PauliString

Base class: Object

Object that represents a numerically efficient Pauli String

Represents a Pauli string and it's complex coefficient efficiently using a bitstring representation. This class leverages bit logic to perform common operations on pauli strings much faster than those represented by OperatorProducts and OperatorSums of OperatorNamed Pauli operators. Each Pauli string is represented via a complex coefficient and two integers called xbits and zbits. Bits at the same locations in the integer encode the information of one pauli operator with the following mapping: 00 (I), 10 (X), 01 (Z), 11 (Y). The class takes care of handling the phase accrued during multiplication of different terms.

Constructors

PauliString(const PauliString other) -> PauliString

Copy constructs a PauliString from another PauliString

Parameters

• other: The PauliString to copy.

PauliString(integer num_spins) -> PauliString

Constructs an identity PauliString for a system.

Parameters

• num_spins: The number of spins in the system, from 1 through 256.

PauliString(const string characters, const List<integer> sites, integer num_spins) -> PauliString

Constructs a PauliString from Pauli characters and their sites.

Parameters

• characters: String containing the characters I, X, Y, or Z.
• sites: Sites corresponding to the supplied characters.
• num_spins: The number of spins in the system.

Members

Name	Description
coefficient	Returns the complex coefficient of a PauliString.
commutes_with	Checks whether two PauliStrings commute: $[P,Q] = 0$.‌
display	Displays the coefficient and bit representation of a PauliString.
expval	Calculates the expectation value $\langle\psi\|P\|\psi\rangle$ of a PauliString $P$.‌
multiplied	Right-multiplies the PauliString $P$ by another PauliString $Q$ out of place: $R = PQ$.‌
multiply	Right-multiplies the PauliString $P$ by another PauliString $Q$ in place: $P = PQ$.‌
num_spins	Returns the number of spins represented by a PauliString.
weight	Returns the weight of a PauliString—the number of non-identity operators.
xbits	Returns the X bits of a PauliString as a list of 64-bit chunks. Chunk n contains sites 64n through 64n+63.
zbits	Returns the Z bits of a PauliString as a list of 64-bit chunks. Chunk n contains sites 64n through 64n+63.