Every term this site teaches, in one place, with the page that explains it. The same list drives the definitions that pop up on hover elsewhere, so the two cannot disagree.
Term of the day
twin-field QKD
A quantum key distribution scheme whose rate scales with the square root of the channel's transmittance, which is how fibre links past 1,000 km were reached.
Relaxing a physical system slowly into a Hamiltonian's ground state — proven polynomially equivalent in power to the standard quantum circuit model. The Machinery →
How unevenly spaced a circuit's energy levels are — zero for a plain LC tank, and the one property a superconducting qubit cannot work without. What is a qubit made of? →
A proof, worked out before the algorithm is run, that its answer is always within a fixed factor of the true optimum — the certificate that separates a trustworthy heuristic from a hopeful one. The Feasible Region →
B
barren plateaus Formalalso: barren plateau
Gradients that vanish exponentially with qubit count, so the variational circuit has nothing to descend. Will quantum boost AI? →
Bell inequality Workingalso: CHSH, Bell test, Bell's theorem, Tsirelson bound, Tsirelson
The experiment that proves entanglement is real: play it and watch the win rate cross a ceiling classical physics cannot pass. Quantum mechanics vs computing →
birthday bound Workingalso: birthday attack
Hash k inputs to n-bit digests and a collision turns up after about 2^(n/2) of them, the square root of the output space: the reason digests are twice as long as the security they give. Crypto 02 →
The class of problems a quantum computer solves efficiently. None of its containments is proven strict. Quantum mechanics vs computing →
branch and bound Workingalso: branch-and-bound
How to search a space too big to search, by proving whole regions cannot contain the answer. The Feasible Region →
C
certificate chain Workingalso: chain of trust
A leaf certificate signed by an intermediate that is signed by a root your browser already trusts. Each link is a signature, so a certificate carries two algorithms: its own key and its issuer's. Crypto 06 →
chemical accuracy Working
An energy error of 1 kcal/mol, which is 1.59 milli-hartree: the threshold below which a computed reaction energy is useful to a chemist. Where quantum might help →
CNSA 2.0 Workingalso: CNSA, Commercial National Security Algorithm Suite
The NSA's post-quantum timetable. Not one date: software signing and networking are 2030, not 2033. Post-quantum on the wire →
How many single failures a code can absorb before the logical bit flips. Raising it by two buys one more power of suppression; raising an odd d by one buys nothing. What is a logical qubit? →
coherence time Workingalso: coherence, decoherence, T1, T2, dephasing, relaxation time
How long a qubit holds its state before the environment scrambles it — T1 is the fall back to |0>, T2 the shorter time for phase to wash out. Quantum mechanics vs computing →
Encodes information in a continuous quantity — a light mode's amplitude and phase — instead of a discrete qubit; the architecture behind both Jiuzhang's and Xanadu Borealis's headline photonic advantage claims. How the companies compare →
corrections also: error bounty, correction log
Every mistake we have made, run louder than the original claim. Corrections →
crypto-agility Workingalso: cryptographic agility
Building systems so that an algorithm is a setting rather than code, so that the next change, and there will be one, does not need a rebuild. Crypto 10 →
A machine big enough to break real cryptography. Nobody knows the date, so the honest treatment is a probability curve, not a year. Post-quantum on the wire →
cryptographic bill of materials Workingalso: CBOM, CycloneDX, crypto inventory
A machine-readable list of every algorithm in your estate. Paste certificates and the page decodes the ASN.1 itself. Post-quantum on the wire →
D
data-loading problem Workingalso: input problem, data loading, state preparation
The toll that kills most quantum-ML speedups: getting classical data into the machine costs what the speedup saved. Will quantum boost AI? →
Classical algorithms that matched several claimed quantum speedups once the same data assumptions were granted. Will quantum boost AI? →
Deutsch-Jozsa algorithm Formalalso: Deutsch Jozsa, DJ algorithm
One query beats an exponential classical worst case for the same constant-or-balanced promise, scaled to n bits — an oracle separation, proven exactly. The Machinery →
Deutsch's algorithm Formalalso: Deutsch algorithm, constant or balanced
One query settles whether a 1-bit function is constant or balanced, where a classical algorithm needs two — the first proof of phase kickback plus interference. Machinery 08 →
Diffie-Hellman Workingalso: Diffie–Hellman, ECDH
Two strangers agree on a shared secret in public by each mixing a private exponent into a public base; it rests on the discrete logarithm being hard, which Shor's algorithm solves. Crypto 04 →
duality Workingalso: shadow price, shadow prices, dual problem
Every optimisation problem has a shadow twin that tells you where the next rupee should go. The Feasible Region →
The signature scheme protecting Bitcoin — and the one Shor's algorithm actually targets. Can quantum break Bitcoin? →
economic order quantity Workingalso: EOQ, inventory management, inventory optimization, reorder point, safety stock, bullwhip effect, supply chain optimization
The oldest formula in operations research (Harris, 1913): order sqrt(2KD/h) at a time to balance ordering cost against holding cost — with reorder points, safety stock, and the bullwhip effect it scales into across a supply chain. Region 24 →
entanglement Workingalso: entangled, entangled pair, Bell pair, Bell state
Correlations two particles share that no classical strategy can fake — and which still cannot carry a message. Quantum mechanics vs computing →
Computing reliably out of unreliable parts — the regime the whole roadmap is aimed at. Start here →
FeMoco Workingalso: FeMo-cofactor, FeMo cofactor
The metal cluster at nitrogenase's active site, and the standard benchmark for quantum chemistry: a model of 54 electrons in 54 orbitals is 108 qubits, and classical groups are now closing in on it. Where quantum might help →
Why exponential state space is not the reason quantum computers are hard to simulate — stabilizer circuits have it too and simulate efficiently. Quantum mechanics vs computing →
Build a solution by taking whatever looks best right now and never reconsidering — sometimes provably optimal (matroids, minimum spanning tree), more often provably within a fixed factor of optimal. The Feasible Region →
Quantum search: a quadratic speedup, not an exponential one — and one step too many makes it worse. The Arcade →
H
harvest now, decrypt later Workingalso: harvest-now-decrypt-later, HNDL, store now decrypt later, retrospective decryption
Traffic recorded today, decrypted whenever a quantum computer arrives. It is why key exchange is urgent and signatures are not. Post-quantum on the wire →
hash function Workingalso: cryptographic hash
A function that turns any input into a fixed-size fingerprint and is built so that you cannot find an input from a digest, or two inputs with one digest. A quantum computer only halves the exponent of a preimage search. Crypto 02 →
Heisenberg limit Working
The best precision quantum mechanics allows for N probes: error falling as 1/N. Noise usually reduces the gain to a constant factor. Sensors and networks →
HHL algorithm Workingalso: HHL, quantum linear systems
The exponential-speedup headline that dies on its own fine print: sparsity, conditioning, and getting the answer out. Will quantum boost AI? →
HQC Workingalso: Hamming Quasi-Cyclic
NIST's fifth post-quantum standard, selected March 2025 as a code-based backup to ML-KEM specifically because it rests on different math — so one break can't take both down. Post-quantum on the wire →
A physical network — built from coupled oscillators or lasers — engineered so its own resting state solves an optimisation problem. The classical rival every quantum annealer actually competes against. Classical vs quantum optimisation →
Two superconductors separated by a gap thin enough to tunnel through — the one component in the circuit that isn't a straight line, which is the entire trick. What is a qubit made of? →
K
Kerckhoffs's principle Workingalso: Kerckhoffs
A cipher should stay safe if everything about it except the key is public: algorithms leak and are costly to change, keys are cheap to replace. Stated in 1883. Crypto 01 →
How much the error rate falls per two steps of code distance. Google's Willow measured 2.14 for the d=5 to d=7 step. The Race →
Lamport signature Formalalso: one-time signature
A signature made of secrets revealed once: for each bit of the digest, reveal the secret matching the bit. Secure given only a hash function, and safe for one use only. Crypto 09 →
lattice problems Workingalso: shortest vector problem
Given a long skewed basis of a lattice, find a short vector in it. Easy in two dimensions, believed hard in hundreds, including for quantum computers. Crypto 08 →
lattice surgery Formal
Executing a logical two-qubit gate by physically merging adjacent surface-code patches and measuring the joint stabilizers, instead of needing two patches' qubits to sit side by side. Error correction →
A coil and a capacitor trading energy back and forth at one fixed rate — the harmless-looking oscillator that turns out to be useless as a qubit on its own. What is a qubit made of? →
learning with errors Formalalso: LWE
Noisy linear equations in a secret vector: without the noise, elimination solves them; with it, no efficient classical or quantum method is known. The basis of ML-KEM and ML-DSA, and not proven hard. Crypto 08 →
linear programming Workingalso: LP, simplex, simplex method, vertex theorem
Why you can skip infinitely many points and only check the corners. The Feasible Region →
local Hamiltonian problem Formalalso: k-local Hamiltonian problem
The decision version of finding a Hamiltonian's ground energy — the formal problem VQE is a heuristic for, and QMA's own natural complete problem. The Machinery →
Clifford gates alone are classically simulable, so universality is smuggled in via a purified magic state — consume several noisy copies, distill out fewer higher-fidelity ones. Error correction →
The Bellman equation once the world stops guaranteeing your action lands where you aimed it — and what changes when nobody hands you the transition probabilities at all. The Feasible Region →
Compute by measuring a fixed, pre-entangled cluster state one qubit at a time, adapting each basis choice to earlier outcomes — no gate ever applied after the state is built, and the model closest to how a photonic machine actually wants to compute. How the companies compare →
Designing the rules of a game so that honesty becomes the winning move. The Feasible Region →
Merkle tree Workingalso: hash tree
A tree of hashes in which one root stands for many leaves; a short path of hashes proves a leaf belongs. It lets one public key stand for many one-time signature keys. Crypto 09 →
metaheuristics Workingalso: metaheuristic, local search, tabu search, genetic algorithm
What you do when proof is out of reach and you still need a good answer today. The Feasible Region →
The standard hand-written decoder: pair up the alarms using the cheapest explanation. Optimal under uniform noise, and only under uniform noise. Error correction →
ML-DSA Workingalso: Dilithium, CRYSTALS-Dilithium, FIPS 204, ML-DSA-65
When goals genuinely conflict, 'optimal' becomes a set — the Pareto front of non-wasteful trade-offs — and choosing a point on it is a values call, not a theorem; weighted-sum scalarisation silently misses the non-convex parts. The Feasible Region →
The outcome nobody can improve on alone — even when everyone would rather be somewhere else together. The Feasible Region →
network flow Workingalso: max-flow, min-cut, max-flow min-cut, maximum flow
How much you can push through a network — and the bottleneck that answers the same question backwards. The Feasible Region →
neutral atom Workingalso: neutral atoms, Rydberg
Optical tweezers holding thousands of identical atoms, with rearrangeable geometry. How the companies compare →
newsvendor model Workingalso: newsvendor problem, newsboy problem, critical fractile, critical ratio
The one-decision stochastic problem: order Q before demand is known, and the optimal Q is the demand quantile at Cu/(Cu+Co) — the rule behind airline seat protection and inventory safety stock alike. Region 22 →
Noisy Intermediate-Scale Quantum, the era the field is actually in — and the still-unsettled tug-of-war between Google's 2019 Sycamore claim and classical simulations that have matched, lost to, and matched it again since. How the companies compare →
no-cloning theorem Formalalso: no cloning, quantum no-cloning, cannot be cloned
A four-line proof that no machine can copy an unknown quantum state — the reason QEC can't just keep a backup. The Machinery →
O
one-time pad Working
The one cipher that is safe against unlimited computing power: a truly random key as long as the message, used once. Shannon proved in 1949 that nothing weaker has perfect secrecy. Crypto 01 →
operations research Plainalso: OR, operational research, mathematical optimisation, mathematical optimization
The field that already decides your delivery route, your shift roster and your power grid — and the classical baseline quantum optimisation has to beat. The Feasible Region →
optical lattice clock Plain
A clock that counts the light oscillations of atoms held in a laser lattice; the best reach a fractional uncertainty below 10⁻¹⁸. Sensors and networks →
A unit that keeps fluctuating between 0 and 1 instead of settling, with the odds of each set by its neighbours — a physical Boltzmann machine, now demonstrated at a million-unit scale. Classical vs quantum optimisation →
period finding via continued fractions Formalalso: continued fraction algorithm, Shor period finding, modular period
Turns phase estimation's measured decimal back into the exact period Shor's algorithm needs — and, when the measured numerator shares a factor with the period, only a divisor of it, provably. Machinery 13 →
phase kickback Working
A controlled gate applied to a target already in one of its eigenstates leaves the target untouched and dumps the eigenvalue's phase onto the control instead — the mechanism inside Deutsch-Jozsa, Grover's and phase estimation alike. Why the algorithms work →
The same hybrid quantum-classical loop — a tunable circuit, measured, adjusted by a classical optimizer — pointed at a graph's cost Hamiltonian (QAOA) or a molecule's (VQE); neither has a proven speedup over its best classical rival. The Machinery →
QMA Formalalso: Quantum Merlin-Arthur, Quantum Merlin Arthur
The quantum analogue of NP: a claim is true if some quantum witness convinces a fast quantum verifier, false if every witness fails to. The Machinery →
QMA-completeness Formalalso: quantum Cook-Levin theorem, Feynman-Kitaev clock, history state
Kitaev's proof that the local Hamiltonian problem is as hard as anything in QMA, by encoding a quantum circuit's entire computation as one Hamiltonian's ground state. The Machinery →
quantum annealing Plainalso: D-Wave
Physical hardware that deforms a system toward a problem's Ising-model ground state instead of applying gates — real and commercially built by D-Wave since 2011, but solves exactly one problem shape and is not a universal quantum computer. How the companies compare →
The classical discrete Fourier transform applied to a quantum superposition's amplitudes — built from O(n^2) gates, exponentially fewer than the classical FFT needs. The Machinery →
Reach a target state in as few gates as possible. Every par is a proven minimum. The Arcade →
quantum key distribution Workingalso: QKD, BB84, B92, Ekert91, E91, Micius
Uses quantum measurement disturbance (BB84, B92) or Bell-inequality violation (Ekert91) to let two parties detect an eavesdropper directly — real physics, flown on China's Micius satellite, and not a substitute for the classical/post-quantum cryptography this page's tools actually measure. Post-quantum on the wire →
The chain-of-purified-hops fix for the fact that an unknown quantum state can't be amplified like a classical signal — proposed in 1998, still mostly lab-scale (a real three-node network exists), and the reason a satellite sidesteps the whole problem for one specific link. How the companies compare →
quantum PCP conjecture Formalalso: qPCP, NLTS
The still-open question of whether the local Hamiltonian problem stays QMA-hard even at coarse, constant-fraction precision — the quantum analogue of the classical PCP theorem. The Machinery →
Chopping time into many small steps to approximate the evolution of a Hamiltonian whose terms don't commute — the mechanical trick that turns Feynman's 1982 intuition into Lloyd's 1996 algorithm, and the route from a molecule's Hamiltonian to its ground-state energy. The Machinery →
quantum teleportation Formalalso: teleportation, teleport a qubit, Bell measurement
Moving an unknown qubit's state using a shared entangled pair and two classical bits — no quantum channel, no cloning, no faster-than-light signal. The Machinery →
qubit Plainalso: qubits
The quantum bit: the unit everything else is counted in. Start here →
A resonant drive swinging a qubit's population between two levels — stop it exactly halfway (a pi-pulse) and you have physically performed an X gate. What is a qubit made of? →
Optimising the worst case over a set of possible data rather than the average, buying a hard guarantee at a measurable cost in expected performance — the same instinct as a noise-robust quantum control pulse. The Feasible Region →
RSA Workingalso: RSA-2048
The public-key system built on the difficulty of factoring a product of two large primes: anyone can lock with the public pair, only someone who knows the factors can unlock. Shor's algorithm factors in polynomial time. Crypto 05 →
S
Schmidt decomposition Formalalso: Schmidt rank, Schmidt coefficients, how entangled is a state
The one basis pair in which any two-part quantum state collapses to a short matched list — the honest, basis-independent measure of how entangled it is. The Machinery →
The relaxation that turns a hard combinatorial problem into unit vectors on a sphere — and the actual classical benchmark quantum optimisation has to beat. The Feasible Region →
Shannon entropy Formalalso: information entropy, classical entropy, bits of uncertainty
The expected number of bits needed to resolve a random outcome — zero for a sure thing, log2(n) at most, achieved only by a uniform distribution over n outcomes. The Machinery →
Shapley value Workingalso: cooperative game theory, SHAP, coalition game
The one fair way to split credit a group earned together — proven unique in 1953, now explaining ML predictions. The Feasible Region →
The algorithm that breaks RSA and elliptic-curve cryptography, given a large enough error-corrected machine. Can quantum break Bitcoin? →
Simon's algorithm Formalalso: Simon algorithm, hidden period, hidden subgroup problem
Finds a function's secret XOR-period in O(n) queries against a classical birthday-bound floor of about root-2^n — the direct forerunner of Shor's period-finding. The Machinery →
Hot early to cross ridges, cold late to settle. Play the cooling schedule, not the climber. The Arcade →
SLH-DSA Formalalso: SPHINCS+, SPHINCS, FIPS 205, hash-based signature
The conservative hash-based signature. Its real cost is not the 7,856-byte signature — it is the seconds it takes to produce one. Post-quantum on the wire →
A single electron or nuclear spin in a silicon quantum dot as the qubit — betting the entire existing chip-fabrication industry instead of building bespoke hardware, and already past 99% fidelity in a real 300mm foundry. How the companies compare →
Light with less noise in the quantity you measure and more in the one you do not; LIGO uses it to hear fainter gravitational waves. Sensors and networks →
Deciding now against a probability distribution over what comes later, minimising expected cost with a corrective 'recourse' decision once the uncertainty resolves — how day-ahead power-grid unit commitment is actually solved. Region 22 →
submodular optimization Formalalso: submodularity, diminishing returns, submodular function
Set functions with diminishing returns, where greedy is a guaranteed (1 - 1/e)-approximation and provably nothing polynomial beats it — the bound under sensor placement, feature selection and influence maximisation. Region 21 →
Fast gates, short coherence, fabrication that scales like chips. Google and IBM's bet. How the companies compare →
superdense coding Formalalso: dense coding, two bits one qubit
Sending two classical bits by physically transmitting just one qubit, spending a pre-shared entangled pair — teleportation's mirror image. The Machinery →
superposition Plainalso: superposed, in superposition
The alarm pattern a code emits. It says whether neighbours disagree, never what they are — which is why measuring it does not destroy the data. Error correction →
T
the AI-quantum loop Plainalso: symbiosis, AI fixes quantum, quantum supercharges AI
SymbiQ's whole thesis in one diagram: one direction is shipping now, the other is mostly ahead. Will quantum boost AI? →
The Bench Workingalso: three methods, many replays
Random restart, simulated annealing and oscillator relaxation race on the same graph, 200 replays each — move the time budget and the winner changes. Classical vs quantum optimisation →
The Calibration Workingalso: calibration agent, detuned Rabi game
You configure a calibration agent's per-round behaviour — Trust, Nudge or Recalibrate — while a qubit's true detuning drifts out of sight; scored against a paired replay of the same drift under a fixed strategy. What is a qubit made of? →
The Question also: daily question, the daily question
One question at a time, at three depths, with a fault-tolerant streak. Playhub →
thermodynamic computing Workingalso: thermodynamic AI, stochastic processing unit
Treating a circuit's own electrical noise as the computational resource — for sampling, Bayesian inference and diffusion models — rather than something to engineer away. Classical vs quantum optimisation →
the simplex algorithm Working
How you actually find the best corner once you know the optimum is one: walk the edges of the feasible region, only ever uphill, until no neighbour scores higher. The Feasible Region →
The Solver's Path also: the campaign, the six acts
Six acts where the character's flaw is the mechanic, and the physics does the judging. The Solver's Path →
the transportation problem Workingalso: transportation problem
A flow network with no interior — supply nodes and demand nodes only — so the optimum sits at a vertex before you even start solving. The Feasible Region →
The proof that arbitrarily long fault-tolerant computation is possible at all, provided the physical error rate sits below a fixed constant and the code scales up to compensate. Error correction →
topological qubits Plainalso: topological qubit, Majorana zero mode, Majorana zero modes, Majorana fermion, non-abelian anyon, Majorana 1
A bet that braided Majorana zero modes protect quantum information by topology alone, before any error correction runs — and, as of Microsoft's disputed 2025 Majorana 1 announcement, still an unresolved experimental claim, not a settled one. How the companies compare →
transmon Workingalso: transmons, transmon qubit
A capacitor wired across a single Josephson junction — the most common superconducting qubit design, and almost the same circuit as a plain LC tank with one piece swapped. What is a qubit made of? →
A gate applied to every physical qubit of a logical block independently, so one faulty gate can't spread — but Eastin-Knill proves no code can make a gate set both transversal and universal. Error correction →
trapped ion Workingalso: trapped ions, ion trap, trapped-ion
twin-field QKD Workingalso: twin-field quantum key distribution
A quantum key distribution scheme whose rate scales with the square root of the channel's transmittance, which is how fibre links past 1,000 km were reached. Sensors and networks →
V
von Neumann entropy Formalalso: quantum entropy, entanglement entropy, Holevo bound
Shannon entropy applied to a density matrix's eigenvalues — zero for any pure state, yet a pure whole can split into two individually maximally-uncertain halves, the number that quantifies entanglement itself. The Machinery →
Z
zero-sum games Workingalso: minimax, minimax theorem, mixed strategy, von Neumann minimax
Why bluffing only works if it's genuinely random — and why solving it is a linear program in disguise. The Feasible Region →