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Quantum Computing

Quantum computers process information with qubits, which can be in superpositions of 0 and 1 and can be entangled, so n qubits can hold a superposition of 2ⁿ combinations. That does not mean they try every answer at once: a measurement reveals only a little information, so useful quantum algorithms — such as Shor's 1994 factoring algorithm — must be cleverly designed. Today's machines have hundreds of error-prone qubits; large, error-corrected quantum computers remain a goal, not a reality.

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State space and readout

∣ψ⟩=∑x∈{0,1}nαx ∣x⟩,∑x∣αx∣2=1|\psi\rangle = \sum_{x \in \{0,1\}^{n}} \alpha_{x}\, |x\rangle, \quad \sum_{x} |\alpha_{x}|^{2} = 1

An n-qubit state is a superposition over all 2ⁿ bit strings with complex amplitudes; measurement returns x with probability |αₓ|².

The exponential state space is not directly accessible: measuring returns a single n-bit string. Useful algorithms such as Shor's are designed so that the final measurement extracts information about the whole set of results computed in superposition. For hard combinatorial search the speed-up is only modest.

  • Physical platforms include trapped ions, neutral atoms, superconducting circuits, electrons trapped in semiconductors and photons; trapped ions hold superpositions long but compute slowly, superconducting circuits compute fast but are more fragile.
  • Current devices are noisy and intermediate-scale ('NISQ'); noise limits the size of circuits that can run reliably.
  • Fault tolerance requires quantum error correction with large qubit overheads.
Common misconception: Claims of 'quantum advantage' are task-specific; NIST notes that in some cases classical computers were later shown to equal or exceed the quantum result.
Full explanation — the complete reference version every reading depth is based on

Bits versus qubits

A classical bit is either 0 or 1. A qubit can be in state 0, state 1, or a superposition — a combination of the two — and several qubits can be entangled, so their states are linked. Two qubits can hold a superposition of four combinations, three qubits eight, and each extra qubit doubles the count.

N=2nN = 2^{n}

n qubits can hold a superposition of N = 2ⁿ combinations of 0s and 1s.

Why this is not 'trying every answer'

Measuring qubits at the end of a computation gives ordinary 0s and 1s and extracts only a small amount of information about everything computed in superposition. A useful quantum algorithm is designed so that the measurement extracts useful information about the whole set of results. For hard combinatorial search, quantum computers are expected to help only modestly.

What they might do

  • Simulate molecules and materials, the idea Richard Feynman raised in 1981 when he spoke about simulating physics with computers.
  • Factor large numbers with Shor's 1994 algorithm — a threat to widely used encryption if a large enough machine is ever built.
  • Possibly speed up some optimisation problems; how much remains an open research question.

Where things stand

Qubits are fragile: stray fields, temperature changes or even a cosmic ray can destroy a superposition. NIST's explainer (last updated 28 May 2026) reports that the best machines have hundreds of interconnected qubits and err roughly once per thousand operations, against about one error per quintillion calculations for a classical computer. Running Shor's algorithm on real encryption keys may need millions of error-free qubits. Anticipating that, NIST finalised its first post-quantum cryptography standards (FIPS 203, 204 and 205) on 13 August 2024.

Worked example: why errors matter

Our calculation: if each operation independently has a 1-in-1000 chance of error, the chance that 1000 operations all succeed is 0.999¹⁰⁰⁰ ≈ 0.37 — the computation fails more often than not. Quantum error correction can fix this in principle, but encoding protected qubits costs many additional physical qubits.

How we know

The description of qubits and the current state of the field comes from NIST, the US national measurement laboratory, whose explainer is dated and updated; the limits of quantum speed-ups and the cost of error correction come from John Preskill's peer-reviewed 2018 paper that coined the term 'NISQ'. Because the field moves quickly, every statement about current machines should be read with its date.

Assumptions and limits

The threat from Shor's algorithm assumes that factoring stays hard for classical computers — something believed after decades of effort, not proved. Claims of 'quantum advantage' are task-specific: NIST notes that in some cases classical computers were later shown to equal or beat the quantum result.

Common misconception: Misconception: 'quantum computers are just faster computers that will replace laptops'. They speed up only particular kinds of problem and are not expected to make NP-hard problems easy; NIST says they will not replace classical computers, and many experts expect them to live in computing centres, labs and universities rather than on desks or in pockets.
Info: Connections: start from classical bits in Computers and the CPU; leading qubits are built from trapped Atoms and ions, superconducting circuits or Semiconductors; quantum computing contrasts with classical computing at the level of the information unit itself.

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Sources and methodology

  • Unlike a classical bit, a qubit can be put into a superposition — state 0, state 1, or a combination of the two — and the quantum states of separate qubits can be entangled with each other. (awaiting scientific review)
  • Two qubits can hold a superposition of four combinations of 0s and 1s, three qubits eight and four qubits sixteen: each additional qubit doubles the number of combinations. (awaiting scientific review)
  • Quantum computers cannot efficiently brute-force search over all potential solutions at once, because the measurement at the end of a computation extracts only a small amount of information about the computations done in superposition. (awaiting scientific review)
  • Qubits are fragile: a stray electric or magnetic field, temperature fluctuations or even a cosmic ray can ruin a superposition or entanglement, forcing the qubits into ordinary 0 or 1 states. (awaiting scientific review)
  • According to NIST's explainer (created 18 March 2025, last updated 28 May 2026), the best quantum computers contain hundreds of interconnected qubits and make an error roughly once in every thousand operations, whereas a classical computer makes around one error per quintillion calculations. (awaiting scientific review)
  • Trapped-ion qubits can sustain quantum superpositions for a long time but are relatively slow at computing, whereas superconducting-circuit qubits allow fast computations and can be made with existing chip-manufacturing techniques but have more fragile, shorter-lived quantum states. (awaiting scientific review)
  • Topological qubits, which might have built-in immunity to errors, have proved challenging to build, and as of NIST's 2026 update researchers were still seeking definitive evidence that one has been made. (awaiting scientific review)
  • In 1994 Peter Shor published a quantum algorithm that could quickly factor the very large numbers that are products of huge primes, potentially putting widely used encryption at risk. (awaiting scientific review)
  • Running Shor's code-breaking algorithm may require millions of qubits that run error-free indefinitely, and NIST describes such a quantum computer as probably still much further away than near-term devices. (awaiting scientific review)
  • On 13 August 2024 NIST released its first three finalised post-quantum cryptography standards, FIPS 203, FIPS 204 and FIPS 205, specifying algorithms designed to withstand attack by a quantum computer. (awaiting scientific review)
  • Quantum computers are not expected to solve hard instances of NP-hard problems such as the travelling salesman problem efficiently; they can speed up exhaustive search, but only modestly. (awaiting scientific review)
  • Preskill (2018) gives three reasons for thinking quantum computers surpass classical ones: quantum algorithms for problems believed to be classically hard such as factoring, complexity-theory arguments about sampling, and the fact that no known classical algorithm can simulate a quantum computer. (awaiting scientific review)
  • Quantum error correction protects quantum information by encoding it in highly entangled states, but its overhead in additional physical qubits is large, so reliable error-corrected quantum computers were not expected to be available very soon (Preskill, 2018). (awaiting scientific review)
  • Richard Feynman's 1981 talk on simulating physics with computers is often credited with launching the field of quantum computing. (awaiting scientific review)

Claims marked “awaiting scientific review” cite the sources listed but have not yet been signed off by a scientific reviewer.

Content status: published 1 October 2026.

  • Scientific review: this version has not yet been signed off by a scientific reviewer.
  • The Advanced explanation has not yet been reviewed for age suitability.