In one line
A qubit is the basic unit of quantum information that can exist in a superposition of the states \(|0\rangle\) and \(|1\rangle\) at the same time, unlike a classical bit, which is either 0 or 1.
Explained simply
A classical bit is like a light switch: off (0) or on (1). A qubit is more like a spinning coin in the air: until it lands, it is in a combination of heads and tails. When you measure it (the coin lands), you get either 0 or 1, with probabilities set by the superposition.
How it works
- A qubit state: \(|\psi\rangle = \alpha|0\rangle + \beta|1\rangle\), where \(\alpha, \beta\) are complex numbers (probability amplitudes).
- Normalisation: \(|\alpha|^2 + |\beta|^2 = 1\). On measurement, the result is 0 with probability \(|\alpha|^2\) and 1 with probability \(|\beta|^2\).
- Measurement collapses the superposition to the observed state, so you cannot read \(\alpha\) and \(\beta\) directly in one go.
- Many qubits: \(n\) qubits can be in a superposition of all \(2^n\) basis states at once; quantum gates act on this whole superposition.
- Entanglement: qubits can be correlated so that measuring one immediately fixes the outcome of the other, which has no classical equivalent.
- Single-qubit states can be pictured as points on the Bloch sphere: \(|0\rangle\) at the north pole, \(|1\rangle\) at the south pole.
- Physical qubits: electron spin (up/down), photon polarisation, energy levels of trapped ions, and superconducting circuits.
| Classical bit | Qubit |
|---|---|
| 0 or 1 | \(\alpha|0\rangle + \beta|1\rangle\) |
| Reading does not change it | Measurement collapses it |
| \(n\) bits hold one of \(2^n\) values | \(n\) qubits can be in a superposition of \(2^n\) states |
| Can be copied freely | Cannot be copied (no-cloning) |
| No entanglement | Can be entangled |
Key formula
\(|\psi\rangle = \alpha|0\rangle + \beta|1\rangle\), \(|\alpha|^2 + |\beta|^2 = 1\). \(|0\rangle, |1\rangle\): basis states, \(\alpha, \beta\): complex amplitudes.
Quick example
A qubit in \(|\psi\rangle = \frac{1}{\sqrt{2}}|0\rangle + \frac{1}{\sqrt{2}}|1\rangle\) gives 0 with probability \(1/2\) and 1 with probability \(1/2\). Three qubits can be in a superposition of all \(2^3 = 8\) states from \(|000\rangle\) to \(|111\rangle\), while three classical bits hold only one of these at a time.
Common mistakes
- Saying a qubit stores 0 and 1 "as two answers you can read"; measurement gives only one.
- Forgetting the normalisation condition \(|\alpha|^2 + |\beta|^2 = 1\).
- Claiming quantum computers are faster for every task; the advantage is only for specific problems.
How MU asks it
Asked as "Explain the concept of qubit" or "Differentiate between bit and qubit" (3 to 5 marks). Define qubit with \(\alpha|0\rangle + \beta|1\rangle\), explain superposition, measurement and entanglement briefly, and add a comparison table and two physical realisations.