Quantum entanglement is one of the most fascinating and counterintuitive phenomena in quantum mechanics. When two or more qubits become entangled, the state of one qubit becomes directly related to the state of the other, no matter how far apart they are. This means that measuring one qubit instantly determines the state of the other, even if they are light-years apart.
qumatIn this section, we will explore how to create and measure entangled states using the qumat library. We will start by creating a simple entangled state known as a Bell state, which is a maximally entangled quantum state of two qubits.
A Bell state can be created by applying a Hadamard gate to the first qubit, followed by a CNOT gate with the first qubit as the control and the second qubit as the target. This results in a state where the two qubits are perfectly correlated.
from qumat import QuMat
# Initialize the quantum circuit with 2 qubits
backend_config = {'backend_name': 'qiskit', 'backend_options': {'simulator_type': 'qasm_simulator', 'shots': 1000}}
qc = QuMat(backend_config)
qc.create_empty_circuit(2)
# Apply a Hadamard gate to the first qubit
qc.apply_hadamard_gate(0)
# Apply a CNOT gate with the first qubit as control and the second as target
qc.apply_cnot_gate(0, 1)
# Execute the circuit and measure the results
result = qc.execute_circuit()
print(result)
The output will show the measurement results of the two qubits. Since the qubits are entangled, you should observe that the states of the two qubits are perfectly correlated. For example, if the first qubit is measured as 0, the second qubit will also be 0, and if the first qubit is 1, the second qubit will also be 1.
You can also visualize the circuit to better understand the sequence of operations:
qc.draw()
Once the qubits are entangled, measuring one qubit will instantly determine the state of the other. This is a key feature of quantum entanglement and is used in various quantum algorithms and protocols.
# Execute the circuit and measure the results
result = qc.execute_circuit()
print(result)
The output will show the measurement counts for the two qubits. Since the qubits are entangled, the results will show a strong correlation between the states of the two qubits.
Quantum entanglement is a fundamental resource in quantum computing and is used in various applications, including:
Quantum teleportation is a protocol that allows the transfer of quantum information from one qubit to another, even if they are far apart. This is achieved using entanglement and classical communication.
# Example implementation of quantum teleportation
qc.create_empty_circuit(3)
# Create an entangled pair between qubit 1 and qubit 2
qc.apply_hadamard_gate(1)
qc.apply_cnot_gate(1, 2)
# Prepare the qubit to be teleported (qubit 0)
qc.apply_hadamard_gate(0)
# Perform the teleportation protocol
qc.apply_cnot_gate(0, 1)
qc.apply_hadamard_gate(0)
qc.apply_cnot_gate(1, 2)
qc.apply_toffoli_gate(0, 1, 2)
# Measure the qubits
result = qc.execute_circuit()
print(result)
The output will show the measurement results, demonstrating that the state of qubit 0 has been successfully teleported to qubit 2.
Quantum entanglement is a powerful and essential concept in quantum computing. By understanding how to create and manipulate entangled states using qumat, you can begin to explore more advanced quantum algorithms and applications. In the next section, we will delve into quantum algorithms, starting with the Deutsch-Jozsa algorithm.