grover_example.py

#!/usr/bin/env python

"""Grover's quantum search algorithm example."""

from sympy import pprint
from sympy.physics.quantum import qapply
from sympy.physics.quantum.qubit import IntQubit
from sympy.physics.quantum.grover import (OracleGate, superposition_basis,
        WGate, grover_iteration)


def demo_vgate_app(v):
    for i in range(2**v.nqubits):
        print 'qapply(v*IntQubit(%i, %r))' % (i, v.nqubits)
        pprint(qapply(v*IntQubit(i, v.nqubits)))
        qapply(v*IntQubit(i, v.nqubits))


def black_box(qubits):
    return True if qubits == IntQubit(1, qubits.nqubits) else False


def main():
    print
    print 'Demonstration of Grover\'s Algorithm'
    print 'The OracleGate or V Gate carries the unknown function f(x)'
    print '> V|x> = ((-1)^f(x))|x> where f(x) = 1 when x = a (True in our case)'
    print '> and 0 (False in our case) otherwise'
    print

    nqubits = 2
    print 'nqubits = ', nqubits

    v = OracleGate(nqubits, black_box)
    print 'Oracle or v = OracleGate(%r, black_box)' % nqubits
    print

    psi = superposition_basis(nqubits)
    print 'psi:'
    pprint(psi)
    demo_vgate_app(v)
    print 'qapply(v*psi)'
    pprint(qapply(v*psi))
    print

    w = WGate(nqubits)
    print 'WGate or w = WGate(%r)' % nqubits
    print 'On a 2 Qubit system like psi, 1 iteration is enough to yield |1>'
    print 'qapply(w*v*psi)'
    pprint(qapply(w*v*psi))
    print

    nqubits = 3
    print 'On a 3 Qubit system, it requires 2 iterations to achieve'
    print '|1> with high enough probability'
    psi = superposition_basis(nqubits)
    print 'psi:'
    pprint(psi)

    v = OracleGate(nqubits, black_box)
    print 'Oracle or v = OracleGate(%r, black_box)' % nqubits
    print

    print 'iter1 = grover.grover_iteration(psi, v)'
    iter1 = qapply(grover_iteration(psi, v))
    pprint(iter1)
    print

    print 'iter2 = grover.grover_iteration(iter1, v)'
    iter2 = qapply(grover_iteration(iter1, v))
    pprint(iter2)
    print

if __name__ == "__main__":
    main()