def __cNot(self, gate_info):
"""
Creates an arbitrary sized controlled not gate between two arbitrary qbits.
:param gate_info: (tuple(int, int)) Position in the circuit of the control qubit and the controlled qubit
:return: (SparseMatrix) The cnot gate entangling the two qubits given.
"""
qbit1, qbit2 = gate_info
if qbit1 > qbit2:
control_bit = np.abs(qbit2 - qbit1)
controlled_bit = 0
else:
control_bit = 0
controlled_bit = qbit2 - qbit1
elements = [Sparse.MatrixElement(0, 0, 1)]
dimension = 2**(np.abs(qbit2 - qbit1) + 1)
for i in range(1, dimension):
if self.__bitactive(i, control_bit):
col = self.__toggle(i, controlled_bit)
elements.append(Sparse.MatrixElement(i, col, 1))
else:
elements.append(Sparse.MatrixElement(i, i, 1))
return Sparse.SparseMatrix(dimension, elements)
def __ccNot(self, gate_info):
"""
Creates a Sparsematrix representing the controlled-controlled-not (ccnot or Tiffoli)
gate for the given qubits. Can be applied to any exisiting qubits.
:param gate_info: (tuple(int, int, int)) first, second qubit controlling the gate and the qubit controlled by the other two
:return: (SparseMatrix) Matrix representation of the gate
"""
control1, control2, qbit3 = gate_info
# Reset the values to range from 0 to maxval
minval = min(control1, control2, qbit3)
maxval = max(control1, control2, qbit3) - minval
control1 = control1 - minval
control2 = control2 - minval
qbit3 = qbit3 - minval
# Create elements and calculate dimensions
elements = [Sparse.MatrixElement(0, 0, 1)]
dimension = 2**(maxval + 1)
# For each possible bit check whether the control qubits are active
for i in range(1, dimension):
if self.__bitactive(i, control1) and self.__bitactive(i, control2):
# if control qubits are active, calculate the new value and insert into matrix
col = self.__toggle(i, qbit3)
elements.append(Sparse.MatrixElement(i, col, 1))
else:
elements.append(Sparse.MatrixElement(i, i, 1))
return Sparse.SparseMatrix(dimension, elements)
def __cP(self, gate_info):
"""
Creates a controlled phase gate for the given qubits
:param gate_info: (tuple(int, int, float)) The information supplied to the gate. Control qubits as ints, float as the phase.
:return: (SparseMatrix) Representation of the cp gate
"""
qbit1, qbit2, phi = gate_info
elements = [Sparse.MatrixElement(0, 0, 1)]
dimension = 2**(np.abs(qbit2 - qbit1) + 1)
for i in range(1, dimension):
if self.__bitactive(i, qbit1) and self.__bitactive(i, qbit2):
elements.append(Sparse.MatrixElement(i, i, np.exp(1j * phi)))
else:
elements.append(Sparse.MatrixElement(i, i, 1))
return Sparse.SparseMatrix(dimension, elements)
def __cZ(self, gate_info):
"""
Creates a controlled z gate given 2 qubits
:param gate_info: (tuple(int, int)) The two gates to control the z
:return: (SparseMatrix) Representation of the cz gate
"""
qbit1, qbit2 = gate_info
shift = min(qbit1, qbit2)
qbit1 = qbit1 - shift
qbit2 = qbit2 - shift
elements = [Sparse.MatrixElement(0, 0, 1)]
dimension = 2**(np.abs(qbit2 - qbit1) + 1)
for i in range(1, dimension):
if self.__bitactive(i, qbit1) and self.__bitactive(i, qbit2):
elements.append(Sparse.MatrixElement(i, i, -1))
else:
elements.append(Sparse.MatrixElement(i, i, 1))
return Sparse.SparseMatrix(dimension, elements)
def __NCZ(self, gate_info):
"""
Adds a z gate controlled by an arbitrary number of bits
:param gate_info: (tuple(int, int, int...,)) Control qubits as ints, arbitrary number
:return: (SparseMatrix) Matrix representatin of the gate
"""
bits = np.array(gate_info)
bits = bits - min(bits)
elements = [Sparse.MatrixElement(0, 0, 1)]
dimension = 2**(max(bits) - min(bits) + 1)
for i in range(1, dimension):
active = True
for bit in bits:
if not self.__bitactive(i, bit):
active = False
break
if active: elements.append(Sparse.MatrixElement(i, i, -1))
else: elements.append(Sparse.MatrixElement(i, i, 1))
return Sparse.SparseMatrix(dimension, elements)
def makeMatrices(self):
"""
Creates the matrices that will be applied to the wavevector
:return: (array) list of np matrices that will be applied to the statevector
"""
gates = np.array(self.gates, dtype=object).T
bigmats = []
for i, slot in enumerate(gates):
bigmat = Sparse.SparseMatrix(1, [Sparse.MatrixElement(0, 0, 1)])
for j in slot:
if type(j) == tuple:
bigmat = self.__addLargeGate(j).tensorProduct(bigmat)
elif j == 's':
continue
else:
bigmat = Sparse.makeSparse(
self.singlegates[j]).tensorProduct(bigmat)
bigmats.append(bigmat)
return np.array(bigmats)
def __Swap(self, gate_info):
"""
Creates the matrix representing the swap operation between two qubits.
:param gate_info: (tuple(int, int)) The two gates to be swapped.
:return: (SparseMatrix) Matrix representation of the swap gate.
"""
qbit1, qbit2 = gate_info
shift = min(qbit1, qbit2)
qbit1 = qbit1 - shift
qbit2 = qbit2 - shift
elements = []
dimension = 2**(np.abs(qbit2 - qbit1) + 1)
for i in range(0, dimension):
col = i
if (self.__bitactive(i, qbit1) and not self.__bitactive(i, qbit2)
) or (not self.__bitactive(i, qbit1)
and self.__bitactive(i, qbit2)):
col = self.__toggle(self.__toggle(i, qbit1), qbit2)
elements.append(Sparse.MatrixElement(i, col, 1))
return Sparse.SparseMatrix(dimension, elements)
def simulate2(self):
"""
Applies the circuit to the initialized statevector without storing the operations
:return: The register and any measurements made
"""
gates = np.array(self.gates, dtype=object).T
for i, slot in enumerate(gates):
bigmat = Sparse.SparseMatrix(1, [Sparse.MatrixElement(0, 0, 1)])
for j in slot:
if type(j) == tuple:
bigmat = self.__addLargeGate(j).tensorProduct(bigmat)
elif j == 's':
continue
else:
bigmat = Sparse.makeSparse(
self.singlegates[j]).tensorProduct(bigmat)
self.register.Statevec = bigmat.apply(self.register.Statevec)
if i in self.measurements[0]:
self.measurements[1].append(self.register.Statevec.Elements)
return self.register, self.measurements
def __NCP(self, gate_info):
"""
Adds a phase gate controlled by an arbitrary number of bits
:param gate_info: (tuple(int, int, int..., float)) Control qubits as ints, phase as a float.
:return: (SparseMatrix) Matrix representation of gate.
"""
bits = np.array(gate_info[:-1])
bits = bits - min(bits)
phi = gate_info[-1]
elements = [Sparse.MatrixElement(0, 0, 1)]
dimension = 2**(max(bits) - min(bits) + 1)
for i in range(1, dimension):
active = True
for bit in bits:
if not self.__bitactive(i, bit):
active = False
break
if active:
elements.append(Sparse.MatrixElement(i, i, np.exp(1j * phi)))
else:
elements.append(Sparse.MatrixElement(i, i, 1))
return Sparse.SparseMatrix(dimension, elements)
def Grover_Circuit(n_qubits, measured_bits, plot_results=True):
"""
Constructs a circuit representing Grover's algorithm for a given number of qubits and
bits that we are interested in. Plots measurements after each iteration of the algorithm.
:param n_qubits: (int) Number of qubits in the circuit.
:param measured_bits: (list) list of bits that we are interested in and want to increase the amplitude of.
"""
grover_circuit = QuantumCircuit.QuantumCircuit('Grover', n_qubits)
grover_circuit.addGate('h', [i for i in range(n_qubits)])
repetitions = int(np.pi/4*np.sqrt(2**n_qubits)) - 1
grover_circuit.addmeasure()
# calculate oracle
elements = []
for i in range(2**n_qubits):
if i in measured_bits:
elements.append(Sparse.MatrixElement(i,i,-1))
else: elements.append(Sparse.MatrixElement(i,i,1))
oracle_gate = Sparse.SparseMatrix(2**n_qubits, elements) # Creates a sparseMatrix representation of the oracle
#print(oracle_gate.makedense())
#Add Oracle
grover_circuit.addCustom(0, n_qubits-1, oracle_gate, 'oracle')
#grover_circuit.addmeasure()
#Add diffuser
diffuser(grover_circuit)
grover_circuit.addmeasure()
# Repeat if necessary
for i in range(repetitions):
# Add Oracle
grover_circuit.addCustom(0, n_qubits-1, oracle_gate, 'oracle')
#Add diffuser
diffuser(grover_circuit)
grover_circuit.addmeasure()
#print(np.array(grover_circuit.gates, dtype=object)[:,:6])
#show results
#print(grover_circuit.return_measurements())
final_statevec, measurements = grover_circuit.simulate2()
#for m in measurements[1]:
# print(m)
if plot_results:
# plots the results in a snazzy way
figure, axis = plt.subplots(1, len(measurements[1]))
for j, measurement in enumerate(measurements[1]):
axis[j].bar([i for i in range(measurement.size)], measurement*np.conj(measurement))
axis[j].set_ylim([0,1])
axis[j].set_xlabel("State |N>", fontsize = '13')
if j>0:
axis[j].set_yticklabels("")
#print((results[2][1][j]*np.conj(results[2][1][j])).sum())
axis[0].set_ylabel("Probability", fontsize = '13')
#figure.set_ylabel("Probability of Measuring State")
figure.suptitle("Probability of measuring state N",fontweight='bold', fontsize='15')
plt.show()
print(grover_circuit)