`pygsti.modelmembers.states`

Sub-package holding model state preparation objects.

Submodules

Package Contents

Classes

`ComputationalBasisPOVM`	A POVM that "measures" states in the computational "Z" basis.
`ComposedState`	TODO: update docstring
`ComputationalBasisState`	A static state vector that is tensor product of 1-qubit Z-eigenstates.
`CPTPState`	TODO: update docstring
`FullPureState`	A "fully parameterized" state vector where each element is an independent parameter.
`FullState`	A "fully parameterized" state vector where each element is an independent parameter.
`State`	TODO: update docstring
`StaticPureState`	A pure state vector that is completely fixed, or "static" (i.e. that posesses no parameters).
`StaticState`	A state vector that is completely fixed, or "static" (i.e. that posesses no parameters).
`TensorProductState`	A state vector that is a tensor-product of other state vectors.
`TPState`	A fixed-unit-trace state vector.
`Basis`	An ordered set of labeled matrices/vectors.

Functions

`sum_of_negative_choi_eigenvalues_gate`(op_mx, op_mx_basis)	Compute the sum of the negative Choi eigenvalues of a process matrix.
`create_from_pure_vector`(pure_vector, state_type[, ...])	TODO: docstring -- create a State from a state vector
`create_from_dmvec`(superket_vector, state_type[, ...])
`state_type_from_op_type`(op_type)	Decode an op type into an appropriate state type.
`convert`(state, to_type, basis[, ideal_state, ...])	TODO: update docstring
`finite_difference_deriv_wrt_params`(state[, ...])	Computes a finite-difference Jacobian for a State object.
`check_deriv_wrt_params`(state[, deriv_to_check, ...])	Checks the deriv_wrt_params method of a State object.
`optimize_state`(vec_to_optimize, target_vec)	Optimize the parameters of vec_to_optimize.

class pygsti.modelmembers.states.ComputationalBasisPOVM(nqubits, evotype='default', qubit_filter=None, state_space=None)

Bases: pygsti.modelmembers.povms.povm.POVM, pygsti.modelmembers.errorgencontainer.NoErrorGeneratorInterface

A POVM that “measures” states in the computational “Z” basis.

Parameters

nqubitsint: The number of qubits
evotypeEvotype or str, optional: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
qubit_filterlist, optional: An optional list of integers specifying a subset of the qubits to be measured.
state_spaceStateSpace, optional: The state space for this POVM. If None a default state space with the appropriate number of qubits is used.

Initialize a new ModelMember

nqubits

qubit_filter = 'None'

classmethod from_pure_vectors(pure_vectors, evotype, state_space)

keys(): An iterator over the effect (outcome) labels of this POVM.

values(): An iterator over the effect vectors of this POVM.

items(): An iterator over the (effect_label, effect_vector) items in this POVM.

simplify_effects(prefix='')

Creates a dictionary of simplified effect vectors.

Returns a dictionary of effect POVMEffects that belong to the POVM’s parent Model - that is, whose gpindices are set to all or a subset of this POVM’s gpindices. Such effect vectors are used internally within computations involving the parent Model.

Parameters

prefixstr: A string, usually identitying this POVM, which may be used to prefix the simplified gate keys.

Returns

OrderedDict of POVMEffects

to_memoized_dict(mmg_memo)

Create a serializable dict with references to other objects in the memo.

Parameters

mmg_memo: dict: Memo dict from a ModelMemberGraph, i.e. keys are object ids and values are ModelMemberGraphNodes (which contain the serialize_id). This is NOT the same as other memos in ModelMember (e.g. copy, allocate_gpindices, etc.).

Returns

mm_dict: dict: A dict representation of this ModelMember ready for serialization This must have at least the following fields: module, class, submembers, params, state_space, evotype Additional fields may be added by derived classes.

class pygsti.modelmembers.states.ComposedState(static_state, errormap)

Bases: pygsti.modelmembers.states.state.State

TODO: update docstring A Lindblad-parameterized State (that is also expandable into terms).

Parameters

pure_vecnumpy array or State: An array or State in the full density-matrix space (this vector will have dimension 4 in the case of a single qubit) which represents a pure-state preparation or projection. This is used as the “base” preparation or projection that is followed or preceded by, respectively, the parameterized Lindblad-form error generator. (This argument is not copied if it is a State. A numpy array is converted to a new StaticState.)
errormapMapOperator: The error generator action and parameterization, encapsulated in a gate object. Usually a LindbladOp or ComposedOp object. (This argument is not copied, to allow ComposedStates to share error generator parameters with other gates and spam vectors.)

Initialize a new state Vector

property total_term_magnitude

Get the total (sum) of the magnitudes of all this state vector’s terms.

The magnitude of a term is the absolute value of its coefficient, so this function returns the number you’d get from summing up the absolute-coefficients of all the Taylor terms (at all orders!) you get from expanding this state vector in a Taylor series.

Returns

float

property total_term_magnitude_deriv

The derivative of the sum of all this state vector’s terms.

Get the derivative of the total (sum) of the magnitudes of all this state vector’s terms with respect to the operators (local) parameters.

Returns

numpy array: An array of length self.num_params

property parameter_labels: An array of labels (usually strings) describing this model member’s parameters.

property num_params

Get the number of independent parameters which specify this state vector.

Returns

int: the number of independent parameters.

state_vec

error_map

terms

local_term_poly_coeffs

submembers(): Get the ModelMember-derived objects contained in this one.

Returns

list

set_gpindices(gpindices, parent, memo=None)

Set the parent and indices into the parent’s parameter vector that are used by this ModelMember object.

Parameters

gpindicesslice or integer ndarray: The indices of this objects parameters in its parent’s array.
parentModel or ModelMember: The parent whose parameter array gpindices references.
memodict, optional: A memo dict used to avoid circular references.

Returns

None

to_dense(on_space: pygsti.SpaceT = 'minimal', scratch=None)

Return this state vector as a (dense) numpy array.

The memory in scratch maybe used when it is not-None.

Parameters

on_space{‘minimal’, ‘Hilbert’, ‘HilbertSchmidt’}: The space that the returned dense operation acts upon. For unitary matrices and bra/ket vectors, use ‘Hilbert’. For superoperator matrices and super-bra/super-ket vectors use ‘HilbertSchmidt’. ‘minimal’ means that ‘Hilbert’ is used if possible given this operator’s evolution type, and otherwise ‘HilbertSchmidt’ is used.
scratchnumpy.ndarray, optional: scratch space available for use.

Returns

numpy.ndarray

taylor_order_terms(order, max_polynomial_vars=100, return_coeff_polys=False)

Get the order-th order Taylor-expansion terms of this state vector.

This function either constructs or returns a cached list of the terms at the given order. Each term is “rank-1”, meaning that it is a state preparation followed by or POVM effect preceded by actions on a density matrix rho of the form:

rho -> A rho B

The coefficients of these terms are typically polynomials of the State’s parameters, where the polynomial’s variable indices index the global parameters of the State’s parent (usually a Model) , not the State’s local parameter array (i.e. that returned from to_vector).

Parameters

orderint: The order of terms to get.
max_polynomial_varsint, optional: maximum number of variables the created polynomials can have.
return_coeff_polysbool: Whether a parallel list of locally-indexed (using variable indices corresponding to this object’s parameters rather than its parent’s) polynomial coefficients should be returned as well.

Returns

termslist: A list of RankOneTerm objects.
coefficientslist: Only present when return_coeff_polys == True. A list of compact polynomial objects, meaning that each element is a (vtape,ctape) 2-tuple formed by concatenating together the output of Polynomial.compact().

taylor_order_terms_above_mag(order, max_polynomial_vars, min_term_mag)

Get the order-th order Taylor-expansion terms of this state vector that have magnitude above min_term_mag.

This function constructs the terms at the given order which have a magnitude (given by the absolute value of their coefficient) that is greater than or equal to min_term_mag. It calls taylor_order_terms() internally, so that all the terms at order order are typically cached for future calls.

Parameters

orderint: The order of terms to get.
max_polynomial_varsint, optional: maximum number of variables the created polynomials can have.
min_term_magfloat: the minimum term magnitude.

Returns

list

deriv_wrt_params(wrt_filter=None)

The element-wise derivative this state vector.

Construct a matrix whose columns are the derivatives of the state vector with respect to a single param. Thus, each column is of length dimension and there is one column per state vector parameter.

Parameters

wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Array of derivatives, shape == (dimension, num_params)

hessian_wrt_params(wrt_filter1=None, wrt_filter2=None)

Construct the Hessian of this state vector with respect to its parameters.

This function returns a tensor whose first axis corresponds to the flattened operation matrix and whose 2nd and 3rd axes correspond to the parameters that are differentiated with respect to.

Parameters

wrt_filter1list or numpy.ndarray: List of parameter indices to take 1st derivatives with respect to. (None means to use all the this operation’s parameters.)
wrt_filter2list or numpy.ndarray: List of parameter indices to take 2nd derivatives with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Hessian with shape (dimension, num_params1, num_params2)

to_vector()

Extract a vector of the underlying gate parameters from this gate.

Returns

numpy array: a 1D numpy array with length == num_params().

from_vector(v, close=False, dirty_value=True)

Initialize the state vector using a 1D array of parameters.

Parameters

vnumpy array: The 1D vector of state vector parameters. Length must == num_params()
closebool, optional: Whether v is close to this state vector’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.
dirty_valuebool, optional: The value to set this object’s “dirty flag” to before exiting this call. This is passed as an argument so it can be updated recursively. Leave this set to True unless you know what you’re doing.

Returns

None

transform_inplace(s)

Update state (column) vector V as inv(s) * V or s^T * V for preparation or effect state vectors, respectively.

Note that this is equivalent to state preparation vectors getting mapped: rho -> inv(s) * rho and the transpose of effect vectors being mapped as E^T -> E^T * s.

Generally, the transform function updates the parameters of the state vector such that the resulting vector is altered as described above. If such an update cannot be done (because the gate parameters do not allow for it), ValueError is raised.

Parameters

sGaugeGroupElement: A gauge group element which specifies the “s” matrix (and it’s inverse) used in the above similarity transform.

Returns

None

depolarize(amount)

Depolarize this state vector by the given amount.

Generally, the depolarize function updates the parameters of the State such that the resulting vector is depolarized. If such an update cannot be done (because the gate parameters do not allow for it), ValueError is raised.

Parameters

amountfloat or tuple: The amount to depolarize by. If a tuple, it must have length equal to one less than the dimension of the spam vector. All but the first element of the spam vector (often corresponding to the identity element) are multiplied by amount (if a float) or the corresponding amount[i] (if a tuple).

Returns

None

errorgen_coefficient_labels(label_type='global')

The elementary error-generator labels corresponding to the elements of errorgen_coefficients_array().

Parameters

label_typestr, optional (default ‘global’): String specifying which type of ElementaryErrorgenLabel to use as the keys for the returned dictionary. Allowed options are ‘global’ for GlobalElementaryErrorgenLabel and ‘local’ for LocalElementaryErrorgenLabel.

Returns

tuple: A tuple of (<type>, <basisEl1> [,<basisEl2]) elements identifying the elementary error generators of this gate.

errorgen_coefficients_array()

The weighted coefficients of this state prep’s error generator in terms of “standard” error generators.

Constructs a 1D array of all the coefficients returned by errorgen_coefficients(), weighted so that different error generators can be weighted differently when a errorgen_penalty_factor is used in an objective function.

Returns

numpy.ndarray: A 1D array of length equal to the number of coefficients in the linear combination of standard error generators that is this state preparation’s error generator.

errorgen_coefficients(return_basis=False, logscale_nonham=False, label_type='global')

Constructs a dictionary of the Lindblad-error-generator coefficients of this state.

Note that these are not necessarily the parameter values, as these coefficients are generally functions of the parameters (so as to keep the coefficients positive, for instance).

Parameters

return_basisbool, optional: Whether to also return a Basis containing the elements with which the error generator terms were constructed.
logscale_nonhambool, optional: Whether or not the non-hamiltonian error generator coefficients should be scaled so that the returned dict contains: (1 - exp(-d^2 * coeff)) / d^2 instead of coeff. This essentially converts the coefficient into a rate that is the contribution this term would have within a depolarizing channel where all stochastic generators had this same coefficient. This is the value returned by error_rates().
label_typestr, optional (default ‘global’): String specifying which type of ElementaryErrorgenLabel to use as the keys for the returned dictionary. Allowed options are ‘global’ for GlobalElementaryErrorgenLabel and ‘local’ for LocalElementaryErrorgenLabel.

Returns

lindblad_term_dictdict: Keys are (termType, basisLabel1, <basisLabel2>) tuples, where termType is “H” (Hamiltonian), “S” (Stochastic), or “A” (Affine). Hamiltonian and Affine terms always have a single basis label (so key is a 2-tuple) whereas Stochastic tuples have 1 basis label to indicate a diagonal term and otherwise have 2 basis labels to specify off-diagonal non-Hamiltonian Lindblad terms. Basis labels are integers starting at 0. Values are complex coefficients.
basisBasis: A Basis mapping the basis labels used in the keys of lindblad_term_dict to basis matrices.

set_errorgen_coefficients(lindblad_term_dict, action='update', logscale_nonham=False, truncate=True)

Sets the coefficients of terms in the error generator of this state.

The dictionary lindblad_term_dict has tuple-keys describing the type of term and the basis elements used to construct it, e.g. (‘H’,’X’).

Parameters

lindblad_term_dictdict: Keys are (termType, basisLabel1, <basisLabel2>) tuples, where termType is “H” (Hamiltonian), “S” (Stochastic), or “A” (Affine). Hamiltonian and Affine terms always have a single basis label (so key is a 2-tuple) whereas Stochastic tuples have 1 basis label to indicate a diagonal term and otherwise have 2 basis labels to specify off-diagonal non-Hamiltonian Lindblad terms. Values are the coefficients of these error generators, and should be real except for the 2-basis-label case.
action{“update”,”add”,”reset”}: How the values in lindblad_term_dict should be combined with existing error-generator coefficients.
logscale_nonhambool, optional: Whether or not the values in lindblad_term_dict for non-hamiltonian error generators should be interpreted as error rates (of an “equivalent” depolarizing channel, see errorgen_coefficients()) instead of raw coefficients. If True, then the non-hamiltonian coefficients are set to -log(1 - d^2*rate)/d^2, where rate is the corresponding value given in lindblad_term_dict. This is what is performed by the function set_error_rates().
truncatebool, optional: Whether to allow adjustment of the errogen coefficients in order to meet constraints (e.g. to preserve CPTP) when necessary. If False, then an error is thrown when the given coefficients cannot be set as specified.

Returns

None

errorgen_coefficients_array_deriv_wrt_params()

The jacobian of errogen_coefficients_array() with respect to this state’s parameters.

Returns

numpy.ndarray: A 2D array of shape (num_coeffs, num_params) where num_coeffs is the number of coefficients of this operation’s error generator and num_params is this operation’s number of parameters.

class pygsti.modelmembers.states.ComputationalBasisState(zvals, basis='pp', evotype='default', state_space=None)

Bases: pygsti.modelmembers.states.state.State, pygsti.modelmembers.errorgencontainer.NoErrorGeneratorInterface

A static state vector that is tensor product of 1-qubit Z-eigenstates.

This is called a “computational basis state” in many contexts.

Parameters

zvalsiterable: A list or other iterable of integer 0 or 1 outcomes specifying which computational basis element this object represents. The length of zvals gives the total number of qubits.
basisBasis or {‘pp’,’gm’,’std’}, optional: The basis used to construct the Hilbert-Schmidt space representation of this state as a super-ket.
evotypeEvotype or str, optional: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this operation. If None a default state space with the appropriate number of qubits is used.

Initialize a new state Vector

property num_params

Get the number of independent parameters which specify this state vector.

Returns

int: the number of independent parameters.

classmethod from_state_vector(vec, basis='pp', evotype='default', state_space=None)

Create a new ComputationalBasisState from a dense vector.

Parameters

vecnumpy.ndarray: A state vector specifying a computational basis state in the standard basis. This vector has length 4^n for n qubits.
basisBasis or {‘pp’,’gm’,’std’}, optional: The basis of vec as a super-ket.
evotypeEvotype or str: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this operation. If None a default state space with the appropriate number of qubits is used.

Returns

ComputationalBasisState

classmethod from_pure_vector(purevec, basis='pp', evotype='default', state_space=None)

Create a new ComputationalBasisState from a pure-state vector.

Currently, purevec must be a single computational basis state (it cannot be a superpostion of multiple of them).

Parameters

purevecnumpy.ndarray: A complex-valued state vector specifying a pure state in the standard computational basis. This vector has length 2^n for n qubits.
basisBasis or {‘pp’,’gm’,’std’}, optional: The basis of vec as a super-ket.
evotypeEvotype or str, optional: The evolution type of the resulting effect vector. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this operation. If None a default state space with the appropriate number of qubits is used.

Returns

ComputationalBasisState

to_dense(on_space: pygsti.SpaceT = 'minimal', scratch=None)

Return this state vector as a (dense) numpy array.

The memory in scratch maybe used when it is not-None.

Parameters

on_space{‘minimal’, ‘Hilbert’, ‘HilbertSchmidt’}: The space that the returned dense operation acts upon. For unitary matrices and bra/ket vectors, use ‘Hilbert’. For superoperator matrices and super-bra/super-ket vectors use ‘HilbertSchmidt’. ‘minimal’ means that ‘Hilbert’ is used if possible given this operator’s evolution type, and otherwise ‘HilbertSchmidt’ is used.
scratchnumpy.ndarray, optional: scratch space available for use.

Returns

numpy.ndarray

taylor_order_terms(order, max_polynomial_vars=100, return_coeff_polys=False)

Get the order-th order Taylor-expansion terms of this state vector.

This function either constructs or returns a cached list of the terms at the given order. Each term is “rank-1”, meaning that it is a state preparation followed by or POVM effect preceded by actions on a density matrix rho of the form:

rho -> A rho B

The coefficients of these terms are typically polynomials of the State’s parameters, where the polynomial’s variable indices index the global parameters of the State’s parent (usually a Model) , not the State’s local parameter array (i.e. that returned from to_vector).

Parameters

orderint: The order of terms to get.
max_polynomial_varsint, optional: maximum number of variables the created polynomials can have.
return_coeff_polysbool: Whether a parallel list of locally-indexed (using variable indices corresponding to this object’s parameters rather than its parent’s) polynomial coefficients should be returned as well.

Returns

termslist: A list of RankOneTerm objects.
coefficientslist: Only present when return_coeff_polys == True. A list of compact polynomial objects, meaning that each element is a (vtape,ctape) 2-tuple formed by concatenating together the output of Polynomial.compact().

to_vector()

Get the state vector parameters as an array of values.

Returns

numpy array: The parameters as a 1D array with length num_params().

from_vector(v, close=False, dirty_value=True)

Initialize the state vector using a 1D array of parameters.

Parameters

vnumpy array: The 1D vector of state vector parameters. Length must == num_params()
closebool, optional: Whether v is close to this state vector’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.
dirty_valuebool, optional: The value to set this object’s “dirty flag” to before exiting this call. This is passed as an argument so it can be updated recursively. Leave this set to True unless you know what you’re doing.

Returns

None

to_memoized_dict(mmg_memo)

Create a serializable dict with references to other objects in the memo.

Parameters

mmg_memo: dict: Memo dict from a ModelMemberGraph, i.e. keys are object ids and values are ModelMemberGraphNodes (which contain the serialize_id). This is NOT the same as other memos in ModelMember (e.g. copy, allocate_gpindices, etc.).

Returns

mm_dict: dict: A dict representation of this ModelMember ready for serialization This must have at least the following fields: module, class, submembers, params, state_space, evotype Additional fields may be added by derived classes.

class pygsti.modelmembers.states.CPTPState(vec, basis, truncate=False, evotype='default', state_space=None)

Bases: pygsti.modelmembers.states.densestate.DenseState

TODO: update docstring A state vector constrained to correspond ot a positive density matrix.

This state vector that is parameterized through the Cholesky decomposition of it’s standard-basis representation as a density matrix (not a Liouville vector). The resulting state vector thus represents a positive density matrix, and additional constraints on the parameters also guarantee that the trace == 1. This state vector is meant for use with CPTP processes, hence the name.

Parameters

vecarray_like or State: a 1D numpy array representing the state operation. The shape of this array sets the dimension of the state.
basis{“std”, “gm”, “pp”, “qt”} or Basis: The basis vec is in. Needed because this parameterization requires we construct the density matrix corresponding to the Lioville vector vec.
trunctatebool, optional: Whether or not a non-positive, trace=1 vec should be truncated to force a successful construction.
evotypeEvotype or str, optional: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this operation. If None a default state space with the appropriate number of qubits is used.

Initialize a new state Vector

property num_params

Get the number of independent parameters which specify this state vector.

Returns

int: the number of independent parameters.

basis

basis_mxs

Lmx

to_memoized_dict(mmg_memo)

Create a serializable dict with references to other objects in the memo.

Parameters

mmg_memo: dict: Memo dict from a ModelMemberGraph, i.e. keys are object ids and values are ModelMemberGraphNodes (which contain the serialize_id). This is NOT the same as other memos in ModelMember (e.g. copy, allocate_gpindices, etc.).

Returns

mm_dict: dict: A dict representation of this ModelMember ready for serialization This must have at least the following fields: module, class, submembers, params, state_space, evotype Additional fields may be added by derived classes.

set_dense(vec)

Set the dense-vector value of this state vector.

Attempts to modify this state vector’s parameters so that the raw state vector becomes vec. Will raise ValueError if this operation is not possible.

Parameters

vecarray_like or State: A numpy array representing a state vector, or a State object.

Returns

None

to_vector()

Get the state vector parameters as an array of values.

Returns

numpy array: The parameters as a 1D array with length num_params().

from_vector(v, close=False, dirty_value=True)

Initialize the state vector using a 1D array of parameters.

Parameters

vnumpy array: The 1D vector of state vector parameters. Length must == num_params()
closebool, optional: Whether v is close to this state vector’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.
dirty_valuebool, optional: The value to set this object’s “dirty flag” to before exiting this call. This is passed as an argument so it can be updated recursively. Leave this set to True unless you know what you’re doing.

Returns

None

deriv_wrt_params(wrt_filter=None)

The element-wise derivative this state vector.

Construct a matrix whose columns are the derivatives of the state vector with respect to a single param. Thus, each column is of length dimension and there is one column per state vector parameter.

Parameters

wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Array of derivatives, shape == (dimension, num_params)

has_nonzero_hessian(): Whether this state vector has a non-zero Hessian with respect to its parameters.

Returns

bool

abstractmethod hessian_wrt_params(wrt_filter1=None, wrt_filter2=None)

Construct the Hessian of this state vector with respect to its parameters.

This function returns a tensor whose first axis corresponds to the flattened operation matrix and whose 2nd and 3rd axes correspond to the parameters that are differentiated with respect to.

Parameters

wrt_filter1list or numpy.ndarray: List of parameter indices to take 1st derivatives with respect to. (None means to use all the this operation’s parameters.)
wrt_filter2list or numpy.ndarray: List of parameter indices to take 2nd derivatives with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Hessian with shape (dimension, num_params1, num_params2)

class pygsti.modelmembers.states.FullPureState(purevec, basis='pp', evotype='default', state_space=None)

Bases: pygsti.modelmembers.states.densestate.DensePureState

A “fully parameterized” state vector where each element is an independent parameter.

Parameters

vecarray_like or State: a 1D numpy array representing the state operation. The shape of this array sets the dimension of the state op.
basisBasis or {‘pp’,’gm’,’std’}, optional: The basis used to construct the Hilbert-Schmidt space representation of this state as a super-ket.
evotypeEvotype or str, optional: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this operation. If None a default state space with the appropriate number of qubits is used.

Initialize a new state Vector

property num_params

Get the number of independent parameters which specify this state vector.

Returns

int: the number of independent parameters.

to_vector()

Get the state vector parameters as an array of values.

Returns

numpy array: The parameters as a 1D array with length num_params().

from_vector(v, close=False, dirty_value=True)

Initialize the state vector using a 1D array of parameters.

Parameters

vnumpy array: The 1D vector of state vector parameters. Length must == num_params()
closebool, optional: Whether v is close to this state vector’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.
dirty_valuebool, optional: The value to set this object’s “dirty flag” to before exiting this call. This is passed as an argument so it can be updated recursively. Leave this set to True unless you know what you’re doing.

Returns

None

deriv_wrt_params(wrt_filter=None)

The element-wise derivative this state vector.

Construct a matrix whose columns are the derivatives of the state vector with respect to a single param. Thus, each column is of length dimension and there is one column per state vector parameter.

Parameters

wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Array of derivatives, shape == (dimension, num_params)

has_nonzero_hessian(): Whether this state vector has a non-zero Hessian with respect to its parameters.

Returns

bool

class pygsti.modelmembers.states.FullState(vec, basis=None, evotype='default', state_space=None)

Bases: pygsti.modelmembers.states.densestate.DenseState

A “fully parameterized” state vector where each element is an independent parameter.

Parameters

vecarray_like or SPAMVec: a 1D numpy array representing the SPAM operation. The shape of this array sets the dimension of the SPAM op.
basisBasis or str: The basis that vec is in.
evotypeEvotype or str, optional: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this state. If None a default state space with the appropriate number of qubits is used.

Initialize a new state Vector

property num_params

Get the number of independent parameters which specify this SPAM vector.

Returns

int: the number of independent parameters.

set_dense(vec)

Set the dense-vector value of this SPAM vector.

Attempts to modify this SPAM vector’s parameters so that the raw SPAM vector becomes vec. Will raise ValueError if this operation is not possible.

Parameters

vecarray_like or SPAMVec: A numpy array representing a SPAM vector, or a SPAMVec object.

Returns

None

to_vector()

Get the SPAM vector parameters as an array of values.

Returns

numpy array: The parameters as a 1D array with length num_params().

from_vector(v, close=False, dirty_value=True)

Initialize the SPAM vector using a 1D array of parameters.

Parameters

vnumpy array: The 1D vector of SPAM vector parameters. Length must == num_params()
closebool, optional: Whether v is close to this SPAM vector’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.
dirty_valuebool, optional: The value to set this object’s “dirty flag” to before exiting this call. This is passed as an argument so it can be updated recursively. Leave this set to True unless you know what you’re doing.

Returns

None

deriv_wrt_params(wrt_filter=None)

The element-wise derivative this SPAM vector.

Construct a matrix whose columns are the derivatives of the SPAM vector with respect to a single param. Thus, each column is of length dimension and there is one column per SPAM vector parameter.

Parameters

wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Array of derivatives, shape == (dimension, num_params)

has_nonzero_hessian(): Whether this SPAM vector has a non-zero Hessian with respect to its parameters.

Returns

bool

class pygsti.modelmembers.states.State(rep, evotype)

Bases: pygsti.modelmembers.modelmember.ModelMember

TODO: update docstring A parameterized state preparation OR POVM effect vector (operator).

This class is the common base class for all specific parameterizations of a state vector.

Parameters

repobject: A representation object containing the core data for this spam vector.
evotypeEvotype: The evolution type.

Attributes

sizeint: The number of independent elements in this state vector (when viewed as a dense array).

Initialize a new state Vector

property dim: Return the dimension of this state (when viewed as a dense array)

Returns

int

property hilbert_schmidt_size: Return the number of independent elements in this state as a dense Hilbert-Schmidt super-ket.

Returns

int

property num_params

Get the number of independent parameters which specify this state vector.

Returns

int: the number of independent parameters.

set_dense(vec)

Set the dense-vector value of this state vector.

Attempts to modify this state vector’s parameters so that the raw state vector becomes vec. Will raise ValueError if this operation is not possible.

Parameters

vecarray_like or State: A numpy array representing a state vector, or a State object.

Returns

None

set_time(t)

Sets the current time for a time-dependent operator.

For time-independent operators (the default), this function does absolutely nothing.

Parameters

tfloat: The current time.

Returns

None

abstractmethod to_dense(on_space: pygsti.SpaceT = 'minimal', scratch=None)

Return this state vector as a (dense) numpy array.

The memory in scratch maybe used when it is not-None.

Parameters

on_space{‘minimal’, ‘Hilbert’, ‘HilbertSchmidt’}: The space that the returned dense operation acts upon. For unitary matrices and bra/ket vectors, use ‘Hilbert’. For superoperator matrices and super-bra/super-ket vectors use ‘HilbertSchmidt’. ‘minimal’ means that ‘Hilbert’ is used if possible given this operator’s evolution type, and otherwise ‘HilbertSchmidt’ is used.
scratchnumpy.ndarray, optional: scratch space available for use.

Returns

numpy.ndarray

abstractmethod taylor_order_terms(order, max_polynomial_vars=100, return_coeff_polys=False)

Get the order-th order Taylor-expansion terms of this state vector.

This function either constructs or returns a cached list of the terms at the given order. Each term is “rank-1”, meaning that it is a state preparation followed by or POVM effect preceded by actions on a density matrix rho of the form:

rho -> A rho B

The coefficients of these terms are typically polynomials of the State’s parameters, where the polynomial’s variable indices index the global parameters of the State’s parent (usually a Model) , not the State’s local parameter array (i.e. that returned from to_vector).

Parameters

orderint: The order of terms to get.
max_polynomial_varsint, optional: maximum number of variables the created polynomials can have.
return_coeff_polysbool: Whether a parallel list of locally-indexed (using variable indices corresponding to this object’s parameters rather than its parent’s) polynomial coefficients should be returned as well.

Returns

termslist: A list of RankOneTerm objects.
coefficientslist: Only present when return_coeff_polys == True. A list of compact polynomial objects, meaning that each element is a (vtape,ctape) 2-tuple formed by concatenating together the output of Polynomial.compact().

highmagnitude_terms(min_term_mag, force_firstorder=True, max_taylor_order=3, max_polynomial_vars=100)

Get terms with magnitude above min_term_mag.

Get the terms (from a Taylor expansion of this state vector) that have magnitude above min_term_mag (the magnitude of a term is taken to be the absolute value of its coefficient), considering only those terms up to some maximum Taylor expansion order, max_taylor_order.

Note that this function also sets the magnitudes of the returned terms (by calling term.set_magnitude(…)) based on the current values of this state vector’s parameters. This is an essential step to using these terms in pruned-path-integral calculations later on.

Parameters

min_term_magfloat: the threshold for term magnitudes: only terms with magnitudes above this value are returned.
force_firstorderbool, optional: if True, then always return all the first-order Taylor-series terms, even if they have magnitudes smaller than min_term_mag. This behavior is needed for using GST with pruned-term calculations, as we may begin with a guess model that has no error (all terms have zero magnitude!) and still need to compute a meaningful jacobian at this point.
max_taylor_orderint, optional: the maximum Taylor-order to consider when checking whether term- magnitudes exceed min_term_mag.
max_polynomial_varsint, optional: maximum number of variables the created polynomials can have.

Returns

highmag_termslist: A list of the high-magnitude terms that were found. These terms are sorted in descending order by term-magnitude.
first_order_indiceslist: A list of the indices into highmag_terms that mark which of these terms are first-order Taylor terms (useful when we’re forcing these terms to always be present).

taylor_order_terms_above_mag(order, max_polynomial_vars, min_term_mag)

Get the order-th order Taylor-expansion terms of this state vector that have magnitude above min_term_mag.

This function constructs the terms at the given order which have a magnitude (given by the absolute value of their coefficient) that is greater than or equal to min_term_mag. It calls taylor_order_terms() internally, so that all the terms at order order are typically cached for future calls.

Parameters

orderint: The order of terms to get.
max_polynomial_varsint, optional: maximum number of variables the created polynomials can have.
min_term_magfloat: the minimum term magnitude.

Returns

list

transform_inplace(s)

Update state preparation (column) vector V as inv(s) * V.

Note that this is equivalent to state preparation vectors getting mapped: rho -> inv(s) * rho.

Generally, the transform function updates the parameters of the state vector such that the resulting vector is altered as described above. If such an update cannot be done (because the gate parameters do not allow for it), ValueError is raised.

Parameters

sGaugeGroupElement: A gauge group element which specifies the “s” matrix (and it’s inverse) used in the above similarity transform.

Returns

None

depolarize(amount)

Depolarize this state vector by the given amount.

Generally, the depolarize function updates the parameters of the State such that the resulting vector is depolarized. If such an update cannot be done (because the gate parameters do not allow for it), ValueError is raised.

Parameters

amountfloat or tuple: The amount to depolarize by. If a tuple, it must have length equal to one less than the dimension of the gate. All but the first element of the spam vector (often corresponding to the identity element) are multiplied by amount (if a float) or the corresponding amount[i] (if a tuple).

Returns

None

to_vector()

Get the state vector parameters as an array of values.

Returns

numpy array: The parameters as a 1D array with length num_params().

from_vector(v, close=False, dirty_value=True)

Initialize the state vector using a 1D array of parameters.

Parameters

vnumpy array: The 1D vector of state vector parameters. Length must == num_params()
closebool, optional: Whether v is close to this state vector’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.
dirty_valuebool, optional: The value to set this object’s “dirty flag” to before exiting this call. This is passed as an argument so it can be updated recursively. Leave this set to True unless you know what you’re doing.

Returns

None

deriv_wrt_params(wrt_filter=None)

The element-wise derivative this state vector.

Construct a matrix whose columns are the derivatives of the state vector with respect to a single param. Thus, each column is of length dimension and there is one column per state vector parameter.

Parameters

wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Array of derivatives, shape == (dimension, num_params)

has_nonzero_hessian(): Whether this state vector has a non-zero Hessian with respect to its parameters.

Returns

bool

hessian_wrt_params(wrt_filter1=None, wrt_filter2=None)

Construct the Hessian of this state vector with respect to its parameters.

This function returns a tensor whose first axis corresponds to the flattened operation matrix and whose 2nd and 3rd axes correspond to the parameters that are differentiated with respect to.

Parameters

wrt_filter1list or numpy.ndarray: List of parameter indices to take 1st derivatives with respect to. (None means to use all the this operation’s parameters.)
wrt_filter2list or numpy.ndarray: List of parameter indices to take 2nd derivatives with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Hessian with shape (dimension, num_params1, num_params2)

class pygsti.modelmembers.states.StaticPureState(purevec, basis='pp', evotype='default', state_space=None)

Bases: pygsti.modelmembers.states.densestate.DensePureState, pygsti.modelmembers.errorgencontainer.NoErrorGeneratorInterface

A pure state vector that is completely fixed, or “static” (i.e. that posesses no parameters).

Parameters

vecarray_like or SPAMVec: a 1D numpy array representing the SPAM operation. The shape of this array sets the dimension of the SPAM op.
basisBasis or {‘pp’,’gm’,’std’}, optional: The basis used to construct the Hilbert-Schmidt space representation of this state as a super-ket.
evotypeEvotype or str, optional: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this operation. If None a default state space with the appropriate number of qubits is used.

Initialize a new state Vector

taylor_order_terms(order, max_polynomial_vars=100, return_coeff_polys=False)

Get the order-th order Taylor-expansion terms of this state vector.

This function either constructs or returns a cached list of the terms at the given order. Each term is “rank-1”, meaning that it is a state preparation followed by or POVM effect preceded by actions on a density matrix rho of the form:

rho -> A rho B

The coefficients of these terms are typically polynomials of the State’s parameters, where the polynomial’s variable indices index the global parameters of the State’s parent (usually a Model) , not the State’s local parameter array (i.e. that returned from to_vector).

Parameters

orderint: The order of terms to get.
max_polynomial_varsint, optional: maximum number of variables the created polynomials can have.
return_coeff_polysbool: Whether a parallel list of locally-indexed (using variable indices corresponding to this object’s parameters rather than its parent’s) polynomial coefficients should be returned as well.

Returns

termslist: A list of RankOneTerm objects.
coefficientslist: Only present when return_coeff_polys == True. A list of compact polynomial objects, meaning that each element is a (vtape,ctape) 2-tuple formed by concatenating together the output of Polynomial.compact().

class pygsti.modelmembers.states.StaticState(vec, basis=None, evotype='default', state_space=None)

Bases: pygsti.modelmembers.states.densestate.DenseState, pygsti.modelmembers.errorgencontainer.NoErrorGeneratorInterface

A state vector that is completely fixed, or “static” (i.e. that posesses no parameters).

Parameters

vecarray_like or State: a 1D numpy array representing the state. The shape of this array sets the dimension of the state.
basisBasis or str: The basis that vec is in.
evotypeEvotype or str, optional: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this operation. If None a default state space with the appropriate number of qubits is used.

Initialize a new state Vector

class pygsti.modelmembers.states.TensorProductState(factors, state_space)

Bases: pygsti.modelmembers.states.state.State

A state vector that is a tensor-product of other state vectors.

Parameters

factorslist of States: a list of the component states to take the tensor product of.
state_spaceStateSpace, optional: The state space for this operation.

Initialize a new state Vector

property parameter_labels: An array of labels (usually strings) describing this model member’s parameters.

property num_params

Get the number of independent parameters which specify this state vector.

Returns

int: the number of independent parameters.

factors

submembers(): Get the ModelMember-derived objects contained in this one.

Returns

list

to_dense(on_space: pygsti.SpaceT = 'minimal', scratch=None)

Return this state vector as a (dense) numpy array.

The memory in scratch maybe used when it is not-None.

Parameters

on_space{‘minimal’, ‘Hilbert’, ‘HilbertSchmidt’}: The space that the returned dense operation acts upon. For unitary matrices and bra/ket vectors, use ‘Hilbert’. For superoperator matrices and super-bra/super-ket vectors use ‘HilbertSchmidt’. ‘minimal’ means that ‘Hilbert’ is used if possible given this operator’s evolution type, and otherwise ‘HilbertSchmidt’ is used.
scratchnumpy.ndarray, optional: scratch space available for use.

Returns

numpy.ndarray

taylor_order_terms(order, max_polynomial_vars=100, return_coeff_polys=False)

Get the order-th order Taylor-expansion terms of this state vector.

This function either constructs or returns a cached list of the terms at the given order. Each term is “rank-1”, meaning that it is a state preparation followed by or POVM effect preceded by actions on a density matrix rho of the form:

rho -> A rho B

The coefficients of these terms are typically polynomials of the State’s parameters, where the polynomial’s variable indices index the global parameters of the State’s parent (usually a Model) , not the State’s local parameter array (i.e. that returned from to_vector).

Parameters

orderint: The order of terms to get.
max_polynomial_varsint, optional: maximum number of variables the created polynomials can have.
return_coeff_polysbool: Whether a parallel list of locally-indexed (using variable indices corresponding to this object’s parameters rather than its parent’s) polynomial coefficients should be returned as well.

Returns

termslist: A list of RankOneTerm objects.
coefficientslist: Only present when return_coeff_polys == True. A list of compact polynomial objects, meaning that each element is a (vtape,ctape) 2-tuple formed by concatenating together the output of Polynomial.compact().

to_vector()

Get the state vector parameters as an array of values.

Returns

numpy array: The parameters as a 1D array with length num_params().

from_vector(v, close=False, dirty_value=True)

Initialize the state vector using a 1D array of parameters.

Parameters

vnumpy array: The 1D vector of state vector parameters. Length must == num_params()
closebool, optional: Whether v is close to this state vector’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.
dirty_valuebool, optional: The value to set this object’s “dirty flag” to before exiting this call. This is passed as an argument so it can be updated recursively. Leave this set to True unless you know what you’re doing.

Returns

None

deriv_wrt_params(wrt_filter=None)

The element-wise derivative this state vector.

Construct a matrix whose columns are the derivatives of the state vector with respect to a single param. Thus, each column is of length dimension and there is one column per state vector parameter.

Parameters

wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Array of derivatives, shape == (dimension, num_params)

has_nonzero_hessian(): Whether this state vector has a non-zero Hessian with respect to its parameters.

Returns

bool

class pygsti.modelmembers.states.TPState(vec, basis=None, evotype='default', state_space=None)

Bases: pygsti.modelmembers.states.densestate.DenseState, pygsti.modelmembers.torchable.Torchable

A fixed-unit-trace state vector.

This state vector is fully parameterized except for the first element, which is frozen to be 1/(d**0.25). This is so that, when the state vector is interpreted in the Pauli or Gell-Mann basis, the represented density matrix has trace == 1. This restriction is frequently used in conjuction with trace-preserving (TP) gates, hence its name.

Parameters

vecarray_like or State: a 1D numpy array representing the state. The shape of this array sets the dimension of the state.
basisBasis or str: The basis that vec is in.
evotypeEvotype or str, optional: The evolution type. The special value “default” is equivalent to specifying the value of pygsti.evotypes.Evotype.default_evotype.
state_spaceStateSpace, optional: The state space for this operation. If None a default state space with the appropriate number of qubits is used.

Initialize a new state Vector

property columnvec: Direct access the the underlying data as column vector, i.e, a (dim,1)-shaped array.

property num_params

Get the number of independent parameters which specify this state vector.

Returns

int: the number of independent parameters.

set_dense(vec)

Set the dense-vector value of this state vector.

Attempts to modify this state vector’s parameters so that the raw state vector becomes vec. Will raise ValueError if this operation is not possible.

Parameters

vecarray_like or State: A numpy array representing a state vector, or a State object.

Returns

None

to_vector()

Get the state vector parameters as an array of values.

Returns

numpy array: The parameters as a 1D array with length num_params().

from_vector(v, close=False, dirty_value=True)

Initialize the state vector using a 1D array of parameters.

Parameters

vnumpy array: The 1D vector of state vector parameters. Length must == num_params()
closebool, optional: Whether v is close to this state vector’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.
dirty_valuebool, optional: The value to set this object’s “dirty flag” to before exiting this call. This is passed as an argument so it can be updated recursively. Leave this set to True unless you know what you’re doing.

Returns

None

stateless_data() → Tuple[int]

Return this ModelMember’s data that is considered constant for purposes of model fitting.

Note: the word “stateless” here is used in the sense of object-oriented programming.

static torch_base(sd: Tuple[int], t_param: torch.Tensor) → torch.Tensor

Suppose “obj” is an instance of some Torchable subclass. If we compute

vec = obj.to_vector() t_param = torch.from_numpy(vec) sd = obj.stateless_data() t = type(obj).torch_base(sd, t_param)

then t will be a PyTorch Tensor that represents “obj” in a canonical numerical way.

The meaning of “canonical” is implementation dependent. If type(obj) implements the .base attribute, then a reasonable implementation will probably satisfy

np.allclose(obj.base, t.numpy()).

deriv_wrt_params(wrt_filter=None)

The element-wise derivative this state vector.

Construct a matrix whose columns are the derivatives of the state vector with respect to a single param. Thus, each column is of length dimension and there is one column per state vector parameter.

Parameters

wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)

Returns

numpy array: Array of derivatives, shape == (dimension, num_params)

has_nonzero_hessian(): Whether this state vector has a non-zero Hessian with respect to its parameters.

Returns

bool

class pygsti.modelmembers.states.Basis(name: str, longname: str, real: bool, sparse: bool)

Bases: pygsti.baseobjs.nicelyserializable.NicelySerializable

An ordered set of labeled matrices/vectors.

The base class for basis objects. A basis in pyGSTi is an abstract notion of a set of labeled elements, or “vectors”. Each basis has a certain size, and has .elements, .labels, and .ellookup members, the latter being a dictionary mapping of labels to elements.

An important point to note that isn’t immediately intuitive is that while Basis object holds elements (in its .elements property) these are not the same as its vectors (given by the object’s vector_elements property). Often times, in what we term a “simple” basis, the you just flatten an element to get the corresponding vector-element. This works for bases where the elements are either vectors (where flattening does nothing) and matrices. By storing elements as distinct from vector_elements, the Basis can capture additional structure of the elements (such as viewing them as matrices) that can be helpful for their display and interpretation. The elements are also sometimes referred to as the “natural elements” because they represent how to display the element in a natrual way. A non-simple basis occurs when vector_elements need to be stored as elements in a larger “embedded” way so that these elements can be displayed and interpeted naturally.

A second important note is that there is assumed to be some underlying “standard” basis underneath all the bases in pyGSTi. The elements in a Basis are always written in this standard basis. In the case of the “std”-named basis in pyGSTi, these elements are just the trivial vector or matrix units, so one can rightly view the “std” pyGSTi basis as the “standard” basis for a that particular dimension.

The arguments below describe the basic properties of all basis objects in pyGSTi. It is important to remember that the vector_elements of a basis are different from its elements (see the Basis docstring), and that dim refers to the vector elements whereas elshape refers to the elements.

For example, consider a 2-element Basis containing the I and X Pauli matrices. The size of this basis is 2, as there are two elements (and two vector elements). Since vector elements are the length-4 flattened Pauli matrices, the dimension (dim) is 4. Since the elements are 2x2 Pauli matrices, the elshape is (2, 2).

As another example consider a basis which spans all the diagonal 2x2 matrices. The elements of this basis are the two matrix units with a 1 in the (0, 0) or (1, 1) location. The vector elements, however, are the length-2 [1, 0] and [0, 1] vectors obtained by extracting just the diagonal entries from each basis element. Thus, for this basis, size=2, dim=2, and elshape=(2, 2) - so the dimension is not just the product of elshape entries (equivalently, elsize).

Parameters

namestring: The name of the basis. This can be anything, but is usually short and abbreviated. There are several types of bases built into pyGSTi that can be constructed by this name.
longnamestring: A more descriptive name for the basis.
realbool: Elements and vector elements are always allowed to have complex entries. This argument indicates whether the coefficients in the expression of an arbitrary vector in this basis must be real. For example, if real=True, then when pyGSTi transforms a vector in some other basis to a vector in this basis, it will demand that the values of that vector (i.e. the coefficients which multiply this basis’s elements to obtain a vector in the “standard” basis) are real.
sparsebool: Whether the elements of .elements for this Basis are stored (when they are stored at all) as sparse matrices or vectors.

Attributes

dimint: The dimension of the vector space this basis fully or partially spans. Equivalently, the length of the vector_elements of the basis.
sizeint: The number of elements (or vector-elements) in the basis.
elshapeint: The shape of each element. Typically either a length-1 or length-2 tuple, corresponding to vector or matrix elements, respectively. Note that vector elements always have shape (dim, ) (or (dim, 1) in the sparse case).
elndimint: The number of element dimensions, i.e. len(self.elshape)
elsizeint: The total element size, i.e. product(self.elshape)
vector_elementslist: The “vectors” of this basis, always 1D (sparse or dense) arrays.

abstract property dim: The dimension of the vector space this basis fully or partially spans. Equivalently, the length of the vector_elements of the basis.

abstract property size: The number of elements (or vector-elements) in the basis.

abstract property elshape: The shape of each element. Typically either a length-1 or length-2 tuple, corresponding to vector or matrix elements, respectively. Note that vector elements always have shape (dim, ) (or (dim, 1) in the sparse case).

property elndim: The number of element dimensions, i.e. len(self.elshape)

Returns

int

property elsize: The total element size, i.e. product(self.elshape)

Returns

int

property first_element_is_identity: True if the first element of this basis is proportional to the identity matrix, False otherwise.

property vector_elements

The “vectors” of this basis, always 1D (sparse or dense) arrays.

Returns

list: A list of 1D arrays.

property to_std_transform_matrix

Retrieve the matrix that transforms a vector from this basis to the standard basis of this basis’s dimension.

Returns

numpy array or scipy.sparse.lil_matrix: An array of shape (dim, size) where dim is the dimension of this basis (the length of its vectors) and size is the size of this basis (its number of vectors).

property from_std_transform_matrix

Retrieve the matrix that transforms vectors from the standard basis to this basis.

Returns

numpy array or scipy sparse matrix: An array of shape (size, dim) where dim is the dimension of this basis (the length of its vectors) and size is the size of this basis (its number of vectors).

property to_elementstd_transform_matrix

Get transformation matrix from this basis to the “element space”.

Get the matrix that transforms vectors in this basis (with length equal to the dim of this basis) to vectors in the “element space” - that is, vectors in the same standard basis that the elements of this basis are expressed in.

Returns

numpy array: An array of shape (element_dim, size) where element_dim is the dimension, i.e. size, of the elements of this basis (e.g. 16 if the elements are 4x4 matrices) and size is the size of this basis (its number of vectors).

property from_elementstd_transform_matrix

Get transformation matrix from “element space” to this basis.

Get the matrix that transforms vectors in the “element space” - that is, vectors in the same standard basis that the elements of this basis are expressed in - to vectors in this basis (with length equal to the dim of this basis).

Returns

numpy array: An array of shape (size, element_dim) where element_dim is the dimension, i.e. size, of the elements of this basis (e.g. 16 if the elements are 4x4 matrices) and size is the size of this basis (its number of vectors).

name

longname

real

sparse

classmethod cast_from_name_and_statespace(name: str, state_space: pygsti.baseobjs.statespace.StateSpace, sparse: bool | None = None) → Basis

classmethod cast_from_name_and_dims(name: str, dim: int | list | tuple, sparse: bool | None = None) → Basis

classmethod cast_from_basis(basis: Basis, dim=None, sparse: bool | None = None) → Basis

classmethod cast_from_arrays(arrays: numpy.ndarray, dim=None, sparse: bool | None = None) → Basis

classmethod cast(arg, dim=None, sparse: bool | None = None) → Basis

is_simple() → bool: Whether the flattened-element vector space is the same space as the space this basis’s vectors belong to.

Returns

bool

is_complete() → bool: Whether this is a complete basis, i.e. this basis’s vectors span the entire space that they live in.

Returns

bool

is_partial() → bool: The negative of is_complete(), effectively “is_incomplete”.

Returns

bool

copy() → Basis: Make a copy of this Basis object.

Returns

Basis

with_sparsity(desired_sparsity: bool) → Basis

Returns either this basis or a copy of it with the desired sparsity.

If this basis has the desired sparsity it is simply returned. If not, this basis is copied to one that does.

Parameters

desired_sparsitybool: The sparsity (True for sparse elements, False for dense elements) that is desired.

Returns

Basis

is_equivalent(other, sparseness_must_match: bool = True) → bool

Tests whether this basis is equal to another basis, optionally ignoring sparseness.

Parameters

otherBasis or str: The basis to compare with.
sparseness_must_matchbool, optional: If False then comparison ignores differing sparseness, and this function returns True when the two bases are equal except for their .sparse values.

Returns

bool

create_transform_matrix(to_basis)

Get the matrix that transforms a vector from this basis to to_basis.

Parameters

to_basisBasis or string: The basis to transform to or a built-in basis name. In the latter case, a basis to transform to is built with the same structure as this basis but with all components constructed from the given name.

Returns

numpy.ndarray (even if basis is sparse)

reverse_transform_matrix(from_basis)

Get the matrix that transforms a vector from from_basis to this basis.

The reverse of create_transform_matrix().

Parameters

from_basisBasis or string: The basis to transform from or a built-in basis name. In the latter case, a basis to transform from is built with the same structure as this basis but with all components constructed from the given name.

Returns

numpy.ndarray (even if basis is sparse)

is_normalized()

Check if a basis is normalized, meaning that Tr(Bi Bi) = 1.0.

Available only to bases whose elements are matrices for now.

Returns

bool

create_equivalent(builtin_basis_name)

Create an equivalent basis with components of type builtin_basis_name.

Create a Basis that is equivalent in structure & dimension to this basis but whose simple components (perhaps just this basis itself) is of the builtin basis type given by builtin_basis_name.

Parameters

builtin_basis_namestr: The name of a builtin basis, e.g. “pp”, “gm”, or “std”. Used to construct the simple components of the returned basis.

Returns

Basis

create_simple_equivalent(builtin_basis_name=None)

Create a basis of type builtin_basis_name whose elements are compatible with this basis.

Create a simple basis and one without components (e.g. a TensorProdBasis, is a simple basis w/components) of the builtin type specified whose dimension is compatible with the elements of this basis. This function might also be named “element_equivalent”, as it returns the builtin_basis_name-analogue of the standard basis that this basis’s elements are expressed in.

Parameters

builtin_basis_namestr, optional: The name of the built-in basis to use. If None, then a copy of this basis is returned (if it’s simple) or this basis’s name is used to try to construct a simple and component-free version of the same builtin-basis type.

Returns

Basis

is_compatible_with_state_space(state_space: pygsti.baseobjs.statespace.StateSpace) → bool

Checks whether this basis is compatible with a given state space.

Parameters

state_spaceStateSpace: the state space to check.

Returns

bool

pygsti.modelmembers.states.sum_of_negative_choi_eigenvalues_gate(op_mx, op_mx_basis)

Compute the sum of the negative Choi eigenvalues of a process matrix.

Parameters

op_mx : np.array

op_mx_basis : Basis

Returns

float: the sum of the negative eigenvalues of the Choi representation of op_mx

pygsti.modelmembers.states.create_from_pure_vector(pure_vector, state_type, basis='pp', evotype='default', state_space=None, on_construction_error='warn'): TODO: docstring – create a State from a state vector

pygsti.modelmembers.states.create_from_dmvec(superket_vector, state_type, basis='pp', evotype='default', state_space=None)

pygsti.modelmembers.states.state_type_from_op_type(op_type)

Decode an op type into an appropriate state type.

Parameters:

op_type: str or list of str: Operation parameterization type (or list of preferences)

Returns

str: State parameterization type

pygsti.modelmembers.states.convert(state, to_type, basis, ideal_state=None, flatten_structure=False, cp_penalty=1e-07)

TODO: update docstring Convert SPAM vector to a new type of parameterization.

This potentially creates a new State object. Raises ValueError for invalid conversions.

Parameters

stateState: State vector to convert
to_type{“full”,”full TP”,”static”,”static unitary”,”clifford”,LINDBLAD}: The type of parameterizaton to convert to. “LINDBLAD” is a placeholder for the various Lindblad parameterization types. See Model.set_all_parameterizations() for more details.
basis{‘std’, ‘gm’, ‘pp’, ‘qt’} or Basis object: The basis for state. Allowed values are Matrix-unit (std), Gell-Mann (gm), Pauli-product (pp), and Qutrit (qt) (or a custom basis object).
ideal_stateState, optional: The ideal (usually pure) version of state, potentially used when converting to an error-generator type.
flatten_structurebool, optional: When False, the sub-members of composed and embedded operations are separately converted, leaving the original state’s structure unchanged. When True, composed and embedded operations are “flattened” into a single state of the requested to_type.
cp_penaltyfloat, optional: CPTP penalty that gets factored into the optimization to find the resulting model when converting to an error-generator type.

Returns

State: The converted State vector, usually a distinct object from the object passed as input.

pygsti.modelmembers.states.finite_difference_deriv_wrt_params(state, wrt_filter=None, eps=1e-07)

Computes a finite-difference Jacobian for a State object.

The returned value is a matrix whose columns are the vectorized derivatives of the spam vector with respect to a single parameter, matching the format expected from the spam vectors’s deriv_wrt_params method.

Parameters

stateState: The spam vector object to compute a Jacobian for.
wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)
epsfloat, optional: The finite difference step to use.

Returns

numpy.ndarray: An M by N matrix where M is the number of gate elements and N is the number of gate parameters.

pygsti.modelmembers.states.check_deriv_wrt_params(state, deriv_to_check=None, wrt_filter=None, eps=1e-07)

Checks the deriv_wrt_params method of a State object.

This routine is meant to be used as an aid in testing and debugging State classes by comparing the finite-difference Jacobian that should be returned by state.deriv_wrt_params with the one that actually is. A ValueError is raised if the two do not match.

Parameters

stateState: The gate object to test.
deriv_to_checknumpy.ndarray or None, optional: If not None, the Jacobian to compare against the finite difference result. If None, state.deriv_wrt_parms() is used. Setting this argument can be useful when the function is called within a LinearOperator class’s deriv_wrt_params() method itself as a part of testing.
wrt_filterlist or numpy.ndarray: List of parameter indices to take derivative with respect to. (None means to use all the this operation’s parameters.)
epsfloat, optional: The finite difference step to use.

Returns

None

pygsti.modelmembers.states.optimize_state(vec_to_optimize, target_vec)

Optimize the parameters of vec_to_optimize.

The optimization is performed so that the the resulting State vector is as close as possible to target_vec.

This is trivial for the case of FullState instances, but for other types of parameterization this involves an iterative optimization over all the parameters of vec_to_optimize.

Parameters

vec_to_optimizeState: The state vector to optimize. This object gets altered.
target_vecState: The state vector used as the target.

Returns

None

pygsti.modelmembers.states

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`pygsti.modelmembers.states`