Chapter 6. Operator Flow

The qiskit.opflow module contains classes for expressing and manipulating quantum states and operations. Some of the functionality is backed by classes in the qiskit.quantum_info module. One of the main purposes of this Operator Flow layer is to facilitate the development of quantum algorithms.

Creating Operator Flow Expressions

The qiskit.opflow module contains an immutable set of operators, shown in Table 6-1, that are useful in creating expressions that contain quantum states and operators.

Table 6-1. Immutable operators in the qiskit.opflow module
Operator Description

X

Pauli X

Y

Pauli Y

Z

Pauli Z

I

Pauli I

H

H gate

S

S gate

T

T gate

CX

CX gate

CZ

CZ gate

Swap

SWAP gate

Zero

Qubit 0 state

One

Qubit 1 state

Plus

Qubit + state

Minus

Qubit - state

In order to use these operators in expressions, we’ll need algebraic operations and predicates, such as those shown in Table 6-2.

Table 6-2. Algebraic operations and predicates in the qiskit.opflow module
Algebraic operation Description

+

Addition

-

Subtraction/negation

*

Scalar multiplication

/

Scalar division

@

Composition

^

Tensor product or tensor power

**

Composition power

==

Equality

~

Adjoint

These algebraic operations are syntactic sugar for underlying methods that perform functions such as computing tensor products and multiplying matrices, which allows representing complex formulas with a concise syntax.

Using operators and algebraic ...

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