pygsti.modelmembers.operations.embeddedop
The EmbeddedOp class and supporting functionality.
Module Contents
Classes
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, allocated_to_parent=None)
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_spaceStateSpace
Specifies the density matrix space upon which this operation acts.
- target_labelslist 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_embedLinearOperator
The operation object that is to be contained within this operation, and that specifies the only non-trivial action of the EmbeddedOp.
Initialize a new LinearOperator
- 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 operation.
Returns
- int
the number of independent parameters.
- property total_term_magnitude
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
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
- set_time(t)
Sets the current time for a time-dependent operator.
For time-independent operators (the default), this function does nothing.
Parameters
- tfloat
The current time.
Returns
None
- to_sparse(on_space='minimal')
Return the operation as a sparse matrix
Returns
scipy.sparse.csr_matrix
- to_dense(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
- to_vector()
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(v, close=False, dirty_value=True)
Initialize the operation using a vector of parameters.
Parameters
- vnumpy array
The 1D vector of operation parameters. Length must == num_params()
- closebool, 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_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 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_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 with shape (dimension^2, num_params)
- taylor_order_terms(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
- 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 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
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
- orderint
The order of terms to get (and filter).
- max_polynomial_varsint, optional
maximum number of variables the created polynomials can have.
- min_term_magfloat
the minimum term magnitude.
Returns
- list
A list of
Rank1Term
objects.
- abstract transform_inplace(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
- sGaugeGroupElement
A gauge group element which specifies the “s” matrix (and it’s inverse) used in the above similarity transform.
Returns
None
- errorgen_coefficients(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_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()
.
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.
- errorgen_coefficient_labels()
The elementary error-generator labels corresponding to the elements of
errorgen_coefficients_array()
.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 operation’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 operation’s error generator.
- errorgen_coefficients_array_deriv_wrt_params()
The jacobian of
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()
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_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 real error rates except for the 2-basis-label case.
- set_errorgen_coefficients(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_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 functionset_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
- set_error_rates(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
error_rates()
for more details.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 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(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
- amountfloat 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(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
- amounttuple 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()
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(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.