pygsti.tools.symplectic

Symplectic representation utility functions

Functions

apply_clifford_to_stabilizer_state(s, p, ...)	Applies a clifford in the symplectic representation to a stabilizer state in the standard stabilizer representation.
apply_internal_gate_to_symplectic(s, ...[, ...])	Applies a Clifford gate to the n-qubit Clifford gate specified by the 2n x 2n symplectic matrix.
bitstring_for_pauli(p)	Get the bitstring corresponding to a Pauli.
bitstring_to_int(b, n)	Converts an n-bit string b to an integer between 0 and 2^`n` - 1.
change_symplectic_form_convention(s[, ...])	Maps the input symplectic matrix between the 'standard' and 'directsum' symplectic form conventions.
check_symplectic(m[, convention])	Checks whether a matrix is symplectic.
check_valid_clifford(s, p)	Checks if a symplectic matrix - phase vector pair (s,p) is the symplectic representation of a Clifford.
colsum(i, j, s, p, n)	A helper routine used for manipulating stabilizer state representations.
colsum_acc(acc_s, acc_p, j, s, p, n)	A helper routine used for manipulating stabilizer state representations.
compose_cliffords(s1, p1, s2, p2[, do_checks])	Multiplies two cliffords in the symplectic representation.
compute_internal_gate_symplectic_representations([...])	Creates a dictionary of the symplectic representations of 'standard' Clifford gates.
compute_num_cliffords(n)	The number of Clifford gates in the n-qubit Clifford group.
compute_num_cosets(n)	Returns the number of different cosets for the symplectic group S(n) over the 2-element finite field.
compute_num_symplectics(n)	The number of elements in the symplectic group S(n) over the 2-element finite field.
compute_symplectic_label(gn[, n])	Returns the "canonical" index of 2n x 2n symplectic matrix gn over the finite field containing 0 and 1.
compute_symplectic_matrix(i, n)	Returns the 2n x 2n symplectic matrix, over the finite field containing 0 and 1, with the "canonical" index i.
construct_valid_phase_vector(s, pseed)	Constructs a phase vector that, when paired with the provided symplectic matrix, defines a Clifford gate.
embed_clifford(s, p, qubit_inds, n)	Embeds the (s,p) Clifford symplectic representation into a larger symplectic representation.
find_pauli_layer(pvec, qubit_labels[, ...])	TODO: docstring pauli_labels defaults to ['I', 'X', 'Y', 'Z'].
find_pauli_number(pvec)	TODO: docstring
find_postmultipled_pauli(s, p_implemented, ...)	Finds the Pauli layer that should be appended to a circuit to implement a given Clifford.
find_premultipled_pauli(s, p_implemented, ...)	Finds the Pauli layer that should be prepended to a circuit to implement a given Clifford.
find_symplectic_transvection(x, y)	A utility function for selecting a random Clifford element.
int_to_bitstring(i, n)	Converts integer i to an length n array of bits.
inverse_clifford(s, p)	Returns the inverse of a Clifford gate in the symplectic representation.
inverse_symplectic(s)	Returns the inverse of a symplectic matrix over the integers mod 2.
one_q_clifford_symplectic_group_relations()	Gives the group relationship between the 'I', 'H', 'P' 'HP', 'PH', and 'HPH' up-to-Paulis operators.
pauli_z_measurement(state_s, state_p, ...)	Computes the probabilities of 0/1 (+/-) outcomes from measuring a Pauli operator on a stabilizer state.
prep_stabilizer_state(nqubits[, zvals])	Construct the (s,p) stabilizer representation for a computational basis state given by zvals.
random_clifford(n[, rand_state])	Returns a Clifford, in the symplectic representation, sampled uniformly at random from the n-qubit Clifford group.
random_phase_vector(s, n[, rand_state])	Generates a uniformly random phase vector for a n-qubit Clifford.
random_symplectic_index(n[, rand_state])	The index of a uniformly random 2n x 2n symplectic matrix over the finite field containing 0 and 1.
random_symplectic_matrix(n[, convention, ...])	Returns a symplectic matrix of dimensions 2n x 2n sampled uniformly at random from the symplectic group S(n).
stabilizer_measurement_prob(state_sp_tuple, ...)	Compute the probability of a given outcome when measuring some or all of the qubits in a stabilizer state.
symplectic_form(n[, convention])	Creates the symplectic form for the number of qubits specified.
symplectic_innerproduct(v, w)	Returns the symplectic inner product of two vectors in F_2^(2n).
symplectic_kronecker(sp_factors)	Takes a kronecker product of symplectic representations.
symplectic_rep_of_clifford_circuit(circuit)	Returns the symplectic representation of the composite Clifford implemented by the specified Clifford circuit.
symplectic_rep_of_clifford_layer(layer[, n, ...])	Constructs the symplectic representation of the n-qubit Clifford implemented by a single quantum circuit layer.
symplectic_transvection(k, v)	Applies transvection Z k to v.
unitary_is_clifford(unitary)	Returns True if the unitary is a Clifford gate (w.r.t the standard basis), and False otherwise.
unitary_to_symplectic(u[, flagnonclifford])	Returns the symplectic representation of a one-qubit or two-qubit Clifford unitary.