How to add two Bits using single Qubit on Quantum Computer

As we knew that a qubit have the capacity to store two bit at a time. I am curious to add two bits using single qubit. I try a lot but failed, please give some hints if someone know.

Code:

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from numpy import pi

qreg_q = QuantumRegister(2, 'q')
creg_c = ClassicalRegister(2, 'c')
circuit = QuantumCircuit(qreg_q, creg_c)

circuit.x(qreg_q[0])
circuit.measure(qreg_q[0], creg_c[0])
circuit.measure(qreg_q[1], creg_c[0])
circuit.x(qreg_q[1])

Circuit Diagram:

To conduct conventional addition (adding two bits) using quantum bits (qubits), at least two qubits are required to represent the two input bits, perform quantum operations on them, and then measure the output.

qreg_q = QuantumRegister(3, 'q')
creg_c = ClassicalRegister(2, 'c')
circuit = QuantumCircuit(qreg_q, creg_c)

# Set the input bits A and B (00 + 01 = 01)
circuit.x(qreg_q[0])  # Set A to 1
circuit.x(qreg_q[1])  # Set B to 1

# Perform addition
circuit.ccx(qreg_q[0], qreg_q[1], qreg_q[2])  # Controlled-X gate for the sum
circuit.cx(qreg_q[0], qreg_q[1])  # Carry

# Measure the result
circuit.measure(qreg_q[1], creg_c[0])  # Result bit
circuit.measure(qreg_q[2], creg_c[1])  # Carry bit

The code in this example conducts quantum addition, measures the result and the carry, and sets A and B to 1 (01 in binary). In this instance, the outcome will be 01 (binary).