Pauli Operators

Quantum operators can be expressed as combinations of Pauli operators I, X, Y, Z:

>>> operator = sZ(0)*sZ(1) + sX(2)*sY(3)
>>> print(operator)
(1+0j)*Z0*Z1 + (1+0j)*X2*Y3

Construction functions

sX(q)	A function that returns the sigma_X operator on a particular qubit.
sY(q)	A function that returns the sigma_Y operator on a particular qubit.
sZ(q)	A function that returns the sigma_Z operator on a particular qubit.
sI([q])	A function that returns the identity operator, optionally on a particular qubit.
ID()	The identity operator.
ZERO()	The zero operator.

Working with operators

simplify_pauli_sum(pauli_sum)	Simplify the sum of Pauli operators according to Pauli algebra rules.
check_commutation(pauli_list, pauli_two)	Check if commuting a PauliTerm commutes with a list of other terms by natural calculation.
commuting_sets(pauli_terms)	Gather the Pauli terms of pauli_terms variable into commuting sets
is_identity(term)	Tests to see if a PauliTerm or PauliSum is a scalar multiple of identity
is_zero(pauli_object)	Tests to see if a PauliTerm or PauliSum is zero.
exponentiate(term)	Creates a pyQuil program that simulates the unitary evolution exp(-1j * term)
exponential_map(term)	Returns a function f(alpha) that constructs the Program corresponding to exp(-1j*alpha*term).
exponentiate_commuting_pauli_sum(pauli_sum)	Returns a function that maps all substituent PauliTerms and sums them into a program.
suzuki_trotter(trotter_order, trotter_steps)	Generate trotterization coefficients for a given number of Trotter steps.
trotterize(first_pauli_term, second_pauli_term)	Create a Quil program that approximates exp( (A + B)t) where A and B are PauliTerm operators.

Classes

class pyquil.paulis.PauliSum(terms)

A sum of one or more PauliTerms.

Parameters

terms (Sequence) – A Sequence of PauliTerms.

Methods

get_qubits()	The support of all the operators in the PauliSum object.
simplify()	Simplifies the sum of Pauli operators according to Pauli algebra rules.
get_programs()	Get a Pyquil Program corresponding to each term in the PauliSum and a coefficient for each program
from_compact_str(str_pauli_sum)	Construct a PauliSum from the result of str(pauli_sum)

class pyquil.paulis.PauliTerm(op, index, coefficient=1.0)

A term is a product of Pauli operators operating on different qubits.

Create a new Pauli Term with a Pauli operator at a particular index and a leading coefficient.

Parameters

• op (str) – The Pauli operator as a string “X”, “Y”, “Z”, or “I”

• index (Union[int, FormalArgument, QubitPlaceholder, None]) – The qubit index that that operator is applied to.

• coefficient (Union[Expression, int, float, complex]) – The coefficient multiplying the operator, e.g. 1.5 * Z_1

Methods

id([sort_ops])	Returns an identifier string for the PauliTerm (ignoring the coefficient).
operations_as_set()	Return a frozenset of operations in this term.
copy()	Properly creates a new PauliTerm, with a completely new dictionary of operators
program	rtype Program
from_list(terms_list[, coefficient])	Allocates a Pauli Term from a list of operators and indices.
pauli_string([qubits])	Return a string representation of this PauliTerm without its coefficient and with implicit qubit indices.