pygsti.modelmembers.operations.embeddedop

The EmbeddedOp class and supporting functionality.

Module Contents

Classes

EmbeddedOp

An operation containing a single lower (or equal) dimensional operation within it.

class pygsti.modelmembers.operations.embeddedop.EmbeddedOp(state_space, target_labels, operation_to_embed)

Bases: pygsti.modelmembers.operations.linearop.LinearOperator

An operation containing a single lower (or equal) dimensional operation within it.

An EmbeddedOp acts as the identity on all of its domain except the subspace of its contained operation, where it acts as the contained operation does.

Parameters
  • state_space (StateSpace) – Specifies the density matrix space upon which this operation acts.

  • target_labels (list of strs) – The labels contained in state_space which demarcate the portions of the state space acted on by operation_to_embed (the “contained” operation).

  • operation_to_embed (LinearOperator) – The operation object that is to be contained within this operation, and that specifies the only non-trivial action of the EmbeddedOp.

_update_denserep(self)

Performs additional update for the case when we use a dense underlying representation.

__getstate__(self)

Don’t pickle parent

__setstate__(self, d)
submembers(self)

Get the ModelMember-derived objects contained in this one.

Returns

list

set_time(self, t)

Sets the current time for a time-dependent operator.

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

Parameters

t (float) – The current time.

Returns

None

_iter_matrix_elements_precalc(self, on_space)
_iter_matrix_elements(self, on_space, rel_to_block=False)

Iterates of (op_i,op_j,embedded_op_i,embedded_op_j) tuples giving mapping between nonzero elements of operation matrix and elements of the embedded operation matrix

to_sparse(self, on_space='minimal')

Return the operation as a sparse matrix

Returns

scipy.sparse.csr_matrix

to_dense(self, on_space='minimal')

Return the operation as a dense matrix

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.

Returns

numpy.ndarray

property parameter_labels(self)

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

property num_params(self)

Get the number of independent parameters which specify this operation.

Returns

int – the number of independent parameters.

to_vector(self)

Get the operation parameters as an array of values.

Returns

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

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

Initialize the operation using a vector of parameters.

Parameters
  • v (numpy array) – The 1D vector of operation parameters. Length must == num_params()

  • close (bool, optional) – Whether v is close to this operation’s current set of parameters. Under some circumstances, when this is true this call can be completed more quickly.

  • dirty_value (bool, 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(self, wrt_filter=None)

The element-wise derivative this operation.

Construct a matrix whose columns are the vectorized derivatives of the flattened operation matrix with respect to a single operation parameter. Thus, each column is of length op_dim^2 and there is one column per operation parameter.

Parameters

wrt_filter (list 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 with shape (dimension^2, num_params)

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

Get the order-th order Taylor-expansion terms of this operation.

This function either constructs or returns a cached list of the terms at the given order. Each term is “rank-1”, meaning that its action on a density matrix rho can be written:

rho -> A rho B

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

Parameters
  • order (int) – The order of terms to get.

  • max_polynomial_vars (int, optional) – maximum number of variables the created polynomials can have.

  • return_coeff_polys (bool) – 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

  • terms (list) – A list of RankOneTerm objects.

  • coefficients (list) – 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 :method:`Polynomial.compact`.

taylor_order_terms_above_mag(self, order, max_polynomial_vars, min_term_mag)

Get the order-th order Taylor-expansion terms of this operation 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 :method:`taylor_order_terms` internally, so that all the terms at order order are typically cached for future calls.

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

Parameters
  • order (int) – The order of terms to get (and filter).

  • max_polynomial_vars (int, optional) – maximum number of variables the created polynomials can have.

  • min_term_mag (float) – the minimum term magnitude.

Returns

list – A list of Rank1Term objects.

property total_term_magnitude(self)

Get the total (sum) of the magnitudes of all this operator’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 operator in a Taylor series.

Returns

float

property total_term_magnitude_deriv(self)

The derivative of the sum of all this operator’s terms.

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

Returns

numpy array – An array of length self.num_params

abstract transform_inplace(self, s)

Update operation matrix O with inv(s) * O * s.

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

In this particular case any TP gauge transformation is possible, i.e. when s is an instance of TPGaugeGroupElement or corresponds to a TP-like transform matrix.

Parameters

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

Returns

None

errorgen_coefficients(self, return_basis=False, logscale_nonham=False)

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

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_basis (bool, optional) – Whether to also return a Basis containing the elements with which the error generator terms were constructed.

  • logscale_nonham (bool, 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 :method:`error_rates`.

Returns

  • lindblad_term_dict (dict) – 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.

  • basis (Basis) – A Basis mapping the basis labels used in the keys of lindblad_term_dict to basis matrices.

errorgen_coefficients_array(self)

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

Constructs a 1D array of all the coefficients returned by :method:`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 operation’s error generator.

errorgen_coefficients_array_deriv_wrt_params(self)

The jacobian of :method:`errogen_coefficients_array` with respect to this operation’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.

error_rates(self)

Constructs a dictionary of the error rates associated with this operation.

The “error rate” for an individual Hamiltonian error is the angle about the “axis” (generalized in the multi-qubit case) corresponding to a particular basis element, i.e. theta in the unitary channel U = exp(i * theta/2 * BasisElement).

The “error rate” for an individual Stochastic error is the contribution that basis element’s term would have to the error rate of a depolarization channel. For example, if the rate corresponding to the term (‘S’,’X’) is 0.01 this means that the coefficient of the rho -> X*rho*X-rho error generator is set such that if this coefficient were used for all 3 (X,Y, and Z) terms the resulting depolarizing channel would have error rate 3*0.01 = 0.03.

Note that because error generator terms do not necessarily commute with one another, the sum of the returned error rates is not necessarily the error rate of the overall channel.

Returns

lindblad_term_dict (dict) – 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 real error rates except for the 2-basis-label case.

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

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

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_dict (dict) – 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_nonham (bool, 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 :method:`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 :method:`set_error_rates`.

  • truncate (bool, 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

set_error_rates(self, lindblad_term_dict, action='update')

Sets the coeffcients of terms in the error generator of this operation.

Values are set so that the contributions of the resulting channel’s error rate are given by the values in lindblad_term_dict. See :method:`error_rates` for more details.

Parameters
  • lindblad_term_dict (dict) – 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 real error rates except for the 2-basis-label case, when they may be complex.

  • action ({"update","add","reset"}) – How the values in lindblad_term_dict should be combined with existing error rates.

Returns

None

depolarize(self, amount)

Depolarize this operation by the given amount.

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

Parameters

amount (float or tuple) – The amount to depolarize by. If a tuple, it must have length equal to one less than the dimension of the operation. In standard bases, depolarization corresponds to multiplying the operation matrix by a diagonal matrix whose first diagonal element (corresponding to the identity) equals 1.0 and whose subsequent elements (corresponding to non-identity basis elements) equal 1.0 - amount[i] (or just 1.0 - amount if amount is a float).

Returns

None

rotate(self, amount, mx_basis='gm')

Rotate this operation by the given amount.

Generally, the rotate function updates the parameters of the operation such that the resulting operation matrix is rotated. If such an update cannot be done (because the operation parameters do not allow for it), ValueError is raised.

Parameters
  • amount (tuple of floats, optional) – Specifies the rotation “coefficients” along each of the non-identity Pauli-product axes. The operation’s matrix G is composed with a rotation operation R (so G -> dot(R, G) ) where R is the unitary superoperator corresponding to the unitary operator U = exp( sum_k( i * rotate[k] / 2.0 * Pauli_k ) ). Here Pauli_k ranges over all of the non-identity un-normalized Pauli operators.

  • mx_basis ({'std', 'gm', 'pp', 'qt'} or Basis object) – The source and destination basis, respectively. Allowed values are Matrix-unit (std), Gell-Mann (gm), Pauli-product (pp), and Qutrit (qt) (or a custom basis object).

Returns

None

has_nonzero_hessian(self)

Whether this operation has a non-zero Hessian with respect to its parameters.

(i.e. whether it only depends linearly on its parameters or not)

Returns

bool

to_memoized_dict(self, 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.

classmethod _from_memoized_dict(cls, mm_dict, serial_memo)

For subclasses to implement. Submember-existence checks are performed, and the gpindices of the return value is set, by the non-underscored :method:`from_memoized_dict` implemented in this class.

_is_similar(self, other, rtol, atol)

Returns True if other model member (which it guaranteed to be the same type as self) has the same local structure, i.e., not considering parameter values or submembers

_oneline_contents(self)

Summarizes the contents of this object in a single line. Does not summarize submembers.

__str__(self)

Return string representation