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.

`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(-1jalphaterm).
`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.

class pyquil.paulis.PauliSum(terms)[source]¶

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)[source]¶

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 (`int`) – The qubit index that that operator is applied to. coefficient (`Union`[`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

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.