# Quantum Computing, plainly Built 2026-09-23. CC BY 4.0. https://nanobotco.github.io/quantum-computing/ ## Theory ### A coin on the table, a coin in the air A bit is a coin lying on the table: heads or tails. A qubit is a coin in the air. Every ordinary computer, from a wristwatch to the biggest machine on earth, works on bits. A bit is one switch, on or off, and there is nothing in between. Eight billion of them on a chip, each one on or off, and that is the whole story. A qubit is different in one way. Until you look at it, it is not on or off. It is in a mix of the two, called a superposition, and the mix has a lean: maybe mostly on with a little off, maybe half and half. When you look, which is called measuring, it lands on one side, on or off, with odds set by the lean. Then it stays there. So the coin picture is this. A bit is a coin on the table. A qubit is a coin spinning in the air. You can shape how it spins. But the moment you slap it flat to read it, it is heads or tails and the spin is gone. The thing that trips most people up: the qubit is not secretly heads or tails the whole time with you not knowing. Einstein thought it must be. The Bell tests, further down, showed it is not. Before you look, there is no answer yet. That is the physics, not a gap in our knowledge. One more thing the coin picture gets wrong, and it matters for everything after. A coin in the air has a chance of heads, say 70%. A qubit has something underneath the chance, called an amplitude, which can be positive or negative or point in any direction on a clock face. The chance is the amplitude squared. Two positive amplitudes add up. A positive and a negative cancel. Chances never cancel; amplitudes do. Hold onto that, because it is the whole trick. Sources: Nielsen & Chuang, Quantum Computation and Quantum Information, ch. 1 ; Qubit ### Where the arrow points One qubit is an arrow that can point anywhere on a ball. Up is 0, down is 1, and the sideways part is what makes it quantum. Physicists draw one qubit as an arrow from the centre of a ball to its surface. This is the Bloch sphere, after Felix Bloch. The north pole is 0. The south pole is 1. Anywhere else is a superposition. How far the arrow tilts from the poles sets the odds. Straight up: 0 every time. Straight down: 1 every time. On the equator: 50-50. The odds only depend on the tilt. Which way round the equator the arrow points, the direction on the clock face, does not change the odds at all. That is the phase. It looks useless, since measuring cannot see it. It is the most useful thing in the machine, because phase is what decides whether two paths add up or cancel when they meet. Every one-qubit operation is a turn of this arrow. A gate called X flips it top to bottom, the quantum version of NOT. A gate called Z spins it half a turn around the pole, changing phase and nothing you could measure. A gate called H, for Hadamard, tips a straight-up arrow onto the equator, which is how a computer puts a qubit 'in the air' to begin with. The ball is a picture of one qubit. Two qubits do not fit on two balls, because they can be entangled, and then neither one has its own arrow. That is the next chapter but one. Sources: Bloch sphere ; Quantum logic gate ### Ripples that cancel Drop two stones in a pond. Where crest meets crest the water leaps; where crest meets trough it goes flat. A quantum computer is arranged so wrong answers meet trough and go flat. This is interference and it is the engine. Everything inside a quantum computer is a wave, which de Broglie said in 1924 and every experiment since has agreed with. Waves add. Two crests make a bigger crest. A crest and a trough make nothing. In the coin chapter the amplitude could be positive or negative. Now it has a picture: positive is a crest, negative is a trough, and the phase is where in the up-and-down the wave is at the moment two waves meet. The famous demonstration is the two-slit experiment. Fire single electrons, one at a time, at a wall with two slits and a screen behind. Each electron lands at one point, like a particle. But the points build up into stripes, a pattern of bright and dark bands, as if each electron went through both slits as a wave and interfered with itself. Cover one slit and the stripes vanish. Watch which slit it goes through and the stripes vanish. Feynman called this the only mystery. A quantum algorithm is a set of turns that gets the amplitudes of the paths leading to wrong answers to point opposite ways, so they cancel, while the paths leading to the right answer point the same way and pile up. Then you measure and the right answer is what you get, most of the time. It is not 'trying every answer at once'. It is arranging the waves so that the bad answers wash each other out. Sources: Double-slit experiment ; Feynman Lectures, vol. III ch. 1 ### Two coins that always match Two entangled qubits are two coins in the air that, when you catch them, always land the same way, no matter how far apart, and neither one had picked before you looked. Put two qubits through the right gates and they become entangled. Measure one and you get 0 or 1 at random. Measure the other, in the next room or the next galaxy, and it matches. Every time. That alone is not strange. Put one left glove and one right glove in two boxes, mail them apart, open one: you know what is in the other. The gloves were decided when they were packed. Einstein said the qubits must be like the gloves, decided from the start, with the decision hidden from us. John Bell, in 1964, found a way to tell gloves from qubits. If you can measure at more than one angle, and the results were fixed in advance, the pattern of matches is limited in a way you can count. Quantum mechanics predicts more matches than that limit allows. The test was run in 1972, 1982, 2015 and many times since, and it always comes out on the quantum side. The 2022 Nobel Prize was for these tests. There is no hidden decision. The coins pick when caught, and they pick together. This does not send messages faster than light. You see random 0s and 1s at your end whatever the other person does. The match only shows up when you compare notes, and the notes travel the ordinary way. What it is good for: entanglement is how qubits share their amplitudes, so that a turn on one path affects the whole computation. It is why the space of a quantum computer grows by doubling with each qubit added. Twenty qubits carry a million amplitudes; three hundred carry more than there are atoms in the known universe. You cannot read them out, but you can make them interfere. Sources: Quantum entanglement ; Bell test ; Nobel Prize in Physics 2022 ### The switches A quantum program is a short list of turns applied to qubits, drawn as wires and boxes. Everything the machine does is a few kinds of turn, over and over. An ordinary chip has logic gates: AND, OR, NOT. A quantum computer has gates too, and a program is drawn as a circuit: one horizontal line per qubit, time running left to right, a box wherever a gate acts. The one-qubit gates are turns of the arrow from the sphere chapter. H puts a qubit in the air. X flips it. Z and its smaller cousins turn the phase. The two-qubit gate that matters most is CNOT: flip the second qubit if the first is 1. Put an H on the first qubit and then a CNOT, and the two are entangled. That two-gate circuit is the hello-world of the field. Every gate is reversible. Run the circuit backwards and you get the input back. Nothing is erased, because erasing is the one thing quantum mechanics does not allow in the middle of a computation. Measurement, at the end, is the exception; it is the only step that throws information away. A small set of gates, H, one phase gate called T, and CNOT, is enough to build any quantum program at all, the way NAND alone builds any ordinary one. Real chips offer a handful of native gates and compile everything else into them. Counts to have in your head: a useful program might need millions of gates on a few thousand error-corrected qubits. Today's machines run a few thousand gates on a few hundred noisy ones before the answer turns to mush. That gap is the field. Sources: Quantum circuit ; Controlled NOT gate ### Finding a needle in fewer tries Grover's method finds one marked item in a million by looking about a thousand times. An ordinary computer looks half a million. The trick is amplifying the right answer's wave a little with every pass. Suppose one name in a phone book of a million has a star next to it and you can only check one name at a time. On average you check half a million. There is no shortcut for an ordinary computer. Grover's method starts by putting all million names in superposition, each with the same small amplitude. Then it does two things, over and over. First, it flips the sign of the starred name's amplitude, crest to trough. Second, it reflects every amplitude about the average. The starred one, being the odd one out, gets pushed up; the rest get pushed down by a hair. Each round the starred amplitude grows. After about a thousand rounds, the square root of a million, it is nearly all the wave, and a measurement reads it out. Go too many rounds and it starts shrinking again, so you have to count. That is a square-root speed-up. A million to a thousand is good. A trillion to a million is better. It is not the exponential leap of Shor's method, but it applies to almost any search or optimisation you can phrase as 'check whether this guess is right', which is why it comes up so much. It has also been proved you cannot do better than the square root for a plain unsorted search. The quantum computer is not magic here. It is a wave doing what a wave can do. Sources: Grover's algorithm ; Grover, 1996, arXiv:quant-ph/9605043 ### Breaking the locks The locks on the internet rest on one fact: multiplying two big primes is easy, and undoing it is not. Shor showed a quantum computer can undo it, by finding a rhythm. When you buy something online, your browser and the shop agree on a secret using a scheme called RSA, or a cousin of it. RSA's lock is a number that is two large primes multiplied together. Anyone can see the number. Finding the two primes, for the sizes used in practice, would take ordinary computers longer than the universe has existed. Peter Shor's idea, in 1994, was to turn factoring into finding a rhythm. Pick a number, say 7, and keep raising it to higher powers, dividing by the lock number each time and keeping the remainder. For lock number 15 the remainders go 7, 4, 13, 1, 7, 4, 13, 1. The pattern repeats every 4. That repeat length, called the period, is enough to work out the primes with a bit of ordinary arithmetic. For 15 it gives 3 and 5. For a big lock number the period is astronomically long and an ordinary computer would take forever to spot it. A quantum computer puts all the powers in superposition at once, and then applies a quantum version of the tool engineers use to find the pitch of a sound, the Fourier transform. The rhythm shows up as interference: every period-length that is wrong cancels out, and the right one is what you measure. Nobody has broken a real key this way. The largest number factored by an honest run of Shor's method is small enough to do in your head. The estimates for breaking a real 2048-bit RSA key have come down over the years, from tens of millions of noisy qubits to about a million as of 2025, running for a week or so. The machines that exist are hundreds of times too small and far too noisy. Governments did not wait. In 2024 NIST published new lock designs that do not rest on factoring, and banks, browsers and phone makers are switching now. The reason to switch early is called harvest now, decrypt later: anything recorded today can be opened whenever the machine arrives. Sources: Shor's algorithm ; Gidney 2025, 'How to factor 2048 bit RSA integers with less than a million noisy qubits' ; NIST post-quantum standards, August 2024 ### Why it falls apart A qubit in the air is a coin balanced on its edge in a barn full of drafts. Anything that touches it, heat, a stray radio wave, a cosmic ray, counts as a look, and the coin falls. The reason quantum computers are hard is not that the physics is exotic. It is that the physics is fragile. A superposition survives only as long as nothing in the outside world learns which way it leans. The world does not have to be a person with a meter. A single air molecule bouncing off, one photon of heat, a magnetic wobble from a passing truck: each one takes a little of the information away, and the qubit slides toward being a plain coin on the table. This is decoherence. It happens on a clock. For a superconducting qubit today the clock runs out in about a hundred millionths of a second, sometimes a thousandth. For a trapped ion it can be seconds or minutes. The number is called T2, and a machine's whole design is an argument with it. So the machines are cold, very cold: the superconducting kind sits at about 15 thousandths of a degree above absolute zero, colder than deep space, in a nested set of gold-plated cans that looks like a chandelier. Ions and atoms float in vacuum held by lasers and electric fields. Everything is shielded. And still every gate errs about once in a thousand, and every second of waiting costs a little. Errors in a quantum computer are worse than a flipped bit. A bit can only flip. A qubit's arrow can drift by any angle in any direction, and drift is continuous, so there is no clean 'right' and 'wrong' to compare against. That is why people thought for a while that error correction was impossible, and why the 1995 discovery that it is possible was the field's second birth. Sources: Quantum decoherence ; Dilution refrigerator ### Fixing errors without looking You cannot copy a qubit and you cannot look at it. So you spread it across many qubits and ask the neighbours whether they still agree, without asking what they say. An ordinary computer fixes errors by keeping three copies and taking a vote. That is out: a qubit cannot be copied, and reading it to compare would wreck it. The way round, found in 1995, is to store one qubit's worth of information in the relationships between several qubits, and then measure only the relationships. You can ask 'are qubits 1 and 2 the same?' without learning what either one is. If they were the same and now they are not, one of them flipped, and asking a second question tells you which. Then you flip it back. The stored information was never read. The surface code is the version the leading machines use. Picture a checkerboard. The qubits that hold the data sit on the white squares. The black squares are checker qubits whose only job is to ask their four neighbours whether they still agree. Run the checks over and over, feed the pattern of complaints to an ordinary computer, and it works out where the errors are. The threshold theorem from 1997 says: if each part errs less than about one time in a hundred, a bigger checkerboard gives a more reliable stored qubit, and you can make the reliability as high as you like by making the board bigger. Above that rate, a bigger board is worse. For 25 years every machine was above the line. In December 2024 Google's Willow chip showed the error halving each time the board grew, from 3×3 to 5×5 to 7×7. That is the line, crossed. The cost is the catch. One good stored qubit, called a logical qubit, takes a board of several hundred to a couple of thousand physical qubits at today's error rates. A useful machine wants a few thousand logical qubits. That multiplies to a few million physical ones. Nobody is close. Newer codes found in 2023 and 2024 cut the multiplier roughly tenfold, and that is where much of the research is. Sources: Quantum error correction ; Toric code ; Google Quantum AI, 'Quantum error correction below the surface code threshold', Nature 2025 ### What it is not It does not try every answer at once, it is not faster at everything, and it is not about to replace your laptop. **It does not try every answer at once.** It holds every answer's amplitude at once, which is different, because you can only read one out. The whole art is in getting the wrong ones to cancel before you read. For most problems nobody knows how to do that, and for some it has been proved impossible. **It is not a faster computer.** For adding up a spreadsheet, rendering a game or serving a web page, a quantum computer is slower, by a lot, and always will be. The gates are slow, the readout is slow, and there is no wave trick for those jobs. The speed-ups are for particular problems: factoring, searching, and above all simulating molecules and materials, which are quantum themselves. **Bigger qubit counts are not the score.** A thousand noisy qubits are worth less than a hundred clean ones. The numbers that matter are the error rate per gate, how long a qubit lasts, and how many error-corrected logical qubits a machine can hold. Companies lead with the count because it is the number that goes up. **It has not broken any code.** Every announced 'factoring record' either used a toy number, or used a shortcut that does not scale, or was an annealer doing something Shor's method is not. The internet's locks are being changed anyway, ahead of time, because a recording made today can be opened later. **Annealers and gate machines are different things.** D-Wave's machines settle into a low-energy state to answer optimisation questions. They are quantum, they are big, and they cannot run Shor's or Grover's method or any general program. When a headline says 'a 5,000-qubit quantum computer', check which kind. **The cat is a joke.** Schrödinger meant the alive-and-dead cat as an argument that something was wrong with the theory as read. The current reading is that a cat is far too big and warm to stay in superposition for any length of time; it decoheres in less time than light takes to cross it. A qubit is the smallest, coldest, most isolated thing people can make, so that it stays in superposition for a fraction of a second. That is the whole engineering problem. Sources: Scott Aaronson, 'The Limits of Quantum Computers', Scientific American 2008 ; Quantum supremacy ## History - 1900 — Planck's lumps of light. Max Planck finds that hot things give off light in fixed-size lumps, not a smooth flow. He calls the lump size a quantum. He was trying to explain the colour of glowing metal and could only make the numbers work by assuming energy came in packets. He thought it was a trick of the math. It was the start of the whole subject. Source: Wikipedia: Planck's law - 1905 — Einstein says light is particles. Albert Einstein explains why light knocks electrons out of metal: light arrives as particles, later called photons. This is the paper that won him the Nobel Prize, not relativity. A photon either has enough energy to knock an electron loose or it does not; a dimmer light sends fewer photons, not weaker ones. Source: Wikipedia: Photoelectric effect - 1913 — Bohr's atom has rungs. Niels Bohr says an electron in an atom can only sit on certain rungs of energy, and jumps between them by giving off or taking in one photon. The rungs are why each element has its own colours when heated. Two of those rungs, picked out and controlled, are what a qubit is in most machines today. Source: Wikipedia: Bohr model - 1924 — Matter is a wave too. Louis de Broglie says that if light can act like a particle, then particles like electrons act like waves. Confirmed three years later when electrons fired at a nickel crystal made a ripple pattern. Everything in a quantum computer rests on this: the things inside it are waves, and waves can add up or cancel. Source: Wikipedia: Matter wave - 1925 — Heisenberg's matrix mechanics. Werner Heisenberg, 23, works out a set of rules for atoms using tables of numbers. It is the first full version of quantum mechanics. He did it on the island of Heligoland, sent there by hay fever. The tables were matrices, and the fact that A times B is not B times A in his tables is the same fact behind the uncertainty principle he wrote down two years later. Source: Wikipedia: Matrix mechanics - 1926 — Schrödinger's wave equation. Erwin Schrödinger writes one equation that says how the wave of a particle changes over time. It is still the equation. It turned out to give the same answers as Heisenberg's tables. The wave it describes is not a wave of water or sound; its size squared is the chance of finding the particle in a place. That 'size squared' rule is what makes quantum odds different from coin odds. Source: Wikipedia: Schrödinger equation - 1927 — The Solvay fight. The founders meet in Brussels and argue about what the theory means. Einstein doubts it; Bohr defends it. Nobody settles it. Heisenberg's uncertainty principle came out the same year: you cannot know both where a particle is and how fast it is going, not because your ruler is bad but because the particle does not have both at once. The Brussels argument is still going on, in a quieter form, in every discussion of what a measurement is. Source: Wikipedia: Solvay Conference - 1935 — Einstein's 'spooky' objection. Einstein, Podolsky and Rosen point out that the theory lets two particles stay linked at any distance. They say this shows the theory is missing something. Schrödinger names the link 'entanglement' the same year, and describes his cat. Einstein wanted a hidden layer of facts underneath. The linked particles he complained about are the resource every quantum computer runs on. The cat was a joke about the same problem: a cat that is alive and dead until you look is what the math seems to say, and Schrödinger thought that was absurd. Source: Wikipedia: EPR paradox - 1936 — Turing describes a universal computer. Alan Turing describes a simple imaginary machine that can do any calculation any other machine can do. Every ordinary computer since is one of these. A quantum computer is a different kind of machine. It cannot compute anything a Turing machine cannot. It can do some things in far fewer steps. Source: Wikipedia: Turing machine - 1947 — The transistor. Bell Labs builds the transistor, the switch that makes every ordinary computer work. It works because of quantum mechanics, but it computes with plain bits. Worth keeping in mind: the phone in your pocket already runs on quantum physics. What a quantum computer adds is using the wave part of the physics to compute, not only the switching part. Source: Wikipedia: Transistor - 1948 — Shannon names the bit. Claude Shannon works out how to measure information, and the unit is the bit: one yes or no. A qubit is what you get when you ask the same question about a quantum system. The answer, worked out over the next fifty years, is that it holds one bit when you read it and something stranger before you do. Source: Wikipedia: A Mathematical Theory of Communication - 1964 — Bell's test. John Bell shows that Einstein's hidden layer of facts would leave a fingerprint in the numbers, and that quantum mechanics predicts a different fingerprint. So it can be tested. Bell was a CERN engineer who did this on a sabbatical. His inequality turned a philosophy argument into an experiment. Every test since has come out on the quantum side. Source: Wikipedia: Bell's theorem - 1973 — Computing without throwing anything away. Charles Bennett at IBM shows a computer can run every step backwards as well as forwards and, in principle, use no energy doing it. Quantum mechanics only allows reversible steps, so this is the bridge. If reversible computing were impossible, quantum computing would be too. Source: Wikipedia: Reversible computing - 1980 — Benioff's quantum Turing machine. Paul Benioff writes down a Turing machine that obeys quantum mechanics. It is the first paper to describe a quantum computer, though it computes nothing an ordinary one could not. Around the same time Yuri Manin in Moscow noted that simulating quantum systems is exponentially hard for ordinary computers and hinted that a quantum machine might do better. Source: Wikipedia: Paul Benioff - 1981 — Feynman: build one. Richard Feynman tells a conference at MIT that ordinary computers cannot keep up with nature, and that a computer built from quantum parts could. 'Nature isn't classical, dammit.' The talk, printed in 1982 as 'Simulating Physics with Computers', is the usual starting gun. His point was narrow and still the strongest case for the machine: to model molecules and materials, which are quantum, use something quantum. Source: Int. J. Theor. Phys. 21, 467 (1982) - 1982 — You cannot copy a qubit. William Wootters, Wojciech Zurek and Dennis Dieks prove that an unknown quantum state cannot be copied. That rules out the backup trick ordinary computers use against errors. The same year Alain Aspect's team in Paris ran a Bell test with the settings changed while the photons were in flight. Quantum won again. Aspect shared the 2022 Nobel for it. Source: Wikipedia: No-cloning theorem - 1984 — Quantum keys. Bennett and Gilles Brassard show two people can share a secret key using photons, and any eavesdropper leaves marks. It is the first quantum technology that does something useful. Called BB84 after their initials and the year. It is not a computer; it is a way to send keys. It is sold commercially now and runs over fibre and by satellite. Source: Wikipedia: BB84 - 1985 — Deutsch's universal quantum computer. David Deutsch in Oxford describes a quantum computer that can run any quantum program, and gives the first problem it solves faster than a plain computer. His first problem was a toy: tell whether a coin is fair or double-headed in one flip instead of two. The point was that the speed-up was real at all. Source: Wikipedia: Quantum Turing machine - 1993 — Teleportation. Bennett and five others show a qubit's state can be moved from one particle to another far away, using an entangled pair and two ordinary bits. Nothing travels faster than light; the original is destroyed. Demonstrated with photons in 1997. Today it is a routine step inside quantum networks and some error-correction schemes. Source: Wikipedia: Quantum teleportation - 1994 — Shor's algorithm. Peter Shor at Bell Labs finds that a big enough quantum computer could break the codes that protect bank transfers and the web, by finding the prime factors of large numbers quickly. This is the moment governments and companies started paying. Ordinary computers take longer than the age of the universe on the numbers used in practice; Shor's method takes hours on a machine that does not yet exist. It also drove the new codes that NIST standardised in 2024. Source: Wikipedia: Shor's algorithm - 1995 — Errors can be fixed after all. Shor shows that spreading one qubit across nine lets you catch and fix errors without reading the qubit. Andrew Steane finds a seven-qubit version. The no-copying rule had made people think this was impossible. The same year Ignacio Cirac and Peter Zoller propose a way to build gates with trapped ions, and in December Chris Monroe and David Wineland's group at NIST runs the first two-qubit gate on a single trapped beryllium ion. Source: Wikipedia: Quantum error correction - 1996 — Grover's search. Lov Grover shows a quantum computer can find one item in an unsorted list of a million by checking about a thousand times, where a plain computer needs about half a million. A square-root speed-up, not the giant one Shor gets. It works on almost any search problem, which is why it comes up so often. The same year Seth Lloyd showed Feynman was right: a quantum computer can simulate any quantum system efficiently. Source: Wikipedia: Grover's algorithm - 1997 — The threshold theorem. Several groups prove that if each part of the machine errs less than some fixed rate, error correction can push the total error as low as you like. Below the line, bigger machines get better instead of worse. Dorit Aharonov and Michael Ben-Or, Alexei Kitaev, and Knill, Laflamme and Zurek got there separately. Kitaev also proposed the toric code, the ancestor of the surface code that the leading machines use today. The whole field since is an effort to get under that line. Source: Wikipedia: Quantum threshold theorem - 1998 — Two qubits in a test tube. Isaac Chuang, Neil Gershenfeld and Mark Kubinec run Deutsch's toy problem on the nuclei of chloroform molecules in a liquid, using a hospital-style magnetic resonance machine. The same year Bruce Kane proposed building qubits from single phosphorus atoms in silicon, the plan Australian groups still follow. Source: Wikipedia: NMR quantum computer - 1999 — A qubit made of wire. Yasunobu Nakamura's group at NEC in Japan shows a tiny superconducting circuit, a loop of metal with no resistance, can act as a qubit for a few billionths of a second. This is the ancestor of the chips at Google and IBM. It is a circuit you can print, which is why it won. Source: Nature 398, 786 (1999) - 2000 — DiVincenzo's checklist. David DiVincenzo at IBM writes the five things any quantum computer must have. It is still the checklist. Qubits you can add more of; a way to set them to zero; long enough before they lose their state; a full set of gates; and a way to read them out. Source: Wikipedia: DiVincenzo's criteria - 2001 — 15 = 3 × 5. IBM and Stanford run Shor's algorithm on seven qubits in a molecule and factor 15. It is the smallest number that counts, and it took a room of equipment. The same year Knill, Laflamme and Milburn showed that photons, mirrors and detectors alone could make a universal quantum computer, the root of today's photonic companies. Source: Nature 414, 883 (2001) - 2007 — The transmon. Yale's group designs the transmon, a superconducting qubit that ignores most electrical noise. Nearly every superconducting chip since uses it. Also 2007: D-Wave in Canada shows a 16-qubit machine of a different kind, an annealer, that settles into a low-energy answer rather than running gates. Whether it beats ordinary computers is still argued. Source: Wikipedia: Transmon - 2011 — First quantum computer sold. Lockheed Martin buys a D-Wave One, 128 qubits, for about ten million dollars. It is an annealer, not a gate machine, and the physics community argues about what it does. Ten years of that argument taught the field how to benchmark. The short version: D-Wave machines are quantum, and no one has shown one beating the best ordinary method on a practical problem. Source: Wikipedia: D-Wave Systems - 2012 — Nobel for handling single particles. Serge Haroche and David Wineland win the Nobel Prize for measuring and controlling single atoms and photons without wrecking them. That is the lab skill quantum computers need. The same year Austin Fowler and others laid out the surface code in a form engineers could build: a checkerboard of qubits where neighbours check each other, tolerating about one error in a hundred. Source: Nobel Prize 2012 - 2016 — A quantum computer on the web. IBM puts a five-qubit chip online for anyone to program. Within a year students and hobbyists had run hundreds of thousands of jobs on it. This is when the machine stopped being a lab instrument and became a thing people could try. Most of what a beginner learns today is learned this way. Source: Wikipedia: IBM Quantum Platform - 2019 — Google's Sycamore. Google's 53-qubit chip does a contrived random-sampling task in 200 seconds that Google says would take a supercomputer 10,000 years. IBM says two and a half days. Either way the gap is real, and the task is useless. Called 'quantum supremacy'. The word and the claim were both argued over. Better ordinary methods later narrowed the gap on this exact task, which is the normal pattern: each claim of advantage moves the target. Source: Nature 574, 505 (2019) - 2020 — Jiuzhang, with light. A team at USTC in Hefei does a different sampling task with photons, and claims a bigger gap than Google's. Jiuzhang is not programmable in the general sense; it does one task. It showed China was in the race with a different technology. Source: Science 370, 1460 (2020) - 2021 — IBM Eagle: 127 qubits. IBM's Eagle chip passes 100 qubits. The qubits are noisy, and the count alone means little, but the count was the headline. The same year USTC's Zuchongzhi 2 (66 superconducting qubits) repeated Google's task with a bigger claimed gap. Source: IBM Research blog - 2022 — Nobel for Bell tests. Alain Aspect, John Clauser and Anton Zeilinger win the Nobel Prize for the experiments that showed entanglement is real and Einstein's hidden layer is not there. Clauser did the first test in 1972 with equipment he built himself; his advisers told him it was a waste of time. IBM's 433-qubit Osprey arrived in November. Source: Nobel Prize 2022 - 2023 — Bigger gets better, a little. Google shows a surface code with 49 qubits errs slightly less than one with 17. It is the first time in a real machine that adding qubits reduced the error instead of adding to it. The gain was small and the paper said so. It mattered because it was the first sign of being under the threshold line from 1997. Source: Nature 614, 676 (2023) - 2023 — 48 logical qubits from atoms. A Harvard, MIT and QuEra team uses 280 atoms held by laser beams to make 48 error-corrected 'logical' qubits and run small programs on them. A logical qubit is a group of physical qubits acting as one reliable qubit. Two days earlier IBM had shown its 1,121-qubit Condor chip and its smaller, cleaner Heron. The field's attention was moving from counts to quality. Source: Nature 626, 58 (2024) - 2024 — Logical qubits that beat their parts. Microsoft and Quantinuum make four logical qubits from 30 trapped ions that err 800 times less often than the raw ions. In August NIST published the first three post-quantum encryption standards (FIPS 203, 204, 205), the replacement locks for the ones Shor's algorithm would pick. Source: Microsoft Azure blog - 2024 — Google Willow: under the line. Google's Willow chip shows the error rate halving each time the code grows from 3×3 to 5×5 to 7×7 qubits. That is the threshold theorem working in hardware. Willow has 105 qubits. The headline claim about a task taking 'ten septillion years' on a supercomputer was the same kind of contrived sampling task as 2019. The error-correction result is the one that matters. Source: Nature 638, 920 (2025) ## Machines ### Superconducting circuits A qubit printed on a chip: a loop of metal with no electrical resistance, cooled so cold it behaves like one big atom. The circuit has energy rungs like an atom's. Microwave pulses move it between the bottom two rungs, and those two are 0 and 1. The transmon design from 2007 is the standard. The chip sits at the bottom of a dilution refrigerator at about 15 thousandths of a degree above absolute zero. Good: Fast gates, tens of billionths of a second. Made with chip-factory methods, so counts grow quickly. Google, IBM and China's USTC all use it, and it is where the error-correction milestones of 2023 to 2025 happened. Bad: Short-lived: a qubit holds its state for around a ten-thousandth of a second. Each qubit can only talk to its neighbours on the chip. Every qubit needs its own wiring into the fridge, which is the wall between hundreds and millions. Biggest: IBM Condor, 1121 qubits (2023-12) Quality: Google Willow: two-qubit gate error about 0.15%; error-corrected memory below threshold (2024-12) ### Trapped ions Single charged atoms held in mid-air by electric fields, in a vacuum, with lasers doing the work. An ion, an atom missing one electron, is held by oscillating electric fields in a trap the size of a fingernail. Two of its energy levels are 0 and 1. Laser pulses, or in newer designs microwave signals through the trap's own electrodes, flip and entangle them. Ions in a chain all feel each other's charge, so any ion can be entangled with any other. Good: The cleanest qubits there are: gate errors below one in ten thousand, and a state that lasts seconds to minutes. Every ion is identical because nature made it. Any-to-any connections. Bad: Slow: a two-qubit gate takes millionths of a second, a thousand times slower than a superconducting chip. Chains get unwieldy past a few dozen ions, so big machines shuttle ions between zones, which costs time. Biggest: Quantinuum Helios, 98 qubits (2025-11) Quality: Oxford single-ion gate: one error in 6.7 million single-qubit operations (2025-06) ### Neutral atoms Ordinary uncharged atoms, hundreds or thousands of them, each pinned in a spot of laser light like a bead in tweezers. A laser is split into a grid of focused spots, and each spot traps one atom. The atoms' electron energy levels are 0 and 1. To entangle two, a laser kicks them into a hugely swollen 'Rydberg' state, in which neighbouring atoms shove each other and so become linked. The tweezers can move atoms around during a computation, so the wiring is whatever you want it to be. Good: Counts scale fast: 6,100 atoms trapped at Caltech in 2025. Atoms can be moved, so error-correcting codes that need odd connections are easy to lay out. This is where the largest logical-qubit demonstrations have been, at Harvard and QuEra. Bad: Atoms fall out of the tweezers and have to be replaced, which until 2025 meant stopping the machine. Gates are slower than superconducting ones and the Rydberg step is delicate. Readout is slow: a camera photographs the array. Biggest: Caltech tweezer array, 6100 qubits (2025-09) Quality: Harvard/MIT/QuEra 448-atom processor: all the pieces of fault tolerance on one machine, errors falling as the code grew (2025-11) ### Photons Particles of light running through channels etched in glass or silicon, with the computation done by how they split, merge and get detected. A qubit is one photon, and 0 or 1 is which of two paths it is on, or which way it is polarised. Beam splitters and phase shifters do the one-qubit turns. Two-qubit gates are the hard part: photons ignore each other, so the trick is to make the gate happen with a measurement and try again when it fails. The 2001 KLM paper showed this can work. Good: Room temperature for the optics (the detectors are cooled). Photons do not decohere in flight and travel down ordinary fibre, so linking modules is natural. Chips come off standard semiconductor lines. Bad: Photons get lost, and a lost photon is an error you cannot fix by waiting. Gates only work some of the time, so the scheme needs enormous numbers of photons and detectors per useful qubit. No photonic machine has yet run a general program of any size; the headline results are sampling tasks. Biggest: USTC Jiuzhang 4.0, 3050 qubits (2026-05) Quality: PsiQuantum Omega chipset: chips made on a GlobalFoundries production line (2025-02) ### Spins in silicon A single electron, or the nucleus of a single atom, sitting in a silicon chip made the same way as the ones in phones. An electron has a spin, a tiny magnet that points up or down, and that is the qubit. It is held in a dot a few billionths of a metre across, and microwaves flip it. Bruce Kane's 1998 idea used single phosphorus atoms in silicon; the newer designs use electrons in tiny transistor-like structures. Good: The smallest qubits there are, and made with the tools of the chip industry, so in principle millions fit on one chip. Runs at about 1 kelvin, warmer than superconducting qubits, which makes the cooling far easier. Bad: Counts are small so far, a dozen or so on one chip. Every dot is slightly different, so each qubit needs tuning. Wiring millions of dots is an unsolved problem, though the industry has a head start. Biggest: Intel Tunnel Falls, 12 qubits (2023-06) Quality: UNSW nuclear spins: two-qubit gate errors below 1% and single-qubit coherence of seconds have been reported (2022) ### Topological qubits A qubit stored in the shape of how particles are arranged along a wire, so that local noise cannot see it. Nobody has shown one working for sure. The idea from Kitaev in 1997: certain exotic particles, Majorana modes, would appear at the ends of a superconducting nanowire, and information shared between the two ends could only be disturbed by something acting on both ends at once. If it works, error correction becomes far cheaper. Good: In principle, a qubit that ignores most noise by construction, so a useful machine needs far fewer physical qubits. Bad: Whether the Majorana modes exist in the devices is disputed. Microsoft's Majorana 1 chip of February 2025 was announced with a Nature paper that did not itself show them, and a peer-reviewed challenge in June 2026 found errors in the test Microsoft used. As of 2026 no topological qubit has run a gate. Biggest: Microsoft Majorana 1, 8 qubits (2025-02) Quality: Majorana 2: parity lifetimes over 20 seconds, per a company paper (2026-06) ### Annealers A different kind of machine: thousands of superconducting qubits that settle into a low-energy arrangement, the way a hot metal cools into its shape. It answers 'what is the cheapest arrangement' questions and cannot run general programs. You write your problem as a landscape of hills and valleys and the machine looks for the lowest valley. It starts every qubit in superposition and slowly turns on the landscape, and quantum tunnelling lets it slip through hills a hot metal would have to climb. There are no gates; you cannot run Shor's or Grover's method on it. Good: Big counts and a commercial product since 2011. Some optimisation and physics-simulation tasks fit it well. Bad: No proof it beats the best ordinary methods on a practical problem. The March 2025 'beyond classical' claim was reproduced on ordinary computers in May 2026. It is not what most of this site is about. Biggest: D-Wave Advantage2, 4400 qubits (2025-05) Quality: Advantage2: the 2025 Science simulation claim, reproduced classically in 2026 (2026-05) ## Developments since 2025 - 2025-01-20 — Alice & Bob: The Paris start-up raised 100 million euros to develop 'cat qubits', a superconducting qubit built so one of the two main kinds of error is suppressed in the hardware, so fewer qubits are needed for error correction. Europe's largest quantum hardware round at the time, and money behind an alternative to the surface code used by Google and IBM. Source: HPCwire - 2025-02-11 — QuEra Computing: The neutral-atom company closed a 230 million dollar round with Google and SoftBank as new investors; NVIDIA's venture arm joined in September 2025. Backing for neutral atoms, the hardware family that went on to produce the year's largest error-correction demonstrations. Source: Bloomberg - 2025-02-19 — Microsoft: Microsoft announced Majorana 1, a chip it said holds eight 'topological' qubits built from a new indium-arsenide and aluminium material, alongside a Nature paper on reading such devices out. The first hardware claim for a qubit type that would in principle need far less error correction. Nature's editors noted the paper itself did not show evidence of the Majorana states the chip relies on. Source: Microsoft Azure Quantum blog - 2025-02-26 — PsiQuantum: PsiQuantum described Omega, a set of light-based (photonic) quantum chips made on a standard GlobalFoundries production line, in a Nature paper. A quantum chipset came off a conventional semiconductor fab rather than a laboratory. Source: PsiQuantum - 2025-03-03 — University of Science and Technology of China: The team published Zuchongzhi 3.0, a 105-qubit superconducting processor, and a random-circuit sampling benchmark it estimates would take the Frontier supercomputer billions of years. China's superconducting hardware at roughly the level of Google's Willow on the same benchmark. Source: Physical Review Letters - 2025-03-11 — NIST: NIST chose HQC, a code-based encryption scheme, as a fifth post-quantum standard to back up the lattice-based ML-KEM adopted in FIPS 203 in 2024, with a draft promised in about a year and a final version by 2027. A second, mathematically different lock for the internet in case the main one is picked. Source: NIST - 2025-03-12 — D-Wave: D-Wave published in Science a simulation of magnetic materials on its Advantage2 annealer that it said would take a supercomputer nearly a million years; other groups said ordinary methods could match parts of it. The first 'beyond classical' claim on a problem with a practical shape. The dispute it started was largely settled against it in May 2026. Source: D-Wave - 2025-03-21 — Henry Legg (St Andrews) and others: Physicists including Legg, Eun-Ah Kim and Javad Shabani said Microsoft's data were too noisy to show topological behaviour and that its 'topological gap protocol' test could give false positives. Majorana 1 became the most contested hardware claim of the period, setting up the formal Nature challenge of 2026. Source: Physics (APS) - 2025-03-26 — Quantinuum, JPMorganChase, Argonne, Oak Ridge, UT Austin: Using a 56-qubit trapped-ion machine, the team generated random numbers and used supercomputers to certify they were fresh and random, published in Nature. The first published task where a quantum computer produced a result an ordinary machine could check but not fake. Source: Nature - 2025-05-21 — Google Quantum AI (Craig Gidney): A preprint estimated that a future error-corrected computer with under one million physical qubits could break RSA-2048 encryption in under a week, down from a 2019 estimate of 20 million. The assumed timeline for the threat to today's encryption got shorter, and migration planning sped up. Source: arXiv - 2025-06-09 — IonQ: IonQ agreed to buy Oxford Ionics for 1.075 billion dollars, mostly in stock; the deal closed on 16 September 2025. The two main trapped-ion companies combined, and IonQ got Oxford Ionics' laser-free electronic qubit control. Source: IonQ - 2025-06-10 — IBM: IBM set out a plan to build Starling, a 200-logical-qubit error-corrected computer, by 2029, using qLDPC codes it says need about a tenth of the physical qubits of the surface code; the steps named were Loon (2025), Kookaburra (2026) and Cockatoo (2027). The first dated, part-by-part roadmap to a large fault-tolerant machine from a major vendor. Source: IBM Newsroom - 2025-06-12 — University of Oxford: Oxford physicists ran a single-qubit operation on a trapped calcium ion with one error in 6.7 million attempts, published in Physical Review Letters. The most accurate qubit operation recorded; the control electronics, not the physics, set the limit. Source: University of Oxford - 2025-06-19 — Microsoft: Microsoft published a family of four-dimensional error-correcting codes it says can cut error rates a thousandfold using five to six times fewer physical qubits than the surface code, for hardware where any qubit can talk to any other. A cheaper error-correction recipe for ion, atom and photonic machines than the one designed for chips. Source: Microsoft Azure Quantum blog - 2025-07-17 — Atom Computing and Microsoft: Denmark's new QuNorth venture ordered Magne, a neutral-atom machine with 1,225 physical and 50 logical (error-corrected) qubits, to be built in Copenhagen and ready around the start of 2027. The first purchase of a computer specified in logical rather than raw qubits. Source: Quantum Computing Report - 2025-09-04 — Quantinuum (Honeywell): Quantinuum raised 600 million dollars at a 10 billion dollar valuation, with NVIDIA's venture arm and Quanta among new investors. The highest valuation for a private quantum company at the time; it paid for the Helios launch. Source: Honeywell - 2025-09-10 — PsiQuantum: PsiQuantum raised 1 billion dollars at a 7 billion dollar valuation, led by BlackRock with NVIDIA participating, to build data-centre-scale photonic machines in Brisbane and Chicago. The largest single private round in the field; it funds the first two purpose-built quantum computing sites. Source: PsiQuantum - 2025-09-17 — Harvard, MIT and QuEra: A neutral-atom system of more than 3,000 qubits ran continuously for over two hours, with lost atoms replaced on the fly by conveyor-belt lasers at up to 300,000 atoms a second, published in Nature. Atom loss had forced these machines to stop and reload; continuous operation removes that limit on run length. Source: Phys.org - 2025-09-24 — Caltech: A Caltech group trapped 6,100 caesium atoms in laser tweezers, held them in superposition for about 13 seconds and controlled single atoms with 99.98 percent accuracy, published in Nature. The largest qubit array assembled, and size did not cost quality. The atoms were not yet entangled. Source: Caltech - 2025-09-25 — Alice & Bob: The company reported its cat qubits resisting bit-flip errors for 33 to 60 minutes, up from about seven minutes in 2024. Past the 13 minutes its 2030 machine design needs, and a sign these qubits shrug off cosmic-ray hits. Source: Alice & Bob - 2025-10-07 — Royal Swedish Academy of Sciences: John Clarke, Michel Devoret and John Martinis won the Nobel Prize in Physics for 1984–85 experiments showing that a superconducting circuit big enough to hold in the hand tunnels and has discrete energy levels like an atom. Those experiments are the physical basis of the superconducting qubits used by Google, IBM and others. Source: NobelPrize.org - 2025-10-21 — IonQ (Oxford Ionics team): IonQ reported a two-qubit operation with better than 99.99 percent accuracy on trapped ions using electronic control, without first cooling the ions to their lowest motional state. Past the 'four nines' level that error-correction designs assume, and beyond Oxford Ionics' 2024 record of 99.97 percent. Source: arXiv - 2025-10-22 — Google Quantum AI: Google's Willow chip ran an algorithm called Quantum Echoes that measures how a disturbance spreads through a quantum system, about 13,000 times faster than the best ordinary method, published in Nature. Unlike the earlier random-sampling benchmarks, the answer is a physical quantity another machine can check. Google calls it the first verifiable quantum advantage. Source: Google Research - 2025-11-05 — Quantinuum: Quantinuum launched Helios, a 98-qubit trapped-ion computer with two-qubit accuracy of 99.921 percent and a new programming language, Guppy, and reported a materials simulation it says ordinary methods cannot match. The most accurate commercial machine on offer, and the first designed for real-time error correction. Source: Quantinuum - 2025-11-06 — DARPA: DARPA moved 11 companies (Atom Computing, Diraq, IBM, IonQ, Nord Quantique, Photonic, Quantinuum, Quantum Motion, QuEra, Silicon Quantum Computing, Xanadu) to Stage B of its Quantum Benchmarking Initiative, a year-long review of their plans for a useful machine by 2033. The first independent government screening of which hardware approaches are credible. Google, Microsoft, PsiQuantum, Rigetti and D-Wave were not on the list. Source: DARPA - 2025-11-12 — IBM: IBM unveiled Nighthawk, a 120-qubit chip with a square grid layout supporting circuits of about 5,000 two-qubit operations, and Loon, a test chip carrying every hardware element its qLDPC error-correction design needs; it also joined an open 'quantum advantage tracker'. Nighthawk is the machine IBM expects to show community-verified advantage on by the end of 2026; Loon is the first physical piece of the Starling plan. Source: IBM Newsroom - 2025-11-12 — Harvard, MIT and QuEra: A 448-atom neutral-atom processor combined every ingredient of an error-corrected computer (entangling, logical operations, 'magic' states for universal computing, and error removal) and showed errors falling as the code grew, published in Nature. Lead author Dolev Bluvstein called it the first architecture that is 'conceptually scalable'; press reports describe 96 logical qubits on the device. Source: Harvard Gazette - 2026-01-07 — D-Wave: D-Wave agreed to buy Quantum Circuits Inc., a Yale spin-out building error-corrected superconducting gate-model machines, for about 550 million dollars; the deal closed 20 January 2026. The annealing company now has a second hardware line and a gate-model roadmap. Source: D-Wave - 2026-01-26 — IonQ: IonQ agreed to buy the chip foundry SkyWater Technology for about 1.8 billion dollars in cash and stock; the purchase closed on 31 July 2026 after FTC clearance. A quantum company with its own US chip fab, shortening the loop between design and hardware. Source: IonQ - 2026-01-27 — University of Chicago, Stanford, MIT, Innsbruck, Delft: A Science paper led by David Awschalom argued quantum technology has reached the point the transistor reached in the late 1940s: the physics works and the remaining problems are engineering, manufacturing and modular design. It framed 2026 as the start of a scaling era rather than a discovery era. Source: ScienceDaily (unconfirmed) - 2026-02 — Iceberg Quantum: A Sydney start-up published an architecture using qLDPC codes that it estimates could break RSA-2048 with fewer than 100,000 physical qubits, about a tenth of Gidney's 2025 figure. The resource bar for the quantum threat moved down again, ahead of the hardware. Source: The Quantum Insider (unconfirmed) - 2026-02-17 — Infleqtion: The neutral-atom company Infleqtion listed on the NYSE as INFQ through a merger with Churchill Capital Corp X, receiving over 550 million dollars. The first neutral-atom hardware company on a public market. Source: Quantum Computing Report - 2026-03-04 — Pasqal: Pasqal raised at least 340 million euros and agreed to merge with Bleichroeder Acquisition Corp. II for a Nasdaq listing at a 2 billion dollar valuation. Europe's leading neutral-atom company becomes publicly traded, with a Paris listing to follow. Source: Pasqal - 2026-03-10 — DARPA: DARPA opened a new Stage A round of the Quantum Benchmarking Initiative for companies not yet in the programme, noting 11 firms in Stage B and two in Stage C; a new director said it 'now seems likely' someone builds a utility-scale machine by 2033. The government's assessment shifted from whether to who. Source: DARPA - 2026-03-24 — Google Quantum AI: Google added a neutral-atom hardware programme, led by Adam Kaufman, alongside its superconducting Willow line, saying the two are complementary: one for deep circuits, the other for large qubit counts. The company behind the most-cited superconducting results is now hedging across two hardware families. Source: Google (The Keyword) - 2026-03-27 — Xanadu: The photonic company Xanadu began trading on Nasdaq and the TSX as XNDU after a 3.1 billion dollar SPAC merger, with about 262 million dollars in net proceeds plus Canadian government investment. The first publicly listed photonic quantum company. Source: BNN Bloomberg - 2026-04-14 — Pasqal: Pasqal reported loading 1,024 atoms into a register with no gaps (under 0.5 percent defects), following a 506-atom register in April 2025. A full, gap-free array of over 1,000 atoms is the starting condition for running error-correction codes on that many qubits. Source: Pasqal - 2026-05-13 — University of Science and Technology of China: Jiuzhang 4.0, a programmable light-based machine, sent 1,024 squeezed light pulses through an 8,176-path circuit and detected up to 3,050 photons in one run, published in Nature; the team says the hardest samples would take a supercomputer over 10^42 years. It answers the ordinary-computer methods that had undermined the earlier Jiuzhang results, and is the largest photonic sampling experiment to date. Source: Chinese Academy of Sciences - 2026-05-21 — Flatiron Institute and Boston University: A new tensor-network method reproduced D-Wave's March 2025 'beyond classical' magnetic simulation on ordinary computers, including a laptop, published in Science. It overturns the D-Wave claim. Ordinary methods keep moving the line that quantum hardware has to beat. Source: Simons Foundation - 2026-06-02 — Microsoft: Microsoft reported Majorana 2, swapping aluminium for lead in its device stack, with a doubled protective energy gap and 'parity lifetimes' over 20 seconds, up from milliseconds, in a company technical paper rather than a peer-reviewed journal. A large measured improvement. Critics said it does not answer whether the devices host Majorana states at all. Source: The Quantum Insider - 2026-06-04 — Quantinuum: Quantinuum listed on Nasdaq as QNT, selling 28 million shares at 60 dollars to raise 1.68 billion dollars; Honeywell kept about 48 percent of the voting power. The largest quantum IPO to date, valuing the company at around 14 to 15 billion dollars. Source: CNBC - 2026-06-23 — US Department of Energy: DOE announced Quantum Genesis, a plan for a fault-tolerant, scientifically useful quantum computer with 'low hundreds' of logical qubits by 2028, plus a National Quantum Supercomputing User Facility. A federal deadline a year ahead of IBM's and Quantinuum's own 2029 targets. Source: US Department of Energy - 2026-06-24 — Henry Legg, University of St Andrews: Nature published a peer-reviewed 'Matters Arising' challenge finding two coding errors in Microsoft's topological gap protocol, including code that showed only the single most favourable data region; Microsoft called the bugs minor and stood by its results. The formal, journal-level version of the dispute that began in 2025. The Majorana claim stays unresolved. Source: University of St Andrews - 2026-07-20 — Google Quantum AI: Google published in Nature a reinforcement-learning system that retunes Willow's control settings during error correction instead of pausing to recalibrate, making logical error rates about 3.5 times more stable and roughly 20 percent lower. Keeping an error-corrected machine tuned for days or weeks without a person recalibrating it is a requirement for long computations. Source: The Next Platform - 2026-07-31 — IonQ: IonQ completed its 1.8 billion dollar purchase of SkyWater after US Federal Trade Commission clearance. The first quantum company to own its own semiconductor fab. Source: Quantum Computing Report - 2026-09-17 — US Department of Energy: DOE opened the Quantum Genesis Q Competition: up to 215 million dollars, up to ten teams, a 10-logical-qubit prototype within about a year and a 100-logical-qubit fault-tolerant machine by autumn 2028, with a 100 million dollar pool for finishers. The June target became a funded contest with dated deliverables. Source: The Register ## Words - Amplitude: The number underneath a quantum probability. It can be positive, negative or point in any direction; the chance of an outcome is its size squared. Amplitudes can cancel each other; chances cannot. - Annealer: A quantum machine that finds a low-energy arrangement instead of running a program step by step. D-Wave builds them. It cannot run Shor's or Grover's methods. - Bell test: An experiment that tells entangled particles apart from particles that secretly decided in advance. Every one run since 1972 has come out on the quantum side. 2022 Nobel Prize. - Bit: One yes or no. The unit of ordinary computing. A coin on the table. - Bloch sphere: The picture of one qubit as an arrow from the centre of a ball: up is 0, down is 1, anywhere else is a mix. - Circuit: A quantum program drawn as wires (one per qubit) and boxes (gates), read left to right. - CNOT: The two-qubit gate that flips the second qubit if the first is 1. With an H gate it makes an entangled pair. - Coherence time: How long a qubit stays in superposition before the outside world wears it down. Written T1 and T2. Millionths of a second for chips, seconds for ions. - Decoherence: The wearing-down. Anything that touches a qubit, heat, stray light, a vibration, counts as a look, and the superposition leaks away. - Entanglement: Two or more qubits sharing one state, so measuring one fixes what the others will say, at any distance, with neither having decided in advance. - Error correction: Storing one qubit's worth of information across many qubits and checking the relationships between them, without reading the information, so errors can be found and undone. - Fault tolerance: Error correction that works even though the correcting itself makes errors. The goal; a machine that has it can run as long as you like. - Fidelity: How close a gate or a state is to the intended one, written as a percentage. 99.9% means one error in a thousand. Error-correction plans want 99.99% or better. - Gate: One step of a quantum program: a turn applied to one or two qubits. - Grover's algorithm: Finding a marked item in an unsorted list in about the square root of the number of looks a plain computer needs. - Hadamard gate (H): The gate that tips a 0 or 1 into an even mix. It puts the coin in the air. - Interference: Waves adding where they agree and cancelling where they disagree. The engine of every quantum speed-up. - Logical qubit: A reliable qubit made out of many unreliable physical ones by error correction. The number that counts. - Measurement: Reading a qubit. It lands on 0 or 1 with the odds its state gives, and the superposition is gone. - NISQ: 'Noisy intermediate-scale quantum': the current era of machines with tens to hundreds of qubits and no error correction. John Preskill's term, 2018. - No-cloning: An unknown quantum state cannot be copied. Proved in 1982. It rules out backups. - Phase: Which way round the equator a qubit's arrow points. Measurement cannot see it; interference is made of it. - Physical qubit: One actual qubit in the hardware, noisy. Hundreds to thousands of them make one logical qubit. - Post-quantum cryptography: New locks for the internet that do not rest on factoring, so Shor's algorithm does not open them. NIST published the first standards in August 2024. - qLDPC code: A newer family of error-correcting codes that needs far fewer physical qubits per logical one than the surface code, in exchange for connections between qubits that are not next to each other. IBM's 2029 plan rests on one. - Quantum advantage: A quantum computer doing a task faster or better than the best ordinary method. 'Supremacy' was the earlier word. Each claim has been followed by a better ordinary method, so the bar moves. - Qubit: A quantum bit: a two-level system that can be in a mix of 0 and 1 until measured. A coin in the air. - Rydberg state: An atom with one electron kicked far out, so the atom swells and shoves its neighbours. Neutral-atom machines use it to entangle. - Shor's algorithm: Finding the prime factors of a big number by finding a rhythm with a quantum Fourier transform. It would break RSA. No real key has been broken. - Superconducting qubit: A qubit printed on a chip as a resistance-free circuit, cooled to a hundredth of a degree above absolute zero. Google's and IBM's kind. - Superposition: Being in a mix of 0 and 1 at once, with a lean. Not 'both' and not 'unknown'; a third thing. - Surface code: The error-correcting code most chip-based machines plan on: a checkerboard where checker qubits keep asking their four neighbours whether they still agree. - Threshold: The error rate, about one in a hundred, below which a bigger error-correcting code gets better instead of worse. Crossed in hardware in December 2024. - Transmon: The 2007 design of superconducting qubit that most chips use. - Trapped ion: A single charged atom held in mid-air by electric fields and worked with lasers. The cleanest kind of qubit. Quantinuum's and IonQ's kind.