# 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)[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 (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.