def grover_invert(f, y, n):
"""Grover's algorithm for inverting a general function f that maps a
sequence of n bits (represented as an int whose binary representation is the
bit sequence) to another sequence of bits.
Args:
f: Function to invert
y: Value of the function at which to evaluate the inverse.
Returns:
The input x such that f(x) = y. If more than one input suffices, it
returns one at random. If no input suffices, returns -1.
"""
if n <= 0:
raise ValueError('n must be positive')
Hn = hadamard_gate(n)
Ui = _function_oracle(f, y, n)
Ud = grover_diffusion_operator(n)
MAX_ITER = 50
count = 0
x = None
# Repeat until a solution is found or the iteration limit is reached
while count < MAX_ITER and (x is None or f(x) != y):
q = QubitSystem(n) # system of n bits in state |0>
# apply Hadamard gate to create uniform superposition of basis states
Hn * q
for _ in range(_r(2**n)):
Ui * q # apply operator that flips the sign of the matching index
Ud * q # apply Grover's diffusion operator
x = q.measure()
count += 1
return x if f(x) == y else -1
def grover_search(match_text, lst):
"""Grover's quantum algorithm for searching.
Args:
match_text: Text to find in the list lst.
lst: List of strings to search to find a string matching match_text.
Returns:
The index i of the item such that lst[i] is the same string as
match_text. The lines must match exactly; it is not enough for the text
to be contained in the line. If two or more lines match, it will only
return one of the line numbers. Returns -1 if no matching line is found,
i.e. the algorithm fails to find a solution.
"""
if len(lst) <= 0:
raise ValueError('List must be of positive length')
n = len(lst)
N = int(ceil(log(n, 2))) # number of qubits needed
Hn = hadamard_gate(N)
Ui = _search_oracle(match_text, lst)
Ud = grover_diffusion_operator(N)
MAX_ITER = 50
count = 0
index = n
# Repeat until a solution is found or the iteration limit is reached
while count < MAX_ITER and (index >= n or lst[index] != match_text):
q = QubitSystem(N) # system of log2(n) bits in state |0>
# apply Hadamard gate to create uniform superposition of basis states
Hn * q
for _ in range(_r(2**N)):
Ui * q # apply operator that flips the sign of the matching index
Ud * q # apply Grover's diffusion operator
index = q.measure()
count += 1
return index if index < n and lst[index] == match_text else -1
