mm.lab_dev.states.Vacuum¶

class mrmustard.lab_dev.states.Vacuum(modes)[source]¶

Bases: Ket

The N-mode vacuum state.

>>> from mrmustard.lab_dev import Vacuum

>>> state = Vacuum([1, 2])
>>> assert state.modes == [1, 2]

Parameters:: modes (Sequence[int]) – A list of modes.

Details and Conventions

The \(N\)-mode vacuum state is defined by

\[V = \frac{\hbar}{2}I_N \text{and } r = \bar{0}_N.\]

Its (A,b,c) triple is given by

\[A = O_{N\text{x}N}\text{, }b = O_N\text{, and }c = 1.\]

Attributes

`L2_norm`	The L2 norm of a `Ket`, or the Hilbert-Schmidt norm of a `DM`.
`adjoint`	The `AdjointView` of this component.
`bargmann_triple`	The `(A, b, c)` triple that describes this state in the Bargmann representation.
`dual`	The `DualView` of this component.
`is_pure`	Whether this state is pure.
`modes`	The sorted list of modes of this component.
`n_modes`	The number of modes in this component.
`name`	The name of this component.
`parameter_set`	The set of parameters characterizing this component.
`probability`	Returns \(\langle\psi\|\psi\rangle\) for `Ket` states \(\|\psi\rangle\) and \(\text{Tr}(\rho)\) for `DM` states \(\rho\).
`purity`	The purity of this state.
`representation`	A representation of this circuit component.
`wires`	The wires of this component.

L2_norm¶: The L2 norm of a Ket, or the Hilbert-Schmidt norm of a DM.

adjoint¶: The AdjointView of this component.

bargmann_triple¶

The (A, b, c) triple that describes this state in the Bargmann representation.

Returns:: The (A, b, c) triple that describes this state in the Bargmann representation.
Raises:: ValueError – If the triple cannot be calculated given the state’s representation.

dual¶: The DualView of this component.

is_pure¶: Whether this state is pure.

modes¶: The sorted list of modes of this component.

n_modes¶: The number of modes in this component.

name¶: The name of this component.

parameter_set¶: The set of parameters characterizing this component.

probability¶

purity¶

representation¶

wires¶: The wires of this component.

Methods

`dm`()	The `DM` object obtained from this `Ket`.
`expectation`(operator)	The expectation value of an operator calculated over this Ket.
`fock_array`([shape])	The array that describes this state in the Fock representation.
`from_bargmann`(modes, triple[, name, batched])	Initializes a state from an `(A, b, c)` triple defining a Bargmann representation.
`from_fock`(modes, array[, name, batched])	Initializes a state from an array describing the state in the Fock representation.
`from_phase_space`(modes, cov, means[, name, ...])	Initializes a state from the covariance matrix and the vector of means of a state in phase space.
`from_quadrature`()	Initializes a state from quadrature.
`light_copy`()	Creates a copy of this component by copying every data stored in memory for it by reference, except for its wires, which are copied by value.
`on`(modes)	Creates a copy of this component that acts on the given `modes` instead of on the original modes.
`phase_space`(s)	Returns the phase space parametrization of a state, consisting in a covariance matrix, a vector of means and a scaling coefficient.
`to_fock_component`([shape])	Returns a circuit component with the same attributes as this component, but with `Fock` representation.
`visualize_2d`([xbounds, pbounds, resolution, ...])	2D visualization of the Wigner function of this state.
`visualize_3d`([xbounds, pbounds, resolution, ...])	3D visualization of the Wigner function of this state on a surface plot.
`visualize_dm`([cutoff, return_fig])	Plots the absolute value \(abs(\rho)\) of the density matrix \(\rho\) of this state on a heatmap.

dm()¶

The DM object obtained from this Ket.

Return type:: DM

expectation(operator)¶

The expectation value of an operator calculated over this Ket.

Given the operator O, this function returns \(Tr\big(|\psi\rangle\langle\psi| O)\), where \(|\psi\rangle\) is the vector representing this state.

The operator is expected to be a component with ket-like wires (i.e., output wires on the ket side), density matrix-like wires (output wires on both ket and bra sides), or unitary-like wires (input and output wires on the ket side).

Parameters:

operator (CircuitComponent) – A ket-like, density-matrix like, or unitary-like circuit component.

Raises:

ValueError – If operator is not a ket-like, density-matrix like, or unitary-like component.
ValueError – If operator is defined over a set of modes that is not a subset of the modes of this state.

fock_array(shape=None)¶

The array that describes this state in the Fock representation.

Uses the mrmustard.physics.converters.to_fock() method to convert the internal representation into a Fock object.

Parameters:

shape (Union[int, Sequence[int], None]) – The shape of the returned array. If shape``is given as an ``int, it is
None (broadcasted to all the dimensions. If) –
of (it defaults to the value) –
settings. (AUTOCUTOFF_MAX_CUTOFF in the) –

Return type:

ndarray[Tuple[int, ...], TypeVar(C, complex64, complex128)]

Returns:

The array that describes this state in the Fock representation.

classmethod from_bargmann(modes, triple, name=None, batched=False)¶

Initializes a state from an (A, b, c) triple defining a Bargmann representation.

>>> from mrmustard.physics.representations import Bargmann
>>> from mrmustard.physics.triples import coherent_state_Abc
>>> from mrmustard.lab_dev import Ket

>>> modes = [0, 1]
>>> triple = coherent_state_Abc(x=[0.1, 0.2])

>>> coh = Ket.from_bargmann(modes, triple)
>>> assert coh.modes == modes
>>> assert coh.representation == Bargmann(*triple)
>>> assert isinstance(coh, Ket)

Parameters:

modes (Sequence[int]) – The modes of this states.
triple (tuple[ndarray[Tuple[int, int], TypeVar(C, complex64, complex128)], ndarray[Tuple[int], TypeVar(C, complex64, complex128)], complex]) – The (A, b, c) triple.
name (Optional[str]) – The name of this state.
batched (bool) – Whether the given triple is batched.

Return type:

Ket

Returns:

A state.

Raises:

ValueError – If the A or b have a shape that is inconsistent with the number of modes.

classmethod from_fock(modes, array, name=None, batched=False)¶

Initializes a state from an array describing the state in the Fock representation.

>>> from mrmustard.physics.representations import Fock
>>> from mrmustard.physics.triples import coherent_state_Abc
>>> from mrmustard.lab_dev import Coherent, Ket

>>> modes = [0]
>>> array = Coherent(modes, x=0.1).to_fock_component().representation.array
>>> coh = Ket.from_fock(modes, array, batched=True)

>>> assert coh.modes == modes
>>> assert coh.representation == Fock(array)
>>> assert isinstance(coh, Ket)

Parameters:

modes (Sequence[int]) – The modes of this states.
array (ndarray[Tuple[int, ...], TypeVar(C, complex64, complex128)]) – The Fock array.
name (Optional[str]) – The name of this state.
batched (bool) – Whether the given array is batched.

Return type:

Ket

Returns:

A state.

Raises:

ValueError – If the given array has a shape that is inconsistent with the number of modes.

classmethod from_phase_space(modes, cov, means, name=None, atol_purity=0.001)¶

Initializes a state from the covariance matrix and the vector of means of a state in phase space.

Parameters:

cov (ndarray[Tuple[int, int], TypeVar(C, complex64, complex128)]) – The covariance matrix.
means (ndarray[Tuple[int, int], TypeVar(C, complex64, complex128)]) – The vector of means.
modes (Sequence[int]) – The modes of this states.
name (Optional[str]) – The name of this state.
atol_purity (Optional[float]) – If atol_purity is given, the purity of the state is computed, and an error is raised if its value is smaller than 1-atol_purity or larger than 1+atol_purity. If None, this check is skipped.

Returns:

A state.

Raises:

ValueError – If the given cov and means have shapes that are inconsistent with the number of modes.
ValueError – If atol_purity is not None and the purity of the returned state is smaller than 1-atol_purity or larger than 1+atol_purity.

classmethod from_quadrature()¶

Initializes a state from quadrature.

Return type:: State

light_copy()¶

Creates a copy of this component by copying every data stored in memory for it by reference, except for its wires, which are copied by value.

Return type:: CircuitComponent

on(modes)¶

Creates a copy of this component that acts on the given modes instead of on the original modes.

Parameters:: modes (Sequence[int]) – The new modes that this component acts on.
Return type:: CircuitComponent
Returns:: The component acting on the specified modes.
Raises:: ValueError – If modes contains more or less modes than the original component.

phase_space(s)¶

Returns the phase space parametrization of a state, consisting in a covariance matrix, a vector of means and a scaling coefficient. When a state is a linear superposition of Gaussians each of cov, means, coeff are arranged in a batch. Phase space representations are labelled by an s parameter (float) which modifies the exponent of \(D_s(\gamma) = e^{\frac{s}{2}|\gamma|^2}D(\gamma)\), which is the operator basis used to expand phase space density matrices. The s parameter typically takes the values of -1, 0, 1 to indicate Glauber/Wigner/Husimi functions. Note that the same (cov, means, coeff) triple can be used to parametrize the characteristic functions as well.

Parameters:

s (float) – The phase space parameter
Returns – The covariance matrix, the mean vector and the coefficient of the state in s-parametrized phase space.

Return type:

tuple[ndarray[Tuple[int, int], TypeVar(C, complex64, complex128)], ndarray[Tuple[int], TypeVar(C, complex64, complex128)], complex]

to_fock_component(shape=None)¶

Returns a circuit component with the same attributes as this component, but with Fock representation.

Uses the mrmustard.physics.converters.to_fock() method to convert the internal representation.

>>> from mrmustard.physics.converters import to_fock
>>> from mrmustard.lab_dev import Dgate

>>> d = Dgate([1], x=0.1, y=0.1)
>>> d_fock = d.to_fock_component(shape=3)

>>> assert d_fock.name == d.name
>>> assert d_fock.wires == d.wires
>>> assert d_fock.representation == to_fock(d.representation, shape=3)

Parameters:: shape (Union[int, Iterable[int], None]) – The shape of the returned representation. If shape``is given as an ``int, it is broadcasted to all the dimensions. If None, it defaults to the value of AUTOCUTOFF_MAX_CUTOFF in the settings.
Return type:: CircuitComponent

visualize_2d(xbounds=(-6, 6), pbounds=(-6, 6), resolution=200, colorscale='viridis', return_fig=False)¶

2D visualization of the Wigner function of this state.

Plots the Wigner function on a heatmap, alongside the probability distributions on the two quadrature axis.

>>> from mrmustard.lab_dev import Coherent

>>> state = Coherent([0], x=1) / 2**0.5 + Coherent([0], x=-1) / 2**0.5
>>> # state.visualize_2d()

Parameters:

xbounds (tuple[int]) – The range of the x axis.
pbounds (tuple[int]) – The range of the p axis.
resolution (int) – The number of bins on each axes.
colorscale (str) – A colorscale. Must be one of Plotly's built-in continuous color scales.
return_fig (bool) – Whether to return the Plotly figure.

Return type:

Optional[Figure]

Returns:

A Plotly figure representing the state in 2D.

Raises:

ValueError – If this state is a multi-mode state.

visualize_3d(xbounds=(-6, 6), pbounds=(-6, 6), resolution=200, colorscale='viridis', return_fig=False)¶

3D visualization of the Wigner function of this state on a surface plot.

Parameters:

xbounds (tuple[int]) – The range of the x axis.
pbounds (tuple[int]) – The range of the p axis.
resolution (int) – The number of bins on each axes.
colorscale (str) – A colorscale. Must be one of Plotly's built-in continuous color scales.
return_fig (bool) – Whether to return the Plotly figure.

Return type:

Optional[Figure]

Returns:

A Plotly figure representing the state in 3D.

Raises:

ValueError – If this state is a multi-mode state.

visualize_dm(cutoff=None, return_fig=False)¶

Plots the absolute value \(abs(\rho)\) of the density matrix \(\rho\) of this state on a heatmap.

Parameters:

cutoff (Optional[int]) – The desired cutoff. Defaults to the value of AUTOCUTOFF_MAX_CUTOFF in the settings.
return_fig (bool) – Whether to return the Plotly figure.

Return type:

Optional[Figure]

Returns:

A Plotly figure representing absolute value of the density matrix of this state.

Raises:

ValueError – If this state is a multi-mode state.

code/api/mrmustard.lab_dev.states.Vacuum

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mm.lab_dev.states.Vacuum¶

Details and Conventions

Attributes

Methods

Contents