Tensorflow simulator backend¶
Module name: strawberryfields.backends.tfbackend
The TFBackend
object implements a simulation of quantum optical circuits using
Tensorflow. The primary component of the TFBackend is a
Circuit
object which is used to simulate a multimode quantum optical system. The
TFBackend
provides the basic APIcompatible interface to the simulator, while the
Circuit
object actually carries out the mathematical simulation.
The Circuit
simulator maintains an internal tensor representation of the quantum state of a multimode quantum optical system
using a (truncated) Fock basis representation. As its various state manipulation methods are called, the quantum state is updated
to reflect these changes. The simulator will try to keep the internal state in a pure (vector) representation
for as long as possible. Unitary gates will not change the type of representation, while state preparations and measurements will.
A number of factors determine the shape and dimensionality of the state tensor:
 the underlying state representation being used (either a ket vector or a density matrix)
 the number of modes \(n\) actively being simulated
 the cutoff dimension \(D\) for the Fock basis
 whether the circuit is operating in batched mode (with batch size \(B\))
When not operating in batched mode, the state tensor corresponds to a single multimode quantum system. If the representation is a pure state, the state tensor has shape \((\underbrace{D,...,D}_{n~\text{times}})\). In a mixed state representation, the state tensor has shape \((\underbrace{D,D,...,D,D}_{2n~\text{times}})\). Indices for the same mode appear consecutively. Hence, for a mixed state, the first two indices are for the first mode, the second are for the second mode, etc.
In batched mode, the state tensor simultaneously encodes an ensemble of \(B\) multimode quantum systems (indexed using the first axis of the state tensor). Pure states thus have shape \((B,\underbrace{D,...,D}_{n~\text{times}})\), while mixed states have shape \((B,\underbrace{D,D,...,D,D}_{2n~\text{times}})\).
TFBackend methods¶
The parameters supplied for these operations can be either numeric (float, complex) values
or Tensorflow Variables
/Tensors
. The Tensorflow objects can either be scalars or vectors. For
vectors, they must have the same dimension as the declared batch size of the underlying circuit.
supports (name) 
Check whether the backend supports the given operating mode. 
begin_circuit (num_subsystems, **kwargs) 
Instantiate a quantum circuit. 
add_mode ([n]) 
Add modes to the circuit. 
del_mode (modes) 
Delete modes from the circuit. 
get_modes () 
Return a list of the active modes for the circuit. 
get_cutoff_dim () 
Returns the Hilbert space cutoff dimension used. 
reset ([pure]) 
Reset the circuit so that all the modes are in the vacuum state. 
state ([modes]) 
Returns the state of the quantum simulation, restricted to the subsystems defined by modes. 
is_vacuum ([tol]) 
Test whether the current circuit state is vacuum (up to given tolerance). 
prepare_vacuum_state (mode) 
Prepare the vacuum state in the specified mode. 
prepare_coherent_state (alpha, mode) 
Prepare a coherent state in the specified mode. 
prepare_squeezed_state (r, phi, mode) 
Prepare a squeezed vacuum state in the specified mode. 
prepare_displaced_squeezed_state (alpha, r, …) 
Prepare a displaced squeezed state in the specified mode. 
prepare_thermal_state (nbar, mode) 
Prepare a thermal state in the specified mode. 
prepare_fock_state (n, mode) 
Prepare a Fock state in the specified mode. 
prepare_ket_state (state, modes) 
Prepare the given ket state in the specified modes. 
prepare_dm_state (state, modes) 
Prepare the given mixed state in the specified modes. 
rotation (phi, mode) 
Apply the phasespace rotation operation to the specified mode. 
displacement (alpha, mode) 
Apply the displacement operation to the specified mode. 
squeeze (z, mode) 
Apply the squeezing operation to the specified mode. 
beamsplitter (t, r, mode1, mode2) 
Apply the beamsplitter operation to the specified modes. 
cubic_phase (gamma, mode) 
Apply the cubic phase operation to the specified mode. 
kerr_interaction (kappa, mode) 
Apply the Kerr interaction \(\exp{(i\kappa \hat{n}^2)}\) to the specified mode. 
cross_kerr_interaction (kappa, mode1, mode2) 
Apply the two mode crossKerr interaction \(\exp{(i\kappa \hat{n}_1\hat{n}_2)}\) to the specified modes. 
loss (T, mode) 
Perform a loss channel operation on the specified mode. 
thermal_loss (T, nbar, mode) 
Perform a thermal loss channel operation on the specified mode. 
measure_homodyne (phi, mode[, shots, select]) 
Perform a homodyne measurement on the specified modes. 
measure_fock (modes[, shots, select]) 
Measure the given modes in the Fock basis. 
graph 
Get the Tensorflow Graph object where the current quantum circuit is defined. 
Code details¶

class
strawberryfields.backends.tfbackend.
TFBackend
(graph=None)[source]¶ TensorFlow backend implementation.

circuit
= None¶ representation of the simulated quantum state
Type: Circuit

begin_circuit
(num_subsystems, **kwargs)[source]¶ Instantiate a quantum circuit.
Instantiates a representation of a quantum optical state with
num_subsystems
modes. The state is initialized to vacuum.The modes in the circuit are indexed sequentially using integers, starting from zero. Once an index is assigned to a mode, it can never be reassigned to another mode. If the mode is deleted its index becomes invalid. An operation acting on an invalid or unassigned mode index raises an
IndexError
exception.Parameters: num_subsystems (int) – number of modes in the circuit
Keyword Arguments:  cutoff_dim (int) – Numerical Hilbert space cutoff dimension for the modes. For each mode, the simulator can represent the Fock states \(\ket{0}, \ket{1}, \ldots, \ket{\text{cutoff_dim}1}\).
 pure (bool) – If True (default), use a pure state representation (otherwise will use a mixed state representation).
 batch_size (None or int) – Size of the batchaxis dimension. If None, no batchaxis will be used.

reset
(pure=True, **kwargs)[source]¶ Reset the circuit so that all the modes are in the vacuum state.
After the reset the circuit is in the same state as it was after the last
begin_circuit()
call. It will have the original number of modes, all initialized in the vacuum state. Some circuit parameters may be changed during the reset, see the keyword args below.Parameters: pure (bool) – if True, initialize the circuit in a pure state representation (will use a mixed state representation if pure is False)
Keyword Arguments:  cutoff_dim (int) – new Hilbert space truncation dimension
 hard (bool) – Whether to reset the underlying TensorFlow graph. If True (default), then resets the underlying tensor graph as well. If False, then the circuit is reset to its initial state, but ops that have already been declared are still accessible.

get_cutoff_dim
()[source]¶ Returns the Hilbert space cutoff dimension used.
Returns: cutoff dimension Return type: int

get_modes
()[source]¶ Return a list of the active modes for the circuit.
A mode is active if it has been created and has not been deleted.
Returns: sorted list of active (assigned, not invalid) mode indices Return type: list[int]

prepare_vacuum_state
(mode)[source]¶ Prepare the vacuum state in the specified mode.
The requested mode is traced out and replaced with the vacuum state. As a result the state may have to be described using a density matrix.
Parameters: mode (int) – which mode to prepare the vacuum state in

prepare_coherent_state
(alpha, mode)[source]¶ Prepare a coherent state in the specified mode.
The requested mode is traced out and replaced with the coherent state \(\ket{\alpha}\). As a result the state may have to be described using a density matrix.
Parameters:  alpha (complex) – coherent state displacement parameter
 mode (int) – which mode to prepare the coherent state in

prepare_squeezed_state
(r, phi, mode)[source]¶ Prepare a squeezed vacuum state in the specified mode.
The requested mode is traced out and replaced with the squeezed state \(\ket{z}\), where \(z=re^{i\phi}\). As a result the state may have to be described using a density matrix.
Parameters:  r (float) – squeezing amplitude
 phi (float) – squeezing angle
 mode (int) – which mode to prepare the squeezed state in

prepare_displaced_squeezed_state
(alpha, r, phi, mode)[source]¶ Prepare a displaced squeezed state in the specified mode.
The requested mode is traced out and replaced with the displaced squeezed state state \(\ket{\alpha, z}\), where \(z=re^{i\phi}\). As a result the state may have to be described using a density matrix.
Parameters:  alpha (complex) – displacement parameter
 r (float) – squeezing amplitude
 phi (float) – squeezing angle
 mode (int) – which mode to prepare the squeezed state in

prepare_fock_state
(n, mode)[source]¶ Prepare a Fock state in the specified mode.
The requested mode is traced out and replaced with the Fock state \(\ket{n}\). As a result the state may have to be described using a density matrix.
Parameters:  n (int) – Fock state to prepare
 mode (int) – which mode to prepare the Fock state in

prepare_ket_state
(state, modes)[source]¶ Prepare the given ket state in the specified modes.
The requested modes are traced out and replaced with the given ket state (in the Fock basis). As a result the state may have to be described using a density matrix.
Parameters:  state (array) – Ket state in the Fock basis. The state can be given in either vector form, with one index, or tensor form, with one index per mode. For backends supporting batched mode, state can be a batch of such vectors or tensors.
 modes (int or Sequence[int]) – Modes to prepare the state in. If modes is not ordered this is taken into account when preparing the state, i.e., when a two mode state is prepared in modes=[3,1], then the first mode of state goes into mode 3 and the second mode goes into mode 1 of the simulator.

prepare_dm_state
(state, modes)[source]¶ Prepare the given mixed state in the specified modes.
The requested modes are traced out and replaced with the given density matrix state (in the Fock basis). As a result the state will be described using a density matrix.
Parameters:  state (array) – Density matrix in the Fock basis. The state can be given in either matrix form, with two indices, or tensor form, with two indices per mode. For backends supporting batched mode, state can be a batch of such matrices or tensors.
 modes (int or Sequence[int]) – which mode to prepare the state in If modes is not ordered this is take into account when preparing the state, i.e., when a two mode state is prepared in modes=[3,1], then the first mode of state goes into mode 3 and the second mode goes into mode 1 of the simulator.

prepare_thermal_state
(nbar, mode)[source]¶ Prepare a thermal state in the specified mode.
The requested mode is traced out and replaced with the thermal state \(\rho(nbar)\). As a result the state may have to be described using a density matrix.
Parameters:  nbar (float) – thermal population (mean photon number) of the mode
 mode (int) – which mode to prepare the thermal state in

rotation
(phi, mode)[source]¶ Apply the phasespace rotation operation to the specified mode.
Parameters:  phi (float) – rotation angle
 mode (int) – which mode to apply the rotation to

displacement
(alpha, mode)[source]¶ Apply the displacement operation to the specified mode.
Parameters:  alpha (complex) – displacement parameter
 mode (int) – which mode to apply the displacement to

squeeze
(z, mode)[source]¶ Apply the squeezing operation to the specified mode.
Parameters:  z (complex) – squeezing parameter
 mode (int) – which mode to apply the squeeze to

beamsplitter
(t, r, mode1, mode2)[source]¶ Apply the beamsplitter operation to the specified modes.
It is assumed that \(r^2+t^2 = t^2+r^2=1\), i.e that t is real.
Parameters:  t (float) – transmitted amplitude
 r (complex) – reflected amplitude (with phase)
 mode1 (int) – first mode that beamsplitter acts on
 mode2 (int) – second mode that beamsplitter acts on

loss
(T, mode)[source]¶ Perform a loss channel operation on the specified mode.
Parameters:  T (float) – loss parameter, \(0\leq T\leq 1\).
 mode (int) – index of mode where operation is carried out

cubic_phase
(gamma, mode)[source]¶ Apply the cubic phase operation to the specified mode.
Applies the operation
\[\exp\left(i \frac{\gamma}{6} (\hat{a} +\hat{a}^\dagger)^3\right)\]to the specified mode.
Note
This method is \(\hbar\) independent. The usual definition of the cubic phase gate is \(\hbar\) dependent:
\[V(\gamma') = \exp\left(i \frac{\gamma'}{3\hbar} \hat{x}^3\right) = \exp\left(i \frac{\gamma' \sqrt{\hbar/2}}{6} (\hat{a} +\hat{a}^\dagger)^3\right).\]Hence the cubic phase gate \(V(\gamma')\) is executed on a backend by scaling the \(\gamma'\) parameter by \(\sqrt{\hbar/2}\) and then passing it to this method, much in the way the \(\hbar\) dependent X and Z gates are implemented through the \(\hbar\) independent
displacement()
method.Warning
The cubic phase gate can suffer heavily from numerical inaccuracies due to finitedimensional cutoffs in the Fock basis. The gate implementation in Strawberry Fields is unitary, but it does not implement an exact cubic phase gate. The Kerr gate provides an alternative nonGaussian gate.
Parameters:  gamma (float) – scaled cubic phase shift, \(\gamma = \gamma' \sqrt{\hbar/2}\)
 mode (int) – which mode to apply it to

kerr_interaction
(kappa, mode)[source]¶ Apply the Kerr interaction \(\exp{(i\kappa \hat{n}^2)}\) to the specified mode.
Parameters:  kappa (float) – strength of the interaction
 mode (int) – which mode to apply it to

cross_kerr_interaction
(kappa, mode1, mode2)[source]¶ Apply the two mode crossKerr interaction \(\exp{(i\kappa \hat{n}_1\hat{n}_2)}\) to the specified modes.
Parameters:  kappa (float) – strength of the interaction
 mode1 (int) – first mode that crossKerr interaction acts on
 mode2 (int) – second mode that crossKerr interaction acts on

state
(modes=None, **kwargs)[source]¶ Returns the state of the quantum simulation, restricted to the subsystems defined by modes.
See
BaseBackend.state()
.Keyword Arguments:  session (tf.Session) – TensorFlow session
 feed_dict (Dict) – Dictionary containing the desired numerical values for Tensors
for numerically evaluating the state. Used with
session
.
Returns: state description
Return type:

measure_fock
(modes, shots=1, select=None, **kwargs)[source]¶ Measure the given modes in the Fock basis.
See
BaseFock.measure_fock()
.Keyword Arguments:  session (tf.Session) – TensorFlow session
 feed_dict (Dict) – Dictionary containing the desired numerical values for Tensors
for numerically evaluating the measurement results. Used with
session
.
Returns: measurement outcomes
Return type: tuple[int] or tuple[Tensor]

measure_homodyne
(phi, mode, shots=1, select=None, **kwargs)[source]¶ Perform a homodyne measurement on the specified modes.
See
BaseBackend.measure_homodyne()
.Keyword Arguments:  session (tf.Session) – TensorFlow session
 feed_dict (Dict) – Dictionary containing the desired numerical values for Tensors
for numerically evaluating the measurement results. Used with
session
.  num_bins (int) – Number of equally spaced bins for the probability distribution function (pdf) simulating the homodyne measurement (default: 100000).
 max (float) – The pdf is discretized onto the 1D grid [max,max] (default: 10).
Returns: measurement outcome
Return type: float or tf.Tensor

is_vacuum
(tol=0.0, **kwargs)[source]¶ Test whether the current circuit state is vacuum (up to given tolerance).
Returns True iff \(\bra{0} \rho \ket{0} 1 \le\)
tol
, i.e., the fidelity of the current circuit state with the vacuum state is within the given tolerance from 1.Parameters: tol (float) – numerical tolerance Returns: True iff current state is vacuum up to tolerance tol Return type: bool

del_mode
(modes)[source]¶ Delete modes from the circuit.
The deleted modes are traced out. As a result the state may have to be described using a density matrix.
The indices of the deleted modes become invalid for the lifetime of the circuit object. They will never be reassigned to other modes. Deleting a mode that has already been deleted raises an
IndexError
exception.Parameters: modes (Sequence[int]) – mode numbers to delete

add_mode
(n=1)[source]¶ Add modes to the circuit.
The new modes are initialized to the vacuum state. They are assigned mode indices sequentially, starting from the first unassigned index.
Parameters: n (int) – number of modes to add Returns: indices of the newly added modes Return type: list[int]

graph
¶ Get the Tensorflow Graph object where the current quantum circuit is defined.
Returns: the circuit’s graph Return type: tf.Graph

FockStateTF¶
This class represents the quantum state
returned by the Tensorflow backend. It extends BaseFockState
with additional functionality
unique to the Tensorflow backend. The primary difference between this class and the Base Fock state
is that its methods and attributes can return either numerical or symbolic values.
The default representation (numerical or symbolic)
is set when creating the state: state = eng.run('backend', eval=True/False)
. The representation can also be specified on a peruse basis when calling a method, e.g., state.mean_photon(eval=True/False)
. Along with the boolean eval
, acceptable keyword arguments are session
(a Tensorflow Session object) and feed_dict
(a dictionary mapping Tensorflow objects to numerical values). These will be used when evaluating any Tensors.
ket (**kwargs) 
Computes the ket representation of the state. 
dm (**kwargs) 
Computes the density matrix representation of the state. 
reduced_dm (modes, **kwargs) 
Computes the reduced density matrix representation of the state. 
trace (**kwargs) 
Computes the trace of the state. 
fock_prob (n, **kwargs) 
Compute the probabilities of a specific Fockbasis matrix element for the state. 
all_fock_probs (**kwargs) 
Compute the probabilities of all possible Fockbasis states for 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. 
is_vacuum ([tol]) 
Computes a boolean which indicates whether the state is the vacuum state. 
quad_expectation (mode[, phi]) 
Compute the expectation value of the quadrature operator \(\hat{x}_\phi\) for the reduced state on the specified mode. 
mean_photon (mode, **kwargs) 
Compute the mean photon number for the reduced state on the specified mode. 
batched 
The number of batches. 
cutoff_dim 
The numerical truncation of the Fock space used by the underlying state. 
graph 
The computational graph. 
Code details¶

class
strawberryfields.backends.tfbackend.states.
FockStateTF
(state_data, num_modes, pure, cutoff_dim, graph, batched=False, mode_names=None, eval=True)[source]¶ 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)

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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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  If this contains the key

fock_prob
(n, **kwargs)[source]¶ Compute the probabilities of a specific Fockbasis 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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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.
 If this contains the key
Returns: the numerical values, or an unevaluated Tensor object, for the Fockstate probabilities.
Return type: float/Tensor

all_fock_probs
(**kwargs)[source]¶ Compute the probabilities of all possible Fockbasis 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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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 Fockbasis probabilities. Return type: array/Tensor  If this contains the key

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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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.
 If this contains the key
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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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.
 If this contains the key
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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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  If this contains the key

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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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.
 If this contains the key
Returns: the boolean value, or an unevaluated Tensor object, for whether the state is in vacuum.
Return type: bool/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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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.
 If this contains the key
Returns: the numerical value, or an unevaluated Tensor object, for the density matrix.
Return type: array/Tensor

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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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.
 If this contains the key
Returns: the numerical value, or an unevaluated Tensor object, for the expectation value
Return type: float/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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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.
 If this contains the key
Returns: tuple containing the numerical value, or an unevaluated Tensor object, for the mean photon number and variance.
Return type: tuple(float/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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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  If this contains the key

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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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  If this contains the key

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
andbatched=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:
Copyright (C) 2011 and later, P.D. Nation, J.R. Johansson, A.J.G. Pitchford, C. Granade, and A.L. Grimsmo. All rights reserved.
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

poly_quad_expectation
(A, d=None, k=0, phi=0, **kwargs)[source]¶ The multimode expectation values and variance of arbitrary 2nd order polynomials of quadrature operators.
Warning
Calculation of multimode quadratic expectation values is currently only supported if
eval=True
andbatched=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 secondorder 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 length2N 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. Wheneval=True
, the return value is numerical; wheneval=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
orfeed_dict
, respectively. If a Session is supplied, theneval
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.
 If this contains the key
Returns: expectation value and variance
Return type: tuple (float, float)

batched
¶ The number of batches.

graph
¶ The computational graph.