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grovers.ipynb
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Grover's Algorithm
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%load_ext sympyprinting
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from sympy import sqrt, symbols, Rational
from sympy import expand, Eq, Symbol, simplify, exp, sin
from sympy.physics.quantum import *
from sympy.physics.quantum.qubit import *
from sympy.physics.quantum.gate import *
from sympy.physics.quantum.grover import *
from sympy.physics.quantum.qft import QFT, IQFT, Fourier
from sympy.physics.quantum.circuitplot import circuit_plot
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nqubits = 3
Grover's algorithm is a quantum algorithm which searches an unordered database (inverts a function).
Provides polynomial speedup over classical brute-force search (O(√N)vs.O(N))
Define a black box function that returns True if it is passed the state we are searching for.
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def black_box(qubits):
return True if qubits == IntQubit(1, qubits.nqubits) else False
Build a uniform superposition state to start the search.
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psi = superposition_basis(nqubits); psi
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v = OracleGate(nqubits, black_box)
Perform two iterations of Grover's algorithm. Each iteration, the amplitude of the target state increases.
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iter1 = qapply(grover_iteration(psi, v)); iter1
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iter2 = qapply(grover_iteration(iter1, v)); iter2
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A single shot measurement is performed to retrieve the target state.
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measure_all_oneshot(iter2)
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