7.4. SWAP

input		output
\(\lvert 00\rangle\)	\(\Rightarrow\)	\(\lvert 00\rangle\)
\(\lvert 01\rangle\)	\(\Rightarrow\)	\(\lvert 10\rangle\)
\(\lvert 10\rangle\)	\(\Rightarrow\)	\(\lvert 01\rangle\)
\(\lvert 11\rangle\)	\(\Rightarrow\)	\(\lvert 11\rangle\)

SWAP gate can be a native gate for certain types of quantum computer through exchange interaction. Here we show a circuit equivalent to SWAP.

import numpy as np
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, Aer
from qiskit.quantum_info import Statevector
backend = Aer.get_backend('statevector_simulator')

Using the built-in SWAP gate: |01⟩⇒|10⟩

cr=ClassicalRegister(2)
qr  = QuantumRegister(2)
qc = QuantumCircuit(qr,cr)
qc.x(0)
qc.barrier()
qc.swap(0,1)
qc.measure([0,1],[0,1])
qc.draw()

      ┌───┐ ░    ┌─┐   
q0_0: ┤ X ├─░──X─┤M├───
      └───┘ ░  │ └╥┘┌─┐
q0_1: ──────░──X──╫─┤M├
            ░     ║ └╥┘
c0: 2/════════════╩══╩═
                  0  1 

result=backend.run(qc).result()
(result.get_statevector()).draw('latex')

\[ |10\rangle\]

• Equivalent circuit to SWAP using CX

qr = QuantumRegister(2)
qc = QuantumCircuit(qr)
qc.x(1)
qc.cnot(0,1)
qc.cnot(1,0)
qc.cnot(0,1)
qc.draw()

                ┌───┐     
q1_0: ───────■──┤ X ├──■──
      ┌───┐┌─┴─┐└─┬─┘┌─┴─┐
q1_1: ┤ X ├┤ X ├──■──┤ X ├
      └───┘└───┘     └───┘

result=backend.run(qc).result()
(result.get_statevector()).draw('latex')

\[ |01\rangle\]

Symmetric property: Swapping qubits themselves (not their states) should give the same results.

qr = QuantumRegister(2)
qc = QuantumCircuit(qr)
qc.x([0,1])
qc.barrier()
qc.cnot(1,0)
qc.cnot(0,1)
qc.cnot(1,0)
qc.draw()

      ┌───┐ ░ ┌───┐     ┌───┐
q2_0: ┤ X ├─░─┤ X ├──■──┤ X ├
      ├───┤ ░ └─┬─┘┌─┴─┐└─┬─┘
q2_1: ┤ X ├─░───■──┤ X ├──■──
      └───┘ ░      └───┘     

result=backend.run(qc).result()
(result.get_statevector()).draw('latex')

\[ |11\rangle\]

There is no particular reason to use X direction. CY should be able to realize SWAP as well.

qr = QuantumRegister(2)
qc = QuantumCircuit(qr)
qc.x(0)
qc.barrier()
qc.cy(1,0)
qc.cy(0,1)
qc.cy(1,0)
qc.draw()

      ┌───┐ ░ ┌───┐     ┌───┐
q3_0: ┤ X ├─░─┤ Y ├──■──┤ Y ├
      └───┘ ░ └─┬─┘┌─┴─┐└─┬─┘
q3_1: ──────░───■──┤ Y ├──■──
            ░      └───┘     

result=backend.run(qc).result()
(result.get_statevector()).draw('latex')

\[ |10\rangle\]