Short, sourced answers to the questions people ask, each with the page that explains it properly.
Last reviewed 2026-10-17. Every figure here is one the linked page carries and sources. If an answer is wrong, tell us and the fix runs with your name on it.
The basics · How qubits and gates work · Algorithms: QAOA, VQE, Grover, Shor and the rest · The harder questions: complexity and theory · Hardware and progress · Noise and error correction, in more depth · Security and encryption · Applications and industry · AI and quantum · Learning it, and the software (added 25 October 2026) · About SymbiQ
A quantum computer stores information in qubits and processes it by steering their amplitudes so that wrong answers cancel and right ones reinforce. It is not a faster laptop: it only helps on problems with the right structure, such as simulating quantum systems and factoring. Start here takes about five minutes.
It prepares qubits, applies gates that rotate their amplitudes, and then measures. The trick is interference: a good algorithm is arranged so that the amplitudes of wrong answers cancel and the right ones add up, so the measurement lands on a useful answer with high probability. Long calculations also need error correction. The five-minute version, or the plain-language lesson.
For almost everything, the supercomputer. A quantum computer can only win on problems with structure it can exploit, such as simulating molecules or factoring, and for those it first has to be large and error-corrected. The experiments where a quantum chip beat a supercomputer used tasks chosen for the purpose, and classical methods keep narrowing them. Advantage Watch tracks each claim.
A qubit is any two-level quantum system you can control: a tiny superconducting circuit, a trapped ion, a neutral atom or a photon. Unlike a bit, its state is described by two amplitudes, so it can sit in a superposition of 0 and 1 until you measure it. See what a qubit is actually made of, or open a quantum computer up in 3D.
No. A register of n qubits can hold amplitudes over all 2ⁿ outcomes, but measuring returns one outcome, chosen at random by its amplitude. An algorithm only helps if it first makes interference cancel the wrong ones. The short version, with sources.
No. Measuring one half of an entangled pair gives a random result on its own; the correlation only shows up when the two sides compare notes over an ordinary channel. Why, and what Bell tests do show, or play both sides of the CHSH game.
It is derived from it, not different: a quantum computer uses the standard rules and adds no new physics. What changed is the question, from “what does nature do?” to “what can we compute with it?”. The full answer.
Yes. The lessons here are free, need no sign-up, and come in three depths: plain, working and formal. Begin with the five-minute start, follow the course map, and go to the maths when you want the proofs.
It holds one unit of quantum information, and it is what the gates act on. A gate rotates its state, an entangling gate such as CNOT links it to another qubit, and a final measurement turns it into an ordinary 0 or 1. What makes it useful is that its amplitudes can cancel or add, so a well-built circuit steers probability toward the right answer. What one is made of, or see it in 3D.
A bit is 0 or 1. A qubit’s state is a pair of complex amplitudes, α and β, with |α|² + |β|² = 1, drawn as a point on the Bloch sphere. Measuring it still returns a single 0 or 1, so a qubit does not hand you more readable information than a bit does (see the Holevo bound below). What differs is how it behaves in between. The postulates, step by step.
A state that is a weighted sum of 0 and 1, written α|0⟩ + β|1⟩. It is not “secretly 0 or 1”: the two amplitudes can interfere, which is what algorithms exploit. Measure it and you get 0 with probability |α|² and 1 with probability |β|². Set the amplitudes yourself.
The state is replaced by the outcome you saw: 0 with probability |α|², 1 with probability |β|². The superposition is gone, and you cannot recover α and β from one measurement, only estimate them by repeating the whole experiment many times. Projective and generalised measurement.
A joint state of two or more qubits that cannot be written as a separate state for each. Its measurable signature is a correlation no classical strategy can match: in the CHSH game, classical players win at most 75% of rounds, entangled ones about 85.4%. Work through the CHSH game, or play it.
A reversible operation on qubits, written as a unitary matrix. The Hadamard gate turns |0⟩ into an equal superposition; CNOT flips a target qubit when the control is 1. A small set of such gates is enough to build any quantum computation. The maths of gates, and Circuit Golf lets you build circuits with the fewest gates.
Because copying an unknown state would break the linearity of quantum mechanics: no operation can take an arbitrary |ψ⟩ and return two independent copies of it. This is the no-cloning theorem, and it is why quantum error correction cannot simply back up a qubit. The proof, worked out.
A picture of every pure single-qubit state as a point on a sphere: |0⟩ at the north pole, |1⟩ at the south, equal superpositions on the equator, with the angle around the equator giving the relative phase. Single-qubit gates are rotations of the sphere, and mixed (noisy) states sit inside it. Try the Bloch sphere.
Complex numbers, vectors and matrices, and basic probability. That is enough for the circuit model; the rest (tensor products, eigenvalues, the density matrix) is introduced as it is needed. The maths, built step by step.
Yes. A laptop can simulate up to roughly 30 qubits, because the state needs 2n amplitudes and every extra qubit doubles the memory. Several companies also give cloud access to real hardware, some with free tiers (check their current terms). Here, the games run entirely in your browser.
The Quantum Approximate Optimization Algorithm (Farhi, Goldstone and Gutmann, 2014) attacks problems like Max-Cut. It writes the cost of every candidate answer as an energy, then alternates two short layers: one that imprints the cost, one that mixes amplitude between answers. A classical optimiser tunes the angles, and the loop repeats. It is designed for noisy, shallow circuits, not for error-corrected machines. QAOA and VQE, explained.
They are the same hybrid loop: a short circuit with adjustable angles, a measurement, and a classical optimiser that nudges the angles. QAOA points it at a combinatorial problem, where the best answer is the extreme eigenvalue of a cost Hamiltonian; VQE points it at a molecule or material and looks for the lowest energy. VQE rests on the variational principle, so the energy it reports can never be below the true ground-state energy. Neither has a proof that it beats the best classical method on problems anyone needs. Both, side by side.
Quantum annealing slowly changes a physical Hamiltonian so the machine settles into a low-energy state; D-Wave builds hardware that does this. QAOA is a gate-model circuit with a fixed number of alternating layers. With many layers it can imitate the slow annealing path (Farhi et al., 2014), but at the few layers real hardware allows it is a different, shallower thing. Both are heuristics. Adiabatic computing and the classical machines it competes with.
Nobody has shown it. For Max-Cut, the classical Goemans–Williamson algorithm guarantees a cut at least 0.878567 of the best possible in polynomial time; whether QAOA crosses that bar on instances anyone needs solved is open. Strong classical solvers (branch and bound, simulated annealing) are the baseline it has to beat. The Goemans–Williamson bound, metaheuristics, and Can a classical machine out-optimise a quantum one?
It is built from quantum devices (superconducting flux qubits) and performs quantum annealing, but it solves one family of optimisation problems instead of running arbitrary circuits, so it cannot run Shor’s or Grover’s algorithm. Whether it beats classical methods is a dated claim we track: D-Wave’s 2025 simulation claim.
Grover searches N unstructured items in about √N steps: a quadratic speedup, and provably the best possible. Shor factors integers (and solves discrete logarithms) far faster than any known classical method, but only because those problems hide a repeating pattern the quantum Fourier transform can find. Grover and AES, what Shor takes.
A circuit that turns a periodic pattern in the amplitudes into a sharp peak at multiples of the inverse period. On n qubits it uses about n² gates, where the classical fast Fourier transform on 2n points needs about n·2n steps. It is the engine inside Shor’s algorithm and phase estimation. The transform, built gate by gate.
No. Proven speedups are few: a quadratic one for unstructured search, a super-polynomial one for factoring, discrete logarithms and simulating quantum systems, and contrived ones for oracle problems such as Simon’s. For most everyday computing there is no known advantage. Where one might actually earn its keep.
Supremacy (John Preskill’s 2012 word) means a quantum device does some task no classical computer can in reasonable time; advantage is the softer word most people use now, partly because classical methods keep catching up. Google’s 2019 53-qubit random-circuit claim was matched by a classical run 743 days later. Neither word means the task is useful. Advantage Watch tracks every claim and what followed.
No efficient quantum algorithm is known, and most researchers expect none. Grover gives only a square-root speedup for brute-force search, and Bennett, Bernstein, Brassard and Vazirani proved in 1997 that no quantum algorithm can do better on unstructured search. Factoring, which Shor handles, is not believed to be NP-complete. The proof, in the AES lesson.
The set of yes/no problems a quantum computer can solve in polynomial time with error at most one third. It contains P and the randomised class BPP, and sits inside PSPACE. Factoring is in BQP and is not known to be in P; whether BQP contains any NP-complete problem is believed no, but unproved. The quantum cousin of NP.
Not for ordinary computation. Proving that BQP is larger than BPP would also prove that P differs from PSPACE, which nobody can yet do. Unconditional separations exist only in restricted settings, such as query problems (Simon’s algorithm) and some communication tasks. Simon’s algorithm and the oracle separation.
QMA is the quantum version of NP: a short quantum proof that a fast quantum verifier can check. Finding whether a local Hamiltonian’s lowest energy is below a threshold is QMA-complete (Kitaev), which is why no near-term algorithm for finding ground energies comes with a general speed guarantee. QMA, worked out and on a small circuit.
The operator for a system’s energy. Its lowest eigenvalue is the ground-state energy, and the state that has it is the ground state. QAOA and VQE both work by encoding a problem (a graph, a molecule) as a Hamiltonian and looking for an extreme eigenvalue. Hamiltonians in QAOA and VQE.
The energy of any trial state is at least the ground-state energy. It is why VQE can be trusted not to report an energy lower than the truth, however poor its circuit is; a bad circuit only gives a higher, less useful number. The proof, in two lines.
A way to describe a state you only know partly: a qubit entangled with something you cannot see, or one that noise has disturbed. A pure state is the special case of rank one; a mixed state has purity below one. You need it as soon as you talk about noise, decoherence or one half of an entangled pair. Density matrices and mixed states.
A limit on how much classical information n qubits can deliver: at most n bits, however many amplitudes they carry. Superdense coding sends two bits per qubit only by using a pre-shared entangled pair. The Holevo bound and superdense coding.
A circuit built only from Clifford gates (Hadamard, phase, CNOT) with stabiliser inputs and Pauli measurements can be simulated efficiently on a classical computer, however many qubits it has. So a quantum advantage needs at least one non-Clifford resource, such as the T gate or a magic state. Stabilisers and the surface code.
Regions of the parameter landscape where the gradient of the cost function shrinks exponentially with the number of qubits (McClean and co-authors, 2018), so a classical optimiser has nothing to follow. They are one reason QAOA and VQE are hard to scale. The variational loop they affect.
It depends on the technology, and the number alone says little. Google’s Willow (2024) has 105 physical qubits, IBM’s Condor (2023) has 1,121, and a 2025 Caltech tweezer array holds 6,100 atoms. Error rates and error correction matter more than the count. The milestones chart keeps the sources.
A logical qubit is many noisy physical qubits working together so that errors can be detected and corrected, giving one reliable unit. The cost grows with the error rate you need: in the standard surface-code layout, a logical qubit of distance d uses about 2d² physical qubits. The calculator and the full answer.
Qubits are fragile and gates are imperfect, so errors pile up faster than a useful computation can finish. Error correction spreads one logical qubit over many physical ones and checks them constantly. Google’s Willow showed errors falling as the code grew, by a factor of about 2.1 per step up in code distance (a fit over distances 3, 5 and 7; Nature 638, 920, 2025). How the surface code works.
Four technologies lead: superconducting circuits, trapped ions, neutral atoms and photonics, with spin qubits and topological qubits earlier-stage. Each trades speed, connectivity and error rate differently. How to compare them, and see each one in 3D.
The famous gold “chandelier” is mostly a refrigerator and its wiring: stacked stages cool a chip the size of a fingernail, at the bottom, to about 10 to 20 millikelvin. Trapped-ion and neutral-atom machines look different again: vacuum chambers, lasers and optics on a table. Open three machines up in 3D.
On benchmark tasks, several experiments claim it, and classical simulations have repeatedly narrowed or erased those gaps. Whether a result counts depends on the task and on the classical baseline you accept. We log the dated claims and check them in the Ledger, and keep a running view on Advantage Watch.
Both. The physics is solid and error correction now works in the lab, but machines that beat classical computers on useful real tasks are not yet shown, and many dated promises slip. The Ledger scores each promise on its deadline, and Reality Check rates movie scenes and myths by how much of the physics holds up.
Neither wins on every axis. Trapped ions have the lowest error rates and connect any qubit to any other, but their gates are slow. Superconducting qubits have far faster gates (tens of nanoseconds against microseconds or longer) and fabricate like chips, but connect to neighbours only and need more qubits for error correction. How the technologies and companies compare.
Nobody knows. Company roadmaps point at 2029 to 2030 for the first large error-corrected machines (IBM’s Starling, Quantinuum’s Apollo), and dated promises like these often slip. We log each one and score it on its deadline: IBM Starling, 2029, Quantinuum Apollo, 2030, and the rest of the Ledger.
Noisy intermediate-scale quantum: John Preskill’s 2018 name for machines with tens to a few hundred qubits and no error correction. QAOA and VQE were designed for them. Whether any NISQ machine can do something useful beyond classical reach is the open question. What has been claimed, and what followed.
Mitigation runs the noisy circuit many times and fixes the statistics afterwards, for example by extrapolating to zero noise; in general its cost grows exponentially with circuit size, so it does not scale. Correction encodes one logical qubit across many physical ones and keeps checking them, and does scale once errors are below threshold. The exchange rate between physical and logical qubits.
If the error rate per operation is below a threshold, you can make the logical error rate as small as you like by adding overhead that grows only slowly with the size of the computation. For the surface code the threshold is roughly 1% (model-dependent). Drag the error rate across it.
A grid of qubits in which data qubits store the information and measure qubits repeatedly check the parity of their neighbours. A decoder reads the pattern of alarms and infers where errors happened. It needs only nearest-neighbour interactions on a 2D chip and has a high threshold, which is why most labs use it. How it works, or see it in 3D.
T1 is how long a qubit keeps its energy before relaxing from 1 to 0; T2 is how long the phase relationship between 0 and 1 survives. T2 cannot exceed 2·T1. Gates have to finish well inside both. Where they come from in a superconducting circuit.
Clifford gates alone are classically simulable (see Gottesman–Knill above), so a useful machine also needs a gate like T. In the surface code T cannot be applied directly; it is built from a specially prepared noisy “magic” state that is purified until it is reliable, which can cost more than the rest of the computation. Google’s 2024 cultivation proposal cuts that cost. The research note.
Their transitions sit at about 4 to 8 GHz, which corresponds to a temperature of roughly 0.2 to 0.4 kelvin, so any warmer and thermal noise flips them at random. Labs run them at about 10 to 20 millikelvin in dilution refrigerators, well below that and below the point where aluminium superconducts. The circuit and the fridge.
Shor’s algorithm would break the public-key systems behind most secure connections today (RSA and elliptic curves), but only on a large error-corrected machine that does not exist yet. Symmetric ciphers such as AES are weakened far less: Grover’s algorithm gives a square-root speedup, so longer keys restore the margin. See the cryptography course and whether a quantum computer breaks AES.
The day a quantum computer can break today’s public-key encryption. Nobody knows the date, but data recorded now can be stored and decrypted later, so the migration has to start before it: if the time your data must stay secret plus the time migration takes is longer than the time until Q-Day, you are already late. Test your own site and see the numbers.
In principle yes, for its signature scheme, on a machine far larger than any built. Published estimates of what it would take fell from about 1.9 billion physical qubits in 2022 to under 500,000 in 2026, while today’s largest superconducting chip, IBM’s Condor, has 1,121. The estimator and the sources.
New public-key algorithms believed to resist quantum attack, running on ordinary computers. NIST published the first standards, FIPS 203 (ML-KEM), 204 (ML-DSA) and 205 (SLH-DSA), on 13 August 2024. A 2026 measurement of 32,011 domains found 49.3% already negotiate a hybrid post-quantum key exchange and none used post-quantum certificates (Dubey and Varshney, arXiv 2606.16473). Check a site and measure the size cost.
Not for most uses. Security agencies including the NSA and the UK’s NCSC prefer post-quantum cryptography, because quantum key distribution needs dedicated hardware, still needs authenticated channels, and is distance-limited without trusted relays. The sourced comparison.
Craig Gidney’s 2025 estimate is fewer than a million noisy physical qubits running for under a week, assuming 0.1% gate errors and the surface code. That is down from 20 million qubits in his 2019 estimate with Ekerå. The largest superconducting chip today has 1,121. How RSA works and why Shor breaks it.
An attacker records encrypted traffic today and stores it until a quantum computer can decrypt it. It is why data that must stay secret for many years needs post-quantum protection before Q-Day, not after. Work out your own deadline.
Yes, on current knowledge. Grover’s algorithm halves the effective key length, so AES-256 behaves like a 128-bit key, which nobody can brute-force. The NSA’s CNSA 2.0 suite asks for AES-256 for this reason. The calculation, step by step.
Cryptography whose security rests on finding short vectors or solving noisy linear equations in high dimensions (learning with errors), problems with no known quantum shortcut. ML-KEM and ML-DSA, two of the NIST standards, are lattice-based. Lattices, explained.
The strongest case is simulating quantum matter, molecules and materials, the job Feynman proposed in 1982. Factoring and related number problems follow, and so do quadratic speedups for search-like tasks. As of 2026 none has beaten the best classical method on a task anyone needs. What would have to be true, and who is checking.
Possibly, and it is not shown yet. The flagship target, the nitrogenase cofactor FeMoco, is estimated at about four million physical qubits and under four days, and classical methods have since narrowed the case. The full picture, and how a molecule is simulated.
Proposals exist, but most promise at best a quadratic speedup, which the overhead of error correction can swallow on near-term machines, and no advantage has been demonstrated. Classical optimisation is very strong. Quantum and AI, the routes ranked and the classical rivals.
They already ship. The best optical clock is uncertain by 8.1 × 10−19, and LIGO has injected squeezed light into its detectors since 2019. Neither needs an error-corrected machine. Quantum sensing and networks.
No to both, in any useful sense. A quantum computer is a co-processor for narrow mathematical problems, with no advantage at graphics or ordinary game logic, and it computes with the probabilities of physics, not with knowledge of what will happen. Games built on quantum ideas are another matter: try ours.
Mostly not yet. The route with the most support is learning from data that is itself quantum; claims of exponential speedups for ordinary machine learning mostly fail on the cost of loading the data. The direction already working is the other way round: AI helping quantum computers. The routes, ranked.
A decoder reads the error alarms and decides what went wrong. Google DeepMind’s AlphaQubit learned to do this from data and beat the standard matching decoders on real Sycamore data, though it was too slow to run in real time (arXiv 2310.05900). The plain story, or play the Decoder Duel.
AI is software that learns patterns from data and runs on ordinary chips. Quantum computing is a different kind of hardware that computes with qubits and interference. They are not rivals: AI already helps run quantum computers (reading their errors, tuning them, designing circuits), while quantum speedups for AI are mostly unproven. The loop between them.
Yes, within limits. In October 2026 a preprint from Anthropic and Harvard reported that Claude, searching against an independent checker, found circuits with fewer gates and fewer qubits than the baseline on 7 of 8 tasks. The widely shared “17 times” is one comparison on one task, bought with 12% more qubits, and nothing ran on quantum hardware. The paper, read in full.
Less than people fear to begin with: none for the plain depth of the lessons here, then complex numbers, vectors and matrices and probability for the working depth. IBM’s Basics of quantum information course lists basic linear algebra, complex numbers and elementary ideas about sets and functions as its starting point. The maths ladder, with the lesson that teaches each rung.
There is no single answer. John Preskill’s lecture notes are free, Nielsen and Chuang is a textbook his course lists as a supplement, and Scott Aaronson’s Quantum Computing since Democritus is the complexity-flavoured one. What each one is, and where we got that.
They are built by different groups for different jobs: Qiskit (IBM) and Cirq (Google) write circuits for simulators and hardware, PennyLane (Xanadu) is for differentiable hybrid and machine-learning work, and CUDA-Q (NVIDIA) is for CPUs, GPUs and quantum processors working together. We found no public source that ranks them, so we do not. The software map, and the same circuits written in Qiskit and in Cirq.
With one program that finds the circuit’s energy levels (scqubits is the free one) and another that follows its state in time, with losses (QuTiP). The Workbench has nineteen interactive explorers (seventeen checked against both programs, two for circuits in Qiskit and Cirq) and eighteen lessons that go from the arrays under a simulation to fitting a chip to a measurement, then to circuits in code.
The two toolkits number the bits of an index from opposite ends: Qiskit writes qubit 0 as the rightmost bit of a bitstring, Cirq as the leftmost, so one state has two indices (an X on qubit 0 of two qubits is index 1 in Qiskit and index 2 in Cirq). Lesson 40 writes a Bell pair and a GHZ state in both, with the Python for each. Lesson 41 compiles a circuit for a stand-in chip and adds noise to a Bell pair. Both run on a laptop; neither runs anything on real hardware or says which toolkit a lab uses.
Not necessarily, according to QuEra’s article on what students ask: engineering and computational skills suit hardware, software, applications and product roles, and deep academic specialisation helps some paths. That is one company’s view, not hiring data. What it says, and what it does not.
It depends what counts, and each claim has a caveat that a one-line answer would lose. The honest list is on three pages: the hardware scoreboard in The Race, the sourced timeline, and the record of advantage claims and the classical responses to them.
A free site about the loop between AI and quantum computing: lessons at three depths, games whose answers are proved, a research desk that explains new papers figure first, and a public Ledger of claims. About the desk.
Each claim is logged on the day it is made, with a rule for deciding it, scored when it falls due, and never deleted. Our own mistakes go in the Corrections log. What each layer of checking can and cannot catch.
The lessons, games, research desk and Ledger are free and need no sign-up.
We are starting a community of people who like checking claims and doing the maths. Join the Discord, take on the daily question on the Play page, or tell us where we got something wrong on the Corrections page.
More: the course map · the glossary · the research desk · the Ledger.