def get_hhl_2x2(A, b, r, qubits):
'''Generate a circuit that implements the full HHL algorithm for the case
of 2x2 matrices.
:param A: (numpy.ndarray) A Hermitian 2x2 matrix.
:param b: (numpy.ndarray) A vector.
:param r: (float) Parameter to be tuned in the algorithm.
:param verbose: (bool) Optional information about the wavefunction.
:return: A Quil program to perform HHL.
'''
p = pq.Program()
p.inst(create_arbitrary_state(b, [qubits[3]]))
p.inst(H(qubits[1]))
p.inst(H(qubits[2]))
p.defgate('CONTROLLED-U0', controlled(scipy.linalg.expm(2j*π*A/4)))
p.inst(('CONTROLLED-U0', qubits[2], qubits[3]))
p.defgate('CONTROLLED-U1', controlled(scipy.linalg.expm(2j*π*A/2)))
p.inst(('CONTROLLED-U1', qubits[1], qubits[3]))
p.inst(SWAP(qubits[1], qubits[2]))
p.inst(H(qubits[2]))
p.defgate('CSdag', controlled(np.array([[1, 0], [0, -1j]])))
p.inst(('CSdag', qubits[1], qubits[2]))
p.inst(H(qubits[1]))
p.inst(SWAP(qubits[1], qubits[2]))
uncomputation = p.dagger()
p.defgate('CRy0', controlled(rY(2*π/2**r)))
p.inst(('CRy0', qubits[1], qubits[0]))
p.defgate('CRy1', controlled(rY(π/2**r)))
p.inst(('CRy1', qubits[2], qubits[0]))
p += uncomputation
return p
def create_initial_state_program(self, initial_state):
"""
Creates a pyquil program representing the initial state for the QAOA.
As an argument it takes either a list with order of the cities, or
a string "all". In the second case the initial state is superposition
of all possible states for this problem.
"""
initial_state_program = pq.Program()
if type(initial_state) is list:
for i in range(self.reduced_number_of_nodes):
initial_state_program.inst(X(i * (self.reduced_number_of_nodes) + initial_state[i]))
elif initial_state == "all":
vector_of_states = np.zeros(2**self.number_of_qubits)
list_of_possible_states = []
initial_order = range(0, self.reduced_number_of_nodes)
all_permutations = [list(x) for x in itertools.permutations(initial_order)]
for permutation in all_permutations:
coding_of_permutation = 0
for i in range(len(permutation)):
coding_of_permutation += 2**(i * (self.reduced_number_of_nodes) + permutation[i])
vector_of_states[coding_of_permutation] = 1
initial_state_program = create_arbitrary_state(vector_of_states)
return initial_state_program
def create_initial_state_program(self):
"""
As an initial state I use state, where in t=i we visit i-th city.
"""
initial_state = pq.Program()
number_of_nodes = len(self.nodes_array)
if type(self.initial_state) is list:
for i in range(number_of_nodes):
initial_state.inst(
X(i * number_of_nodes + self.initial_state[i]))
elif self.initial_state == "all":
vector_of_states = np.zeros(2**self.number_of_qubits)
list_of_possible_states = []
initial_order = range(0, number_of_nodes)
all_permutations = [
list(x) for x in itertools.permutations(initial_order)
]
for permutation in all_permutations:
coding_of_permutation = 0
for i in range(len(permutation)):
coding_of_permutation += 2**(i * number_of_nodes +
permutation[i])
vector_of_states[coding_of_permutation] = 1
initial_state = create_arbitrary_state(vector_of_states)
return initial_state
def wrap(theta):
"""
Creates arbitrary state using stereographic projection.
:param theta: Vector representing the state.
:return: PyQuil program setting up the state.
"""
return create_arbitrary_state(maps.plane_to_sphere(theta, pole))
def wrap(theta: np.ndarray):
"""
Creates arbitrary state.
:param theta: Vector representing the state.
:return: PyQuil program setting up the state.
"""
theta = np.concatenate((np.array([1]) / np.sqrt(dim), theta), axis=0)
return create_arbitrary_state(theta)
def wrap(theta: np.ndarray) -> Program:
"""
Creates arbitrary one-particle state.
:param theta: Coefficients in superposition.
:return: Pyquil program setting up the state.
"""
vector = np.zeros(2**dim)
vector[1] = 1 / np.sqrt(dim)
vector[[2**(i + 1) for i in range(dim - 1)]] = theta
vector *= 1 / np.linalg.norm(vector)
return create_arbitrary_state(vector)
def create_initial_state_program():
initial_state_program = pq.Program()
vector_of_states = np.zeros(2**number_of_qubits)
list_of_possible_states = []
initial_order = range(0, reduced_number_of_nodes)
all_permutations = [list(x) for x in itertools.permutations(initial_order)]
for permutation in all_permutations:
coding_of_permutation = 0
for i in range(len(permutation)):
coding_of_permutation += 2**(i * (reduced_number_of_nodes) +
permutation[i])
vector_of_states[coding_of_permutation] = 1
initial_state_program = create_arbitrary_state(vector_of_states)
return initial_state_program
def verify_with_swap_test_2x2(reference_amplitudes, qubits):
'''Generate a circuit for performing a swap test.
:param program: (pyquil.quil.Program) Program storing the HHL algorithm.
:param reference_amplitudes: (numpy.ndarray) Amplitudes of the state to be
compared against.
:return: A Quil program to do a swap test after inverting 2x2 matrices.
'''
swaptest = pq.Program()
swaptest.inst(create_arbitrary_state(reference_amplitudes, [qubits[4]]))
swaptest.inst(H(qubits[5]))
swaptest.inst(CSWAP(qubits[5], qubits[4], qubits[3]))
swaptest.inst(H(qubits[5]))
c = swaptest.declare('ro', 'BIT', 2)
swaptest += MEASURE(qubits[0], c[0]) # This is actually the post-selection in HHL
swaptest += MEASURE(qubits[5], c[1])
return swaptest
def get_hhl_2x2_corrected(A, b, r, qubits):
""" HHL program with bit code corrections on first two H gates """
p = pq.Program()
p.inst(create_arbitrary_state(b, [qubits[3]]))
# PHASE ESTIMATION
bit_code_H(p, qubits[1], qubits)
bit_code_H(p, qubits[2], qubits)
p.defgate('CONTROLLED-U0', controlled(scipy.linalg.expm(2j*π*A/4)))
p.inst(('CONTROLLED-U0', qubits[2], qubits[3]))
p.defgate('CONTROLLED-U1', controlled(scipy.linalg.expm(2j*π*A/2)))
p.inst(('CONTROLLED-U1', qubits[1], qubits[3]))
p.inst(SWAP(qubits[1], qubits[2]))
p.inst(H(qubits[2]))
p.defgate('CSdag', controlled(np.array([[1, 0], [0, -1j]])))
p.inst(('CSdag', qubits[1], qubits[2]))
p.inst(H(qubits[1]))
p.inst(SWAP(qubits[1], qubits[2]))
p.defgate('CRy0', controlled(rY(2*π/2**r)))
p.inst(('CRy0', qubits[1], qubits[0]))
p.defgate('CRy1', controlled(rY(π/2**r)))
p.inst(('CRy1', qubits[2], qubits[0]))
# HARD CODE THE INVERSE PHASE ESTIMATION :'(
p.inst(SWAP(qubits[1], qubits[2]))
p.inst(H(qubits[1]))
p.defgate('CSdag-INV', controlled(np.array([[1, 0], [0, 1j]])))
p.inst(('CSdag-INV', qubits[1], qubits[2]))
p.inst(H(qubits[2]))
p.inst(SWAP(qubits[1], qubits[2]))
p.defgate('CONTROLLED-U1-INV', controlled(scipy.linalg.expm(-2j*π*A/2)))
p.inst(('CONTROLLED-U1-INV', qubits[1], qubits[3]))
p.defgate('CONTROLLED-U0-INV', controlled(scipy.linalg.expm(-2j*π*A/4)))
p.inst(('CONTROLLED-U0-INV', qubits[2], qubits[3]))
p.inst(H(qubits[2]))
p.inst(H(qubits[1]))
# undoes create_arbitrary_state
p.inst(RY(π/2, qubits[3]))
p.inst(H(qubits[3]))
return p
# We need to do this inc ase registers are entangled.
hhl += uncomputation
# Rejection sampling on the acnilla register and a swap test
# The state |x> = A^-1 |b> is prop to sum_J beta_j lambda_j^-1 |u_j>
# contains info about the solution to Ax = b when measuring 1 on the ancilla state.
# We perform post selection by projecting onto the desired |1>
# To check the solution is the expected one, we prepare the correct output state
# manually to perform a swap test with the outcome.
from grove.alpha.arbitrary_state.arbitrary_state import create_arbitrary_state
reference_amplitudes = [0.9492929682, 0.3143928443]
# Target state prep
hhl += create_arbitrary_state(reference_amplitudes, [4])
# Swap test
hhl += H(5)
hhl += CSWAP(5, 4, 3)
hhl += H(5)
c = hhl.declare('ro', 'BIT', 2)
hhl += MEASURE(0, c[0])
hhl += MEASURE(5, c[1])
# it is a good ex to check if the right result is given by the state
# |x> = 0.949 |0> + 0.314 |1>
# There are tow measuresments performed, one of the ancilla register ( for doing post selection)
# and another one that gives the result of the swap test. To calculate success probabilities, define helper functions
