Returns

dictionary of the form {"mode name":i,...}

Return type

dict

mode_names

Returns a dictionary mapping the mode index to mode names.

The mode names are determined from the initialization argument mode_names. If these were not supplied, the names are generated automatically based on the mode indices.

Returns

dictionary of the form {i:"mode name",...}

Return type

dict

num_modes

Gets the number of modes that the state represents.

Returns

the number of modes in the state

Return type

int

 all_fock_probs(**kwargs) Compute the probabilities of all possible Fock-basis states for the state. dm(**kwargs) Computes the density matrix representation of the state. fidelity(other_state, mode, **kwargs) Compute the fidelity of the reduced state (on the specified mode) with the state. fidelity_coherent(alpha_list, **kwargs) Compute the fidelity of the state with the coherent states specified by alpha_list. fidelity_vacuum(**kwargs) Compute the fidelity of the state with the vacuum state. fock_prob(n, **kwargs) Compute the probabilities of a specific Fock-basis matrix element for the state. is_vacuum([tol]) Computes a boolean which indicates whether the state is the vacuum state. ket(**kwargs) Computes the ket representation of the state. mean_photon(mode, **kwargs) Compute the mean photon number for the reduced state on the specified mode. poly_quad_expectation(A[, d, k, phi]) The multi-mode expectation values and variance of arbitrary 2nd order polynomials of quadrature operators. quad_expectation(mode[, phi]) Compute the expectation value of the quadrature operator $$\hat{x}_\phi$$ for the reduced state on the specified mode. reduced_dm(modes, **kwargs) Computes the reduced density matrix representation of the state. trace(**kwargs) Computes the trace of the state. wigner(mode, xvec, pvec) Calculates the discretized Wigner function of the specified mode.
all_fock_probs(**kwargs)[source]

Compute the probabilities of all possible Fock-basis states for the state. May be numerical or symbolic.

For example, in the case of 3 modes, this method allows the Fock state probability $$|\braketD{0,2,3}{\psi}|^2$$ to be returned via

probs = state.all_fock_probs()
probs[0,2,3]

Parameters

**kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical values, or an unevaluated Tensor object, for the Fock-basis probabilities.

Return type

array/Tensor

dm(**kwargs)[source]

Computes the density matrix representation of the state. May be numerical or symbolic.

Parameters

**kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical value, or an unevaluated Tensor object, for the density matrix.

Return type

array/Tensor

fidelity(other_state, mode, **kwargs)[source]

Compute the fidelity of the reduced state (on the specified mode) with the state. May be numerical or symbolic.

Parameters
• other_state (array) – state vector (ket) to compute the fidelity with respect to

• mode (int) – which subsystem to use for the fidelity computation

• **kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical value, or an unevaluated Tensor object, for the fidelity.

Return type

float/Tensor

fidelity_coherent(alpha_list, **kwargs)[source]

Compute the fidelity of the state with the coherent states specified by alpha_list. May be numerical or symbolic.

Parameters
• alpha_list (Sequence[complex]) – list of coherence parameter values, one for each mode

• **kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical value, or an unevaluated Tensor object, for the fidelity $$\bra{\vec{\alpha}}\rho\ket{\vec{\alpha}}$$.

Return type

float/Tensor

fidelity_vacuum(**kwargs)[source]

Compute the fidelity of the state with the vacuum state. May be numerical or symbolic.

Parameters

**kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical value, or an unevaluated Tensor object, for the fidelity $$\bra{\vec{0}}\rho\ket{\vec{0}}$$.

Return type

float/Tensor

fock_prob(n, **kwargs)[source]

Compute the probabilities of a specific Fock-basis matrix element for the state. May be numerical or symbolic.

Parameters
• n (Sequence[int]) – the Fock state $$\ket{\vec{n}}$$ that we want to measure the probability of

• **kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical values, or an unevaluated Tensor object, for the Fock-state probabilities.

Return type

float/Tensor

is_vacuum(tol=0.0, **kwargs)[source]

Computes a boolean which indicates whether the state is the vacuum state. May be numerical or symbolic.

Parameters
• tol – numerical tolerance. If the state has fidelity with vacuum within tol, then this method returns True.

• **kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the boolean value, or an unevaluated Tensor object, for whether the state is in vacuum.

Return type

bool/Tensor

ket(**kwargs)[source]

Computes the ket representation of the state. May be numerical or symbolic.

Parameters

**kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical value, or an unevaluated Tensor object, for the ket.

Return type

array/Tensor

mean_photon(mode, **kwargs)[source]

Compute the mean photon number for the reduced state on the specified mode. May be numerical or symbolic.

Parameters
• mode (int) – which subsystem to take the mean photon number of

• **kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

tuple containing the numerical value, or an unevaluated Tensor object, for the mean photon number and variance.

Return type

tuple(float/Tensor)

poly_quad_expectation(A, d=None, k=0, phi=0, **kwargs)[source]

The multi-mode expectation values and variance of arbitrary 2nd order polynomials of quadrature operators.

Warning

Calculation of multi-mode quadratic expectation values is currently only supported if eval=True and batched=False.

An arbitrary 2nd order polynomial of quadrature operators over $N$ modes can always be written in the following form:

$P(\mathbf{r}) = \mathbf{r}^T A\mathbf{r} + \mathbf{r}^T \mathbf{d} + k I$

where:

• $$A\in\mathbb{R}^{2N\times 2N}$$ is a symmetric matrix representing the quadratic coefficients,

• $$\mathbf{d}\in\mathbb{R}^{2N}$$ is a real vector representing the linear coefficients,

• $$k\in\mathbb{R}$$ represents the constant term, and

• $$\mathbf{r} = (\x_1,\dots,\x_N,\p_1,\dots,\p_N)$$ is the vector of quadrature operators in $$xp$$-ordering.

This method returns the expectation value of this second-order polynomial,

$\langle P(\mathbf{r})\rangle,$

as well as the variance

$\Delta P(\mathbf{r})^2 = \langle P(\mathbf{r})^2\rangle - \braket{P(\mathbf{r})}^2$
Parameters
• A (array) – a real symmetric 2Nx2N NumPy array, representing the quadratic coefficients of the second order quadrature polynomial.

• d (array) – a symmetric length-2N NumPy array, representing the linear coefficients of the second order quadrature polynomial. Defaults to the zero vector.

• k (float) – the constant term. Default 0.

• phi (float) – quadrature angle, clockwise from the positive $$x$$ axis. If provided, the vector of quadrature operators $$\mathbf{r}$$ is first rotated by angle $$\phi$$ in the phase space.

• **kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

expectation value and variance

Return type

tuple (float, float)

quad_expectation(mode, phi=0.0, **kwargs)[source]

Compute the expectation value of the quadrature operator $$\hat{x}_\phi$$ for the reduced state on the specified mode. May be numerical or symbolic.

Parameters
• mode (int) – which subsystem to take the expectation value of

• phi (float) – rotation angle for the quadrature operator

• **kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical value, or an unevaluated Tensor object, for the expectation value

Return type

float/Tensor

reduced_dm(modes, **kwargs)[source]

Computes the reduced density matrix representation of the state. May be numerical or symbolic.

Parameters
• modes (int or Sequence[int]) – specifies the mode(s) to return the reduced density matrix for.

• **kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical value, or an unevaluated Tensor object, for the density matrix.

Return type

array/Tensor

trace(**kwargs)[source]

Computes the trace of the state. May be numerical or symbolic.

Parameters

**kwargs

Optional keyword arguments.

• If this contains the key eval, then the corresponding argument will be used to determine the return behaviour of this function. When eval=True, the return value is numerical; when eval=False, it is symbolic.

• If eval is not present in kwargs, then state falls back to the an internal evaluation behaviour, which is specified at initialization.

• A Tensorflow Session or feed_dict may also be passed via the keys session or feed_dict, respectively. If a Session is supplied, then eval is overriden and the numerical evaluation takes place in the provided Session. If session and/or feed_dict are not given, then a temporary session and/or empty feed_dict will be used.

Returns

the numerical value, or an unevaluated Tensor object, for the trace.

Return type

float/Tensor

wigner(mode, xvec, pvec)[source]

Calculates the discretized Wigner function of the specified mode.

Warning

Calculation of the Wigner function is currently only supported if eval=True and batched=False.

Note

This code is a modified version of the ‘iterative’ method of the wigner function provided in QuTiP, which is released under the BSD license, with the following copyright notice:

Parameters
• mode (int) – the mode to calculate the Wigner function for

• xvec (array) – array of discretized $$x$$ quadrature values

• pvec (array) – array of discretized $$p$$ quadrature values

Returns

2D array of size [len(xvec), len(pvec)], containing reduced Wigner function values for specified x and p values.

Return type

array