Quantum computing

Qubits and superposition

A classical bit is 0 or 1. A qubit (quantum bit) can be in a superposition: a combination of 0 and 1 at the same time, described by probabilities. When it is measured, it gives a definite 0 or 1.

A register of n qubits can be in a superposition of all 2ⁿ states at once, so a quantum algorithm can work on many possibilities together. 10 qubits span 2¹⁰ = 1024 states; 300 qubits span more states than there are atoms in the observable universe.

Entanglement, interference and decoherence

• Entanglement: qubits can become linked so that the state of one is connected to the state of another, however far apart; measuring one tells you about the other. It lets qubits work together in ways classical bits cannot.
• Interference: the probabilities of different outcomes can reinforce or cancel, like waves. Quantum algorithms are designed so that wrong answers cancel out and right answers are reinforced, making the right answer likely when measured.
• Decoherence: interaction with the environment (heat, vibration, stray fields) destroys the fragile quantum state, causing errors. This is why qubits are kept near absolute zero and isolated, and why building large, reliable quantum computers is so hard.

The threat to cryptography

• RSA (and similar public key systems) is secure because factorising huge numbers takes classical computers an impractical time. Shor's algorithm on a large, error-corrected quantum computer could factorise them efficiently, breaking RSA. Data intercepted now could be decrypted later ('harvest now, decrypt later').
• Grover's algorithm speeds up brute-force searching, effectively halving the length in bits of symmetric keys (a 128-bit key gives only about 64-bit security), so longer keys (for example 256-bit) are used.
• Response: post-quantum cryptography, new algorithms based on maths problems believed hard even for quantum computers, being standardised and rolled out now.

Benefits and drawbacks

Potential benefits: simulating molecules for new drugs and materials; optimisation (logistics, finance); some machine learning tasks; searching large spaces.

Drawbacks: very expensive; need extreme cooling and isolation; high error rates from decoherence; only faster for specific problems; current machines have limited qubits; threaten existing encryption.

Worked example

How many basis states can a register of 8 qubits represent in superposition, and why does that matter?

1. Each qubit doubles the number of states: 2⁸ = 256.
2. A quantum algorithm can act on all 256 at once, then use interference so the right answer is most likely when measured.

Answer: 256 states at once

Check yourself

1. What is a qubit?
   • A bit that is always 1
   • Eight bits grouped together
   • A unit of processor speed
   • A quantum bit that can be in a superposition of 0 and 1
   Show answer

   A quantum bit that can be in a superposition of 0 and 1. Qubits are the basic unit of quantum information.

2. What is superposition?
   • Two qubits being physically joined by a wire
   • A qubit existing in a combination of 0 and 1 states until it is measured
   • A qubit losing its quantum state
   • Storing one bit on top of another
   Show answer

   A qubit existing in a combination of 0 and 1 states until it is measured. Measurement gives a definite value.

3. How many basis states can a register of 12 qubits represent in superposition?
   Show answer

   4096. 2¹² = 4096.

4. What is entanglement?
   • A link between qubits so that the state of one is connected to the state of another
   • The loss of quantum state caused by heat
   • Cancelling out wrong answers
   • Cooling qubits to absolute zero
   Show answer

   A link between qubits so that the state of one is connected to the state of another. Entangled qubits behave as a connected system.

5. What is decoherence?
   • Measuring a qubit on purpose
   • Joining two qubits
   • The loss of a qubit's quantum state through interaction with its environment, causing errors
   • Reinforcing correct answers
   Show answer

   The loss of a qubit's quantum state through interaction with its environment, causing errors. It is the main obstacle to large quantum computers.

6. Why are quantum computers a threat to RSA encryption?
   • Shor's algorithm could factorise the large numbers RSA relies on far faster than classical computers
   • They can guess passwords by reading minds
   • They make hash functions reversible
   • They can delete encryption keys remotely
   Show answer

   Shor's algorithm could factorise the large numbers RSA relies on far faster than classical computers. Fast factorising reveals the private key.

7. How do quantum algorithms use interference?
   • They block radio signals
   • They copy qubits many times
   • They arrange for the probabilities of wrong answers to cancel and right answers to reinforce
   • They keep the qubits warm
   Show answer

   They arrange for the probabilities of wrong answers to cancel and right answers to reinforce. This makes the correct result the likely measurement.

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Sources

• Pearson Edexcel International Advanced Subsidiary and Advanced Level in Computer Science specification (2026), Issue 1
• Pearson Edexcel IAL Computer Science sample assessment materials (Unit 3 paper, resource booklet and mark scheme)

Last updated 8 November 2026. Spotted a mistake? Tell us.