Classical computers store information as bits, which are always 0 or 1 when used in a calculation. Quantum computers use qubits because quantum systems can hold and process information in ways that ordinary switches cannot. A qubit can be in a superposition of 0 and 1, and multiple qubits can become entangled so their states are linked.
These properties make quantum computers powerful for certain tasks, especially problems involving many possible states at once.
A qubit is often shown as a point on a Bloch sphere, where the north and south poles represent 0 and 1 and other points represent superpositions. When a qubit is measured, it gives a classical result, either 0 or 1, with probabilities set by its quantum state. Quantum algorithms use gates to rotate qubits, create interference, and amplify the probability of useful answers.
Real quantum computers are difficult to build because qubits are fragile, so error correction and careful isolation are essential.
Key Facts
- A classical bit has two possible values: 0 or 1.
- A qubit state can be written as |ψ⟩ = α|0⟩ + β|1⟩.
- Qubit probabilities obey |α|^2 + |β|^2 = 1.
- n classical bits store one of 2^n states at a time, while n qubits can represent a superposition over 2^n basis states.
- Measurement turns a qubit state into a classical result, with P(0) = |α|^2 and P(1) = |β|^2.
- Quantum speedups are task-specific, with important examples including factoring, search, optimization, and quantum simulation.
Vocabulary
- Bit
- A bit is the basic unit of classical information and can have the value 0 or 1.
- Qubit
- A qubit is the basic unit of quantum information and can exist in a superposition of 0 and 1 before measurement.
- Superposition
- Superposition is a quantum state that combines multiple possible basis states with probability amplitudes.
- Entanglement
- Entanglement is a quantum link between particles where the state of one cannot be fully described without the others.
- Quantum Error Correction
- Quantum error correction protects fragile quantum information by spreading one logical qubit across many physical qubits.
Common Mistakes to Avoid
- Thinking a qubit is simply both 0 and 1 at the same time. This is incomplete because a qubit has probability amplitudes and phase, not just two ordinary values at once.
- Assuming measuring a qubit reveals all information in its superposition. Measurement gives only one classical outcome and usually changes the quantum state.
- Believing quantum computers are faster for every problem. Quantum speedups apply to specific algorithms and problem types, not ordinary tasks like browsing or word processing.
- Ignoring noise and errors in real qubits. Physical qubits easily lose their quantum state, so practical machines need isolation, calibration, and error correction.
Practice Questions
- 1 A system has 5 qubits. How many computational basis states are in its full superposition space?
- 2 A qubit has amplitudes α = 0.6 and β = 0.8. What are the probabilities of measuring 0 and 1?
- 3 Explain why entanglement can help a quantum algorithm but does not allow instant communication faster than light.