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gate_generation.py
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gate_generation.py
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'''
This module implements the "naive" gate-searching algorithm
'''
import numpy as np
universal_gates = [np.matrix([[0, 1], [1, 0]]), np.matrix([[1, 0], [0, -1]]), np.matrix([[0, -1j], [1j, 0]]), np.matrix([[1, 1], [1, -1]]) / np.sqrt(2), np.matrix([[1, 0], [0, 1j]]), np.matrix([[1, 0], [0, -1j]]), np.matrix([[1, 0], [0, 1/np.sqrt(2) + 1j/np.sqrt(2)]]), np.matrix([[1, 0], [0, 1/np.sqrt(2) - 1j/np.sqrt(2)]])]
rotation_gates = [np.matrix([[1, 0], [0, 1j]]), np.matrix([[1, 0], [0, -1j]]), np.matrix([[1, 0], [0, 1/np.sqrt(2) + 1j/np.sqrt(2)]]), np.matrix([[1, 0], [0, 1/np.sqrt(2) - 1j/np.sqrt(2)]])]
other_gates = [np.matrix([[0, 1], [1, 0]]), np.matrix([[1, 0], [0, -1]]), np.matrix([[0, -1j], [1j, 0]]), np.matrix([[1, 1], [1, -1]]) / np.sqrt(2)]
num_of_gates = len(universal_gates)
X = np.matrix([[0, 1], [1, 0]])
Z = np.matrix([[1, 0], [0, -1]])
whole_representation = []
curr_A_representation = []
curr_B_representation = []
start_with_rotation = True
# determines if two matrices are "close enough" to each other (this function is required due to Python's float inprecision)
def are_close_enough(mat1, mat2):
epsilon = 1e-4
def flatten(mat):
if len(mat) == 0:
return []
else:
return mat[0] + flatten(mat[1:])
return all(map(lambda x, y: np.abs(x - y) < epsilon, flatten(mat1.tolist()), flatten(mat2.tolist())))
# a helper function, not meant to be used externally
def iter_whole_representation_universal(whole_representation):
length = len(whole_representation)
for i in range(length - 1, -1, -1):
if whole_representation[i] != num_of_gates - 1:
whole_representation[i] += 1
for j in range(i + 1, length):
whole_representation[j] = 0
return whole_representation
print("Finished searching size", length)
whole_representation = [0] * (length + 1)
return whole_representation
# another helper function
def mult_all_universal(rep):
curr = np.matrix([[1, 0], [0, 1]])
for i in range(len(rep)):
curr = np.matmul(curr, universal_gates[rep[i]])
return curr
def find_controlled_gate_AXBXC(matrix_rep):
whole_representation = []
while True:
length = len(whole_representation) + 1
for i in range(length):
A = mult_all_universal(whole_representation[0:i])
B = mult_all_universal(whole_representation[i:length])
C = np.linalg.inv(np.matmul(A, B))
mul = np.matmul
if are_close_enough(matrix_rep, mul(A, mul(X, mul(B, mul(X, C))))):
return whole_representation[0:i], whole_representation[i:length]
whole_representation = iter_whole_representation_universal(whole_representation)
def find_controlled_gate_AXBX(matrix_rep):
whole_representation = []
while True:
A = mult_all_universal(whole_representation)
B = np.linalg.inv(A)
mul = np.matmul
if are_close_enough(matrix_rep, mul(X, mul(B, mul(X, A)))):
return whole_representation
whole_representation = iter_whole_representation_universal(whole_representation)
def find_controlled_gate_AXBX_optimized(matrix_rep):
global whole_representation
global start_with_rotation
whole_representation = []
start_with_rotation = True
def iter_whole_representation():
global start_with_rotation
if start_with_rotation:
start_with_rotation = False
return
global whole_representation
length = len(whole_representation)
start_with_rotation = True
for i in range(length - 1, -1, -1):
if whole_representation[i] != 3:
whole_representation[i] += 1
for j in range(i + 1, length):
whole_representation[j] = 0
return
print("Finished searching size", length)
whole_representation = [0] * (length + 1)
def mult_all_rotation(rep):
curr = np.matrix([[1, 0], [0, 1]])
for i in range(len(rep)):
if i % 2 == 0:
curr = np.matmul(curr, rotation_gates[rep[i]])
else:
curr = np.matmul(curr, other_gates[rep[i]])
return curr
def mult_all_other(rep):
curr = np.matrix([[1, 0], [0, 1]])
for i in range(len(rep)):
if i % 2 == 0:
curr = np.matmul(curr, other_gates[rep[i]])
else:
curr = np.matmul(curr, rotation_gates[rep[i]])
return curr
def mult_all(rep):
if start_with_rotation:
return mult_all_rotation(rep)
else:
return mult_all_other(rep)
while True:
A = mult_all(whole_representation)
B = np.linalg.inv(A)
mul = np.matmul
if are_close_enough(matrix_rep, mul(X, mul(B, mul(X, A)))):
return whole_representation
iter_whole_representation()
def find_controlled_gate_AZBZ(matrix_rep):
whole_representation = []
while True:
A = mult_all_universal(whole_representation)
B = np.linalg.inv(A)
mul = np.matmul
if are_close_enough(matrix_rep, mul(Z, mul(B, mul(Z, A)))):
return whole_representation
whole_representation = iter_whole_representation_universal(whole_representation)
def find_controlled_gate_AZBZ_optimized(matrix_rep):
global whole_representation
global start_with_rotation
whole_representation = []
start_with_rotation = True
def iter_whole_representation():
global start_with_rotation
if start_with_rotation:
start_with_rotation = False
return
global whole_representation
length = len(whole_representation)
start_with_rotation = True
for i in range(length - 1, -1, -1):
if whole_representation[i] != 3:
whole_representation[i] += 1
for j in range(i + 1, length):
whole_representation[j] = 0
return
print("Finished searching size", length)
whole_representation = [0] * (length + 1)
def mult_all_rotation(rep):
curr = np.matrix([[1, 0], [0, 1]])
for i in range(len(rep)):
if i % 2 == 0:
curr = np.matmul(curr, rotation_gates[rep[i]])
else:
curr = np.matmul(curr, other_gates[rep[i]])
return curr
def mult_all_other(rep):
curr = np.matrix([[1, 0], [0, 1]])
for i in range(len(rep)):
if i % 2 == 0:
curr = np.matmul(curr, other_gates[rep[i]])
else:
curr = np.matmul(curr, rotation_gates[rep[i]])
return curr
def mult_all(rep):
if start_with_rotation:
return mult_all_rotation(rep)
else:
return mult_all_other(rep)
while True:
A = mult_all(whole_representation)
B = np.linalg.inv(A)
mul = np.matmul
if are_close_enough(matrix_rep, mul(Z, mul(B, mul(Z, A)))):
return whole_representation
iter_whole_representation()
def find_controlled_gate_AXB(matrix_rep):
whole_representation = []
while True:
A = mult_all_universal(whole_representation)
B = np.linalg.inv(A)
mul = np.matmul
if are_close_enough(matrix_rep, mul(A, mul(X, B))):
return whole_representation
whole_representation = iter_whole_representation_universal(whole_representation)