sf.backends.tfbackend.states.FockStateTF¶

class FockStateTF(state_data, num_modes, pure, cutoff_dim, batched=False, mode_names=None, dtype=tf.complex64)[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
batched (bool) – (optional) default False means no batching
mode_names (Sequence) – (optional) this argument contains a list providing mode names for each mode in the state
dtype (tf.DType) – (optional) complex Tensorflow Tensor type representation, either tf.complex64 (default) or tf.complex128

Attributes

`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.
`dtype`	The circuit dtype
`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.

dtype¶: The circuit dtype

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

Methods

`all_fock_probs`(**kwargs)	Compute the probabilities of all possible Fock-basis states for the state.
`diagonal_expectation`(modes, values)	Calculates the expectation value of an operator that is diagonal in the number basis
`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.
`number_expectation`(modes)	Calculates the expectation value of a product of number operators acting on given modes
`p_quad_values`(mode, xvec, pvec)	Calculates the discretized p-quadrature probability distribution of the specified mode.
`parity_expectation`(modes)	Calculates the expectation value of a product of parity operators acting on given modes
`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.
`x_quad_values`(mode, xvec, pvec)	Calculates the discretized x-quadrature probability distribution 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]

Args:

Returns: the numerical values, or an unevaluated Tensor object, for the Fock-basis probabilities.
Return type: array/Tensor

diagonal_expectation(modes, values)¶: Calculates the expectation value of an operator that is diagonal in the number basis

dm(**kwargs)[source]¶

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

Args:

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

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
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.

Args:

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
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.
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.

Args:

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
Returns: tuple containing the numerical value, or an unevaluated Tensor object, for the mean photon number and variance.
Return type: tuple(float/Tensor)

number_expectation(modes)¶: Calculates the expectation value of a product of number operators acting on given modes

p_quad_values(mode, xvec, pvec)¶

Calculates the discretized p-quadrature probability distribution of the specified mode.

Parameters

mode (int) – the mode to calculate the p-quadrature probability values of
xvec (array) – array of discretized $x$ quadrature values
pvec (array) – array of discretized $p$ quadrature values

Returns

1D array of size len(pvec), containing reduced p-quadrature probability values for a specified range of x and p.

Return type

array

parity_expectation(modes)¶: Calculates the expectation value of a product of parity operators acting on given modes

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.

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

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.
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.

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

x_quad_values(mode, xvec, pvec)¶

Calculates the discretized x-quadrature probability distribution of the specified mode.

Parameters

mode (int) – the mode to calculate the x-quadrature probability values of
xvec (array) – array of discretized $x$ quadrature values
pvec (array) – array of discretized $p$ quadrature values

Returns

1D array of size len(xvec), containing reduced x-quadrature probability values for a specified range of x and p.

Return type

array

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sf.backends.tfbackend.states.FockStateTF¶

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