Two-Qubit States

Combining Qubits

To build quantum systems, we combine multiple qubits using the tensor product ($otimes$). Two qubits [alpha, eta] and $[gamma, delta]$ combine into a 4-element state:

[alpha, eta] otimes [gamma, delta] = [alphagamma, alphadelta, etagamma, etadelta]

The four elements represent amplitudes for the four basis states:

• Index 0: $|00 angle$ (first=0, second=0)
• Index 1: $|01 angle$ (first=0, second=1)
• Index 2: $|10 angle$ (first=1, second=0)
• Index 3: $|11 angle$ (first=1, second=1)

def tensor_product(q1, q2):
    return [
        q1[0] * q2[0],   # |00⟩
        q1[0] * q2[1],   # |01⟩
        q1[1] * q2[0],   # |10⟩
        q1[1] * q2[1],   # |11⟩
    ]

zero = [1.0, 0.0]
one  = [0.0, 1.0]

print(tensor_product(zero, zero))  # [1.0, 0.0, 0.0, 0.0] — |00⟩
print(tensor_product(one,  one))   # [0.0, 0.0, 0.0, 1.0] — |11⟩

Your Task

Implement tensor_product(q1, q2) that combines two single-qubit states.