Construct a Circuit State function from a state vector.

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In quantum computing, a circuit state function represents a quantum state as a linear combination of basis states, often denoted as |0⟩, |1⟩, |2⟩, and so on. This is similar to expressing a classical vector in terms of its components. To construct a circuit state function from a state vector, you need to find the coefficients of the basis states that make up the quantum state.

Here's an example of how to construct a circuit state function from a given state vector using Qiskit, a popular quantum computing library:

Code: Select all

from qiskit import QuantumCircuit, QuantumState, Aer, execute

# Define the state vector (as complex amplitudes)
state_vector = [0.70710678 + 0j, 0.70710678 + 0j]

# Create a quantum circuit with the number of qubits matching the state vector
n_qubits = int(len(state_vector).bit_length() - 1)  # Determine the number of qubits needed
circuit = QuantumCircuit(n_qubits)

# Load the state vector onto the quantum circuit
initial_state = QuantumState(state_vector)
circuit.initialize(initial_state, range(n_qubits))

# Simulate the circuit to obtain the final state vector
simulator = Aer.get_backend('statevector_simulator')
result = execute(circuit, simulator).result()
final_state_vector = result.get_statevector()

# Print the final state vector
print("Original State Vector:", state_vector)
print("Constructed State Vector:", final_state_vector)

Replace the state_vector list with your own complex amplitudes to construct the corresponding circuit state function. This example initializes a quantum circuit with the given state vector and simulates the resulting state to verify that the constructed state vector matches the original one.

Keep in mind that the state vector components must be normalized, meaning the sum of their squared magnitudes should equal 1. Also, the state vector must have a length that is a power of 2 to match the number of qubits in the circuit.