# InnerProduct¶

class InnerProduct(num_qubits)[source]

Bases: qiskit.circuit.quantumcircuit.QuantumCircuit

A 2n-qubit Boolean function that computes the inner product of two n-qubit vectors over $$F_2$$.

This implementation is a phase oracle which computes the following transform.

$\mathcal{IP}_{2n} : F_2^{2n} \rightarrow {-1, 1} \mathcal{IP}_{2n}(x_1, \cdots, x_n, y_1, \cdots, y_n) = (-1)^{x.y}$

The corresponding unitary is a diagonal, which induces a -1 phase on any inputs where the inner product of the top and bottom registers is 1. Otherwise it keeps the input intact.

q0_0: ─■──────────
│
q0_1: ─┼──■───────
│  │
q0_2: ─┼──┼──■────
│  │  │
q0_3: ─┼──┼──┼──■─
│  │  │  │
q1_0: ─■──┼──┼──┼─
│  │  │
q1_1: ────■──┼──┼─
│  │
q1_2: ───────■──┼─
│
q1_3: ──────────■─

Reference Circuit:

Return a circuit to compute the inner product of 2 n-qubit registers.

Parameters

num_qubits (int) -- width of top and bottom registers (half total circuit width)

Attributes

ancillas

Returns a list of ancilla bits in the order that the registers were added.

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form

{'gate_name': {(qubits, params): schedule}}

clbits

Returns a list of classical bits in the order that the registers were added.

data

Return the circuit data (instructions and context).

Returns

a list-like object containing the tuples for the circuit's data.

Each tuple is in the format (instruction, qargs, cargs), where instruction is an Instruction (or subclass) object, qargs is a list of Qubit objects, and cargs is a list of Clbit objects.

Return type

QuantumCircuitData

extension_lib = 'include "qelib1.inc";'
global_phase

Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'
instances = 16
metadata

The user provided metadata associated with the circuit

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

num_ancillas

Return the number of ancilla qubits.

num_clbits

Return number of classical bits.

num_parameters

Convenience function to get the number of parameter objects in the circuit.

num_qubits

Return number of qubits.

parameters

Convenience function to get the parameters defined in the parameter table.

prefix = 'circuit'
qubits

Returns a list of quantum bits in the order that the registers were added.