Measurement (Quantum Computing)

quantum-computing

Definition

Measurement (Quantum Computing)

A measurement in quantum computing is the process of extracting classical information from a quantum state. When measuring a qubit in superposition, the outcome occurs with probability equal to the squared modulus of its corresponding amplitude coefficient.

For a qubit in state

$$|\psi ⟩=\alpha |0⟩+\beta |1⟩,$$

the measurement yields:

• Outcome 0 with probability $|\alpha {|}^2$, leaving the state as $|0⟩$
• Outcome 1 with probability $|\beta {|}^2$, leaving the state as $|1⟩$

Complex Modulus

The probability is given by the squared modulus of the amplitude: $|\alpha {|}^2$.

Example

Measurement of Equal Superposition

Consider a qubit in the state

$$|\psi ⟩=\sqrt{\frac{1}{2}}|0⟩+\sqrt{\frac{1}{2}}|1⟩=\frac{1}{\sqrt{2}}(|0⟩+|1⟩).$$

Potential outcomes:

1. Outcome 0: Classical bit 0 and successor state $|0⟩$ with probability ${\left(\sqrt{\frac{1}{2}}\right)}^2=\frac{1}{2}$
2. Outcome 1: Classical bit 1 and successor state $|1⟩$ with probability $\frac{1}{2}$

Post-Measurement State

After measurement, the quantum state collapses to the measured basis state. This is a non-unitary, irreversible operation that differs fundamentally from the unitary evolution of closed quantum systems.