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Quantum Computing

Quantum computing is a fundamentally different model of computation than the classical model that has dominated information technology since the 1940s. The difference is not speed — quantum computers are not faster classical computers. The difference is that quantum systems can occupy states that have no classical analog, and certain computational problems become tractable on quantum hardware while remaining intractable on classical hardware regardless of how much computation is thrown at them. The discipline has existed as theory since the early 1980s. It has existed as plausible engineering since roughly 2015. It has existed as something that affects the cryptographic decisions made today since the NIST post-quantum standardization process began in 2016.

This page is the umbrella introduction. The subpages linked at the end go deep on the physics, the qubit architectures, the algorithms, the error-correction overhead, and the current state of hardware. The relationship to cryptography is covered separately in the Post-Quantum Cryptography page under Cryptography.

A note on framing before going further: quantum computing is a field where credible practitioners and credible critics agree on the science and disagree sharply on the timeline. The descriptions on this page try to stay grounded in what has been built and what is verifiable, separating engineering reality from the marketing claims that have accumulated around the field. Both the breathless “quantum supremacy is here” framing and the dismissive “it will never work” framing miss the actual state of the discipline, which is genuinely interesting and genuinely unresolved.

What quantum computing is, briefly

A classical computer manipulates bits, each of which is unambiguously either 0 or 1 at any given moment. A quantum computer manipulates qubits, each of which can be in a superposition of 0 and 1 simultaneously — not in some particular intermediate value, but in a quantum state that has measurable probability of being observed as either 0 or 1 when measured. The superposition is not an engineering approximation; it is a genuine property of the underlying quantum system.

This sounds like a description of a probabilistic computer, but it is not. A probabilistic computer can be simulated efficiently on a deterministic classical computer (just run all the random outcomes). A quantum computer cannot, because two qubits in superposition can be entangled, which produces correlations between their measurement outcomes that have no classical explanation. The state space of n entangled qubits has 2^n complex-valued parameters, and simulating that state space on a classical computer requires storage that grows exponentially with n. By 50 qubits, the classical simulation requires petabytes of memory. By 70 qubits, it exceeds the storage capacity of the entire planet’s data centers.

The exponential state space is the entire reason quantum computing is interesting. A quantum computer with a few hundred entangled qubits operates in a state space larger than the number of atoms in the observable universe. For specific problems — not all problems, but specific ones — that state space lets the quantum algorithm explore solutions in parallel in a way that has no classical equivalent.

The catch is that you cannot just read the state space out. Measuring a quantum system collapses it to a single classical outcome with probability determined by the quantum state. Quantum algorithms are therefore not “try every solution in parallel” — they are intricately designed procedures that use interference to amplify the amplitudes of correct answers and cancel out the amplitudes of incorrect ones, so that when measurement happens, the result is more likely to be the correct answer than any specific incorrect answer.

The four concepts in the previous paragraphs — superposition, entanglement, interference, measurement — are the entire physics of quantum computation as an applied discipline. Everything else is engineering on top of them.

The fundamental concepts at the 101 level

Superposition is the property that a qubit can be in a quantum state that is neither cleanly 0 nor cleanly 1, but a complex-valued combination of both. The standard notation writes this as |ψ⟩ = α|0⟩ + β|1⟩, where α and β are complex numbers (called amplitudes) and |α|² + |β|² = 1. The squared magnitudes give the probabilities of measuring 0 or 1. The phases of α and β do not directly affect those probabilities but matter enormously when the qubit interacts with other qubits — phase is where the algorithmic structure of quantum computation lives.

Entanglement is the property that two or more qubits can be in a joint quantum state that cannot be factored into individual states. The most famous example is the Bell state (|00⟩ + |11⟩)/√2, in which two qubits are guaranteed to measure as the same value but neither qubit individually has a definite value before measurement. Entangled qubits exhibit correlations that violate classical inequalities — the famous Bell inequality experiments have demonstrated these correlations across kilometer-scale distances, ruling out any classical “hidden variable” explanation.

Entanglement is the resource that makes quantum computation more powerful than classical computation. A quantum algorithm without entanglement is no more powerful than a probabilistic classical algorithm. The entanglement is where the exponential state space comes from.

Interference is the property that quantum amplitudes can add constructively or destructively, depending on their phases. The structure of a quantum algorithm is essentially: arrange the qubits so that the amplitudes corresponding to correct answers add constructively (amplifying their probability) and the amplitudes corresponding to incorrect answers cancel destructively (suppressing theirs). When measurement happens at the end, the correct answer is overwhelmingly likely to be observed.

Measurement is the final step that converts quantum information into classical information. A measurement of a qubit produces 0 or 1 with probabilities determined by the squared amplitudes, and the qubit collapses to the corresponding classical state. The collapse is irreversible — the quantum state is destroyed. Quantum algorithms therefore have one shot per execution: you cannot examine the state mid-computation and then continue, because examining destroys the very superposition that the computation depends on.

A quantum computation is a sequence of operations (quantum gates) applied to qubits, followed by a final measurement. The gates are reversible (no information is destroyed during the computation), they preserve total probability (the amplitudes always sum to magnitude 1), and they can entangle qubits that were previously independent. The full computation is a unitary transformation of the joint state of all the qubits — a rotation, in the high-dimensional state space — followed by measurement.

What quantum computers can and cannot do

This is the question that gets answered most badly in popular accounts of the field. The honest version:

Quantum computers excel at specific problems with specific structure. The known quantum algorithms with exponential speedups target problems that have particular algebraic properties — periodicity, hidden subgroup structure, certain classes of search problems, certain quantum simulation problems. Most computational problems do not have this structure, and quantum computers offer no advantage over classical computers on most computational tasks.

The known significant quantum algorithms include:

  • Shor’s algorithm (1994) — solves integer factoring and discrete logarithm in polynomial time. Breaks RSA, Diffie-Hellman, and elliptic curve cryptography. The single most cryptographically important quantum algorithm.
  • Grover’s algorithm (1996) — provides quadratic (square-root) speedup for unstructured search. Less dramatic than Shor’s exponential speedup, but applies to a much broader class of problems including brute-force search and certain optimization problems.
  • Quantum phase estimation — the workhorse subroutine underlying Shor’s algorithm and many quantum simulation algorithms.
  • HHL algorithm (Harrow-Hassidim-Lloyd, 2009) — quantum algorithm for solving linear systems of equations under specific conditions. The conditions are restrictive enough that practical speedup over classical methods is contested.
  • Quantum simulation algorithms — simulating the behavior of quantum-mechanical systems (molecules, materials, certain particle physics problems) is the original motivation Feynman proposed for quantum computers in 1982 and remains one of the most credible near-term applications.
  • Variational quantum algorithms (VQE, QAOA, others) — hybrid classical-quantum algorithms designed for current noisy quantum hardware. Performance claims relative to classical methods are heavily contested.

Quantum computers do not provide general-purpose speedups. A quantum computer running a quantum sort algorithm is not faster than a classical computer running a classical sort algorithm. Most database queries, web requests, graph algorithms, machine learning training, image processing, and the bulk of what computers actually do every day get no speedup from quantum hardware. The popular framing of quantum computers as “exponentially faster than classical computers” is wrong; the accurate framing is “exponentially faster on a specific list of problems with specific structure.”

The problems most relevant to deployed information technology are cryptographic — Shor’s algorithm against asymmetric primitives is the most consequential. The other applications (quantum chemistry, materials science, certain optimization problems) matter substantially in their respective domains but do not affect general IT infrastructure decisions.

The qubit architectures

The physics of “a system that can be in a superposition of two states” can be realized in many different physical systems, and the engineering community has pursued several of them in parallel. Each architecture has different strengths and weaknesses, and there is no consensus on which will scale to production cryptographically-relevant systems.

The major architectures:

Superconducting qubits are the dominant approach in 2026, used by IBM, Google, Rigetti, and most Chinese research efforts. The qubits are tiny superconducting circuits (specifically, transmon qubits in most modern implementations) cooled to roughly 15 millikelvin in dilution refrigerators. Gate operations happen in tens to hundreds of nanoseconds. Coherence times — how long the qubits retain their quantum state — are typically 50-200 microseconds. The major engineering challenge is scaling: building larger superconducting processors while maintaining qubit quality and individual addressability.

Trapped-ion qubits use individual ions (typically of ytterbium, beryllium, or calcium) held in vacuum traps and manipulated with lasers. Used by IonQ, Quantinuum, Honeywell (now part of Quantinuum), and several research efforts. Gate operations are slower than superconducting (microseconds to milliseconds), but coherence times are dramatically longer (seconds, or even minutes for certain qubit types). Ion qubits also support all-to-all connectivity — any ion can directly interact with any other ion in the trap — which is a major architectural advantage. The engineering challenge is scaling beyond a single trap.

Photonic qubits use individual photons as qubits, manipulated through optical components. Used by PsiQuantum, Xanadu, and several research efforts. The architecture has theoretical advantages — photons don’t decohere through interaction with the environment the way matter-based qubits do, and they can operate at room temperature in some configurations. The engineering challenges are different: producing individual photons reliably, performing two-qubit gates between photons (which is hard because photons don’t naturally interact), and detecting them efficiently.

Neutral atom qubits use individual atoms (typically of rubidium or cesium) held in optical lattices and manipulated with lasers, similar to ion traps but without the charge. Used by Atom Computing, QuEra, Pasqal, and others. The architecture has been advancing rapidly in 2024-2026, with demonstrations of qubit arrays in the thousands. Coherence times and gate fidelities are competitive with the other leading approaches.

Topological qubits use exotic quasiparticles called non-abelian anyons, particularly Majorana zero modes, which would be inherently resistant to certain classes of error. Microsoft has been pursuing this approach for over a decade. The fundamental physics of the relevant quasiparticles has been controversial — Microsoft researchers have repeatedly claimed observations of Majorana modes that have later been retracted or disputed. Topological qubits remain a research bet rather than an engineering reality as of 2026.

Spin qubits use the spin of individual electrons in semiconductor structures, with the appeal that they could potentially be fabricated using existing silicon manufacturing infrastructure. Pursued by Intel, several university research groups, and Australian quantum computing programs. The technology is less mature than superconducting or trapped-ion approaches.

The Qubit Architectures subpage goes deeper into each of these, the engineering tradeoffs, and the realistic scaling trajectories.

Logical qubits vs physical qubits — the error correction problem

The most important number in quantum computing is the gap between physical qubits (what the hardware contains) and logical qubits (what algorithms operate on).

Quantum systems are extraordinarily fragile. Any interaction with the environment — a stray photon, a temperature fluctuation, a magnetic field — perturbs the quantum state in ways that introduce errors. Physical qubits in 2026 typically have error rates of 0.1% to 1% per gate operation. For a useful algorithm running thousands or millions of gates, those error rates compound to the point where the output is statistically indistinguishable from random.

Quantum error correction is the discipline of using many physical qubits to encode a single logical qubit that has much lower error rate than its physical components. The mathematics is rigorous and well-understood; the engineering overhead is enormous.

The dominant error correction approach is the surface code, which encodes one logical qubit in a 2D grid of physical qubits and corrects errors through repeated measurement of “stabilizer” operators that detect (but do not measure) errors. The encoding overhead depends on the physical error rate and the desired logical error rate. Typical estimates:

  • For a physical error rate of 0.1% and a target logical error rate of 10⁻¹⁵ (suitable for breaking RSA-2048 via Shor’s algorithm), the surface code requires roughly 1,000 to 10,000 physical qubits per logical qubit.
  • A complete Shor’s algorithm execution against RSA-2048 needs roughly 4,000 to 10,000 logical qubits.
  • The product is the requirement: somewhere between 4 million and 100 million physical qubits to break RSA-2048 in a realistic time.

State of the art in 2026 is roughly 1,000-1,500 noisy physical qubits in the leading systems, with logical-qubit demonstrations on the order of single digits. The gap between current capability and cryptographically-relevant capability is several orders of magnitude in physical qubit count.

Recent algorithmic and architectural improvements have been narrowing the gap. Better error correction codes (subsystem codes, color codes, the bivariate bicycle codes published in 2024), more efficient implementations of Shor’s algorithm, and improvements in physical qubit quality have all contributed. The absolute trajectory is favorable; the timeline is genuinely uncertain.

The Quantum Error Correction subpage goes deeper into the codes, the threshold theorem, and the engineering details.

The state of the field in 2026

A few honest observations about where the discipline stands.

Hardware progress has been real and substantial. The leading systems in 2026 are dramatically more capable than the leading systems in 2020. Qubit counts have grown by roughly 10x; qubit quality has improved meaningfully; error correction demonstrations have moved from toy experiments to multi-logical-qubit prototypes. The trajectory is positive.

Quantum advantage has been demonstrated on contrived problems. Google’s 2019 “quantum supremacy” experiment (a random circuit sampling task) and the Chinese USTC group’s Jiuzhang photonic experiments have demonstrated computations that would be prohibitively expensive to perform on classical hardware. These demonstrations are real, but they are on problems that have no practical application — they were chosen specifically because they are hard for classical computers, not because solving them is useful. The leap from “contrived quantum advantage on a useless problem” to “practical quantum advantage on a useful problem” has not been made and is genuinely difficult.

The major commercial deployments are NISQ-era systems. “NISQ” — Noisy Intermediate-Scale Quantum, a term coined by John Preskill in 2018 — refers to quantum systems with 50-1000 physical qubits and no error correction. The hope of the NISQ era was that useful applications would be found that fit within this regime, using variational quantum algorithms and other hybrid approaches. The track record is mixed: NISQ algorithms work on small problem instances but the claimed advantages over classical methods on larger instances have generally not survived rigorous comparison.

The cryptographic threat is structural, not immediate. Shor’s algorithm at cryptographically relevant scale requires millions of physical qubits. No public roadmap from any quantum hardware vendor projects reaching that scale before the 2030s, and the projections that exist are uncertain. The post-quantum cryptography migration is being driven not by an imminent quantum threat but by the long planning horizons of cryptographic systems — data encrypted today must remain confidential for years or decades, and “harvest now, decrypt later” is a real adversarial pattern.

The investment is substantial and continuing. Government quantum programs (the US National Quantum Initiative, the EU Quantum Flagship, the Chinese national quantum program, the UK National Quantum Strategy) are funded at the billions-of-dollars scale. Private investment in quantum hardware companies has produced multiple billion-dollar-plus valuations. The field is not going away regardless of the timeline to practical impact.

Productive skepticism is appropriate. The quantum computing field has a long history of overclaiming. Specific predictions have repeatedly failed (Microsoft’s topological qubit timeline, various “fault-tolerant by 2025” claims, multiple supremacy controversies). The technology may yet deliver on its potential — the underlying physics is sound and the engineering progress is real — but the marketing has frequently outrun the engineering, and consumers of quantum-computing content should weight claims accordingly.

Implications for cryptography

The intersection of quantum computing and cryptography is the most operationally relevant aspect of the field for practitioners in 2026. The cryptographic community has spent the last decade preparing for a quantum-capable adversary. The result is the NIST Post-Quantum Cryptography standardization process and the first generation of post-quantum standards (FIPS 203, 204, 205) finalized in August 2024.

The Post-Quantum Cryptography page covers the cryptographic side in depth — what the standards are, what their mathematical foundations are, and what the migration looks like. The short version: lattice-based and hash-based primitives are replacing RSA and elliptic curve cryptography for asymmetric operations; symmetric primitives (AES, SHA-2) survive the quantum transition with larger parameters.

The two pages are designed to be read together. This page covers the physics and engineering of building quantum computers; the post-quantum page covers the cryptographic response.

Where to go next on this site

The subpages under Quantum Computing will go deeper than this overview can:

  • Quantum Mechanics Fundamentals — the physics underlying the discipline: superposition, entanglement, the measurement problem, Bell inequalities, decoherence.
  • Qubit Architectures — superconducting, trapped-ion, photonic, neutral atom, topological, spin qubits. The engineering tradeoffs and scaling trajectories.
  • Quantum Algorithms — Shor’s, Grover’s, quantum phase estimation, HHL, quantum simulation, variational algorithms. What works, what’s hyped, what’s genuinely promising.
  • Quantum Error Correction — surface codes, the threshold theorem, fault tolerance, the physical-to-logical qubit overhead.
  • Quantum Hardware: State of the Art — the leading systems in 2026, the major vendors, the realistic capability frontier.

Across the Cryptography section, the related material:

  • Post-Quantum Cryptography — the cryptographic response to the quantum threat: the NIST standards (ML-KEM, ML-DSA, SLH-DSA), the mathematical families behind them, and the migration pattern.

The discipline is still in flux. Pages will be updated as the field progresses, particularly the State of the Art subpage which is the part most likely to age. If something on these pages is wrong, outdated, or incomplete, the goal is to fix it — these are meant to be durable references rather than snapshots.