To create a simple quantum circuit simulator without using any quantum libraries in Python, we can represent the state of our qubits using the complex probability amplitudes. Probability amplitudes are complex numbers that represent the probability of the qubit being in a certain state (0 or 1). Then, we can define operations such as Hadamard gates, Pauli gates, and CNOT gates in terms of matrix multiplication.
import numpy as np
class QuantumCircuit:
def __init__(self, num_qubits):
self.num_qubits = num_qubits
self.state = np.zeros(2**num_qubits, dtype=np.complex64)
self.state[0] = 1.0 # initial state is |0>
def h(self, qubit):
"""Applies a Hadamard gate to the given qubit."""
H = np.array([[1, 1], [1, -1]]) / np.sqrt(2)
self.apply_gate(qubit, H)
def x(self, qubit):
"""Applies a Pauli-X gate to the given qubit."""
X = np.array([[0, 1], [1, 0]])
self.apply_gate(qubit, X)
def cx(self, control, target):
"""Applies a CNOT gate to the given qubits."""
CNOT = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])
self.apply_two_qubit_gate(control, target, CNOT)
def apply_gate(self, qubit, gate):
"""Applies a gate to a single qubit."""
gate_matrix = self.get_gate_matrix(qubit, gate)
self.state = np.dot(gate_matrix, self.state)
def apply_two_qubit_gate(self, control, target, gate):
"""Applies a gate to two qubits."""
gate_matrix = self.get_two_qubit_gate_matrix(control, target, gate)
self.state = np.dot(gate_matrix, self.state)
def get_gate_matrix(self, qubit, gate):
"""Returns the matrix for the given single-qubit gate."""
gate_matrix = np.eye(2, dtype=np.complex64)
if qubit == 0:
gate_matrix = np.kron(gate, gate_matrix)
else:
gate_matrix = np.kron(gate_matrix, gate)
return gate_matrix
def get_two_qubit_gate_matrix(self, control, target, gate):
"""Returns the matrix for the given two-qubit gate."""
gate_matrix = np.eye(2, dtype=np.complex64)
gate_matrix = np.kron(gate_matrix, np.eye(2**max(control, target)-2))
gate_matrix = np.kron(gate_matrix, gate)
gate_matrix = np.kron(gate_matrix, np.eye(2**self.num_qubits-2**max(control, target)))
gate_matrix = gate_matrix.reshape(2**self.num_qubits, 2**self.num_qubits)
return gate_matrix
def measure(self, qubit):
"""Measures the given qubit in the standard basis."""
probabilities = np.abs(self.state)**2
outcome = np.random.choice(2**self.num_qubits, p=probabilities)
collapse_mask = np.zeros(2**self.num_qubits)
collapse_mask[outcome] = 1
collapse_matrix = np.diag(collapse_mask)
self.state = np.dot(collapse_matrix, self.state)
return outcome
def run(self, program):
"""Runs a quantum program on the simulator."""
for gate in program:
gate_type, args = gate[0], gate[1:]
if gate_type == 'h':
self.h(*args)
elif gate_type == 'x':
self.x(*args)
elif gate_type == 'cx':
self.cx(*args)
else:
raise ValueError(f"Invalid gate type {gate_type}.")
def get_state(self):
"""Returns the current state of the qubits."""
return self.state
This would apply a Hadamard gate to the first qubit, and then a CNOT gate with the first qubit as the control and the second qubit as the target. The program would then print the current state of the qubits.