How Quantum Computers Work: A Beginner’s Guide to Quantum Computing in 2026

Science & A.I. · Quantum computing

For thirty years quantum computing had a problem that looked like it might be fatal. Adding more qubits to an error-correcting scheme made the errors worse, not better — the extra hardware introduced more noise than the correction code could remove.

That reversed. Google’s Willow processor demonstrated what the field calls operating below threshold — each increase in the size of the error-correcting code cut the logical error rate roughly in half, exactly as surface-code theory predicts. The result was published in Nature.

This is the single most important thing to understand about the field, and it is rarely explained. A quantum computer is not waiting on more qubits. It was waiting on proof that error correction could ever win the race against noise — and that proof now exists. Everything below explains how the machine works and why that threshold mattered so much.

You have heard the phrase “quantum computing” a hundred times. You have probably never had it explained in a way that actually made sense. This is an attempt to fix that — no equations, no hand-waving, just the real ideas.

Companies announce quantum breakthroughs. Governments pour billions into the field. Physicists call it the biggest shift in computing since the transistor. Yet most explanations either assume a physics degree or collapse into a metaphor so vague it teaches nothing.

The truth sits in between, and it is genuinely graspable. A quantum computer is not simply a faster version of your laptop. It is a fundamentally different kind of machine that exploits the strange rules of the very small to solve certain problems in ways ordinary computers never could. Let us build the idea up, one step at a time.

No prior physics is assumed. By the end you should understand what a qubit is, the three ideas that give a quantum computer its power, what it can and cannot do, and why building one is so fiendishly difficult — enough to see through the hype in either direction. It also covers what Google, IBM and Microsoft have actually achieved, and the July 2026 advantage claim that a classical team answered in 37 minutes.

The threshold result described above has changed what this field works on, and the literature shows it. Counting arXiv titles on 1 October 2026 gave 998 papers with “quantum error correction” in the title and 377 on the surface code specifically.

Set that against the marketing vocabulary. The same archive holds 71 papers titled “quantum supremacy” and 368 on quantum advantage. Correcting errors is now more than twice the research subject that claiming a win is.

That is what a field looks like once it has stopped trying to prove a point and started trying to build a machine.

Where the idea came from

Quantum computing is not a recent invention dreamed up by a start-up. Its roots reach back more than forty years, to a simple observation by one of the great physicists of the twentieth century.

In the early 1980s Richard Feynman pointed out that ordinary computers are hopeless at simulating quantum systems, because the number of possibilities explodes beyond any classical machine’s reach. His suggestion was radical: if you want to simulate quantum physics efficiently, build a computer that is itself quantum.

A few years later, in 1985, the physicist David Deutsch worked out what a universal quantum computer would look like in principle, giving the idea a rigorous theoretical footing. The field remained largely abstract until 1994, when Peter Shor’s factoring algorithm showed a quantum computer could do something of real-world consequence.

That result electrified the field, because it linked quantum computing to the security of digital communication. What had been a curiosity for theoretical physicists suddenly mattered to governments and industry, and the long, hard effort to build real machines began in earnest.

Start with the ordinary computer

Every computer you have ever used — phone, laptop, games console, the servers behind every website — runs on bits. A bit is the smallest unit of information, and it can hold exactly one of two values: 0 or 1. Everything else is built from that simple foundation.

Inside the machine, a bit is a tiny switch that is either off or on. String enough of them together and you can represent any number, any letter, any image or sound. A processor manipulates these bits billions of times a second by following logical rules, and that relentless shuffling of zeros and ones is, quite literally, all a computer does.

This design is astonishingly powerful and has reshaped the world. But it has a built-in limitation. A classical computer examines possibilities one at a time. For some problems the number of possibilities grows so fast that no classical machine, however quick, could ever check them all before the universe ended. That is the wall quantum computing is designed to climb.

Consider chemistry. The amount of information needed to describe the electrons in a molecule exactly roughly doubles with every extra electron orbital the calculation includes, so exact simulation of anything but small molecules quickly outruns any classical computer. Chemists rely on clever approximations instead, and those approximations are weakest exactly where electrons interact most strongly. No amount of extra processing power fixes an exponential; the architecture itself is the constraint.

The qubit: a bit that can be both at once

A quantum computer replaces the bit with a quantum bit, or qubit. Like a bit, a qubit can be 0 or 1. Unlike a bit, it can also exist in a blend of both at the same time — a state called superposition. This is the first and most important idea in all of quantum computing.

A common metaphor is a spinning coin. While a normal coin is either heads or tails, a spinning coin is, in a sense, both until it lands. A qubit in superposition is genuinely 0 and 1 together, in defined proportions, right up until you measure it — at which point it settles on a single definite answer.

Here is where the power hides. Two qubits in superposition can represent four combinations at once; three can represent eight; and each qubit you add doubles the number. A few hundred qubits could, in principle, represent more combinations than there are atoms in the observable universe. That explosive scaling is what makes the idea so tantalising.

There is a crucial catch, and beginners are almost always misled on this point. A quantum computer does not simply try every possibility at once and hand you the right one. When you measure the qubits, the superposition collapses to a single random outcome. The whole art of quantum computing is arranging things so the answer you want is the one most likely to appear.

Entanglement: the second quantum trick

The second key idea is entanglement. When two qubits become entangled, their fates are linked: measuring one instantly tells you something about the other, no matter how the two are arranged. They can no longer be described independently, only as a single joined system.

Albert Einstein famously distrusted this, calling it “spooky action at a distance”. Yet decades of experiments have confirmed that entanglement is real, and it is central to how a quantum computer works. It lets the qubits act in concert rather than as a crowd of separate switches.

Entanglement is what allows a quantum computer’s power to grow with every qubit added. Without it, a collection of qubits would behave like many small quantum systems side by side. With it, they form one vast, interconnected state whose possibilities intertwine — the raw material a quantum algorithm shapes into an answer.

Our guide to quantum entanglement explores the phenomenon, and the experiments that confirmed it, in depth.

Interference: how a quantum computer finds the answer

If measurement gives a random result, how does a quantum computer ever compute anything useful? The answer is interference, the third essential idea, and it is what turns superposition and entanglement into a real tool.

Quantum states behave like waves, and waves can add together or cancel out. A quantum algorithm is a carefully choreographed sequence of operations that makes the wrong answers cancel each other and the right answer reinforce itself. By the time you measure, the correct outcome has been made overwhelmingly the most probable.

Think of it as sculpting probability. The machine begins with every possibility equally in play, then uses interference to quietly delete the ones you do not want and amplify the one you do. Designing that choreography, for a specific problem, is exactly what writing a quantum algorithm means.

What quantum computers are actually good at

This is the most misunderstood part of the whole subject. A quantum computer is not a faster computer for everyday tasks. It will not speed up your email, your spreadsheets or your games. For the overwhelming majority of jobs, a classical computer is as good or better, and far cheaper.

Quantum computers shine only on a specific class of problems where that explosive scaling can be harnessed. The most famous is factoring very large numbers. In 1994 the mathematician Peter Shor devised an algorithm showing a quantum computer could do this far faster than any known classical method — which matters because that difficulty is what secures much of today’s online encryption.

A second promising area is simulating nature itself. Molecules, materials and chemical reactions are quantum systems, and a classical computer struggles to model them accurately. A quantum computer speaks their native language, which could accelerate the design of new drugs, catalysts and materials. Searching and certain optimisation problems round out the short list of genuine quantum advantages.

The honest summary is that quantum computers are specialised instruments, not general replacements. They promise to crack a handful of problems that are effectively impossible for classical machines, while leaving everything else to the computers we already have.

A useful example of the more modest kind of advantage is Grover’s algorithm, devised in 1996. It speeds up the task of searching through an unsorted collection of possibilities. The gain is real but limited — a square-root improvement rather than the dramatic leap Shor’s algorithm offers — and it illustrates that quantum advantages come in different sizes, not all of them world-changing.

This nuance matters because the hype often flattens it. A quantum computer is not a magic box that solves everything faster. It is a machine with a specific mathematical profile, brilliant at a few things, ordinary or useless at most others. Understanding which is which is most of what separates realistic expectations from science fiction.

Where quantum computing could matter first

Cryptography and cybersecurity. The most urgent near-term implication is cryptographic. Much of internet security rests on problems, such as factoring very large numbers, that are infeasible for classical computers; a large enough quantum computer running Shor’s algorithm could solve them. How large keeps shrinking on paper, as the section on error correction below explains, and no machine is close. Even so, the US National Institute of Standards and Technology published its first three post-quantum encryption standards on 13 August 2024 and urges organisations to start switching now, partly because data harvested today could be decrypted later, a threat known as “harvest now, decrypt later”. Its draft transition plan proposes deprecating RSA and elliptic-curve methods after 2030 and disallowing them after 2035.

Medicine and materials. Designing a medicine means predicting how a candidate molecule will behave and bind, and the most accurate predictions depend on the quantum behaviour of its electrons. Chemistry is still the application that justifies much of the investment, for the reason Feynman gave: molecules are quantum systems, and the shortcuts classical chemists rely on are weakest where electrons interact most strongly, as they do in many catalysts. The honest record is short. The closest real demonstration is Google’s 2025 molecular experiment, which its authors say is not yet beyond classical, and Boston Consulting Group concluded in July 2024 that quantum computing then provided no tangible advantage over classical computing in either commercial or scientific applications. The same logic applies to materials science — designing new superconductors, batteries and catalysts — where a material’s properties are set by exactly the quantum electron behaviour that classical computers struggle to simulate at scale.

Climate and energy. Quantum chemistry simulations could speed the design of catalysts for carbon capture, more efficient solar cells, and better electrolysers for green hydrogen. In many clean-energy technologies the bottleneck is not funding but a lack of precise understanding of the quantum chemistry involved — exactly what quantum computers are built to provide.

Finance and logistics. Banks and logistics companies are among the earliest commercial explorers, drawn by problems that are essentially giant optimisations — balancing investment portfolios, pricing complex risk, or routing fleets through millions of possible combinations. Quantum approaches to these optimisation and Monte Carlo problems could, in principle, reach better answers faster. No such advantage has yet been shown on a real portfolio or delivery network.

How you actually build one

A qubit needs to be a real physical object that can hold a quantum state, and several very different technologies are competing to be the best one. There is no settled winner yet, and each approach makes its own trade-offs.

The most developed approach uses superconducting circuits, tiny loops of metal cooled until they conduct electricity with no resistance. These are the qubits favoured by companies such as IBM and Google. The foundational physics behind them was honoured with the 2025 Nobel Prize in Physics, awarded for showing that quantum effects can appear in a circuit large enough to hold.

Trapped-ion qubits, used by IonQ and Quantinuum, hold individual charged atoms in electromagnetic fields and manipulate them with lasers, trading speed for exceptional stability.

Newer approaches are gaining ground. Neutral-atom machines arrange atoms in reconfigurable grids held by “optical tweezers.” Photonic designs encode information in particles of light. And Microsoft’s topological qubits take the most radical path of all, storing information in the collective geometry of an exotic quantum state rather than in any single particle. Each design balances speed, stability, and scalability differently, and no one yet knows which will win — or whether several will coexist.

One feature is nearly universal: cold. Superconducting machines operate a tiny fraction of a degree above absolute zero; IBM’s newest cryogenic modules run below 15 millikelvin, which the company describes as more than 180 times colder than deep space. Warmth is a form of noise, and noise is the sworn enemy of a quantum state, which brings us to the field’s central difficulty.

The hard part: decoherence and errors

Quantum states are exquisitely fragile. The faintest vibration, stray heat or electromagnetic whisper can disturb a qubit and scramble the information it holds. This collapse of the delicate quantum state is called decoherence, and it is the reason quantum computers are so hard to build.

A qubit may hold its state for only a tiny fraction of a second before the outside world intrudes. Every operation must be completed within that fleeting window, and each operation itself carries a chance of error. Errors accumulate quickly, and left unchecked they drown any useful computation in noise.

The solution is quantum error correction, which spreads the information of one reliable “logical” qubit across many physical ones, so errors can be caught and fixed without spoiling the calculation. The cost is steep: a single logical qubit may require many physical qubits to protect it, which is why building a genuinely useful machine demands so many.

Overcoming decoherence at scale is the defining engineering challenge of quantum computing. It is not a question of whether the physics works — it does — but of whether enough fragile qubits can be made to cooperate reliably for long enough to matter.

The Threshold That Changed Everything

Almost every introduction to quantum computing counts qubits, as though the field were waiting for a big enough number. That is not what it was waiting for.

Qubits are fragile in the way described above, so quantum error correction spreads the information of one reliable logical qubit across many noisy physical ones. In the surface code — the leading scheme — the physical qubits are arranged in a grid, and the grid’s width is called the code distance. Theory says that increasing the distance should suppress errors exponentially, provided the underlying hardware is good enough.

That proviso is the threshold, and for three decades no superconducting device had met it. Real machines showed the opposite behaviour: enlarge the code, and the logical error rate got worse, because each additional physical qubit brought more noise than the code could remove. The scheme was mathematically sound and practically backwards. If that had proved fundamental, large-scale quantum computing would have been impossible regardless of investment.

Google’s Willow processor broke that pattern. Stepping the surface code up in distance reduced the logical error rate by roughly a factor of two at each step — the behaviour theory predicted and hardware had never delivered. The result, published in Nature, is what the field means by going below threshold. It does not make a useful quantum computer exist. It establishes that building one is an engineering problem rather than a physics obstacle.

The numbers, published in Nature in 2025, are worth having. On a distance-7 code spread over 101 qubits, Willow’s protected qubit made an error in 0.143 per cent of correction cycles, and each step up in code size cut the error rate by a factor of 2.14. The protected qubit also outlived the best individual physical qubit on the chip by a factor of 2.4.

The engineering that remains is formidable, and honesty about it matters. How many physical qubits it takes to protect one logical qubit depends on the code and on how reliable the result must be. In one IBM analysis, keeping 12 logical qubits safe for about a million rounds of checks would take nearly 3,000 physical qubits with the standard surface code, roughly 250 each, while a newer code managed it with 288 in total. Useful algorithms need many logical qubits working together for a long time, and the totals add up quickly. In May 2025 Craig Gidney estimated that breaking a 2048-bit RSA key would take a machine with just under a million noisy qubits running for under a week, down from 20 million in a 2019 estimate he co-authored. Today’s leading processors have around a hundred good qubits.

So the honest summary is neither of the two you usually encounter. Quantum computers are not about to break encryption, and they are not a hoax. A genuine barrier that might have been permanent has been shown to be passable, and what lies beyond it is a very long and expensive construction project.

What IBM, Google, and Microsoft Have Achieved

Since late 2024 the field has delivered milestones it had chased for decades.

Google Willow and Quantum Echoes

In December 2024, Google unveiled Willow, a 105-qubit superconducting chip that marked a real advance in quantum error correction. Google reported that Willow ran a benchmark called random circuit sampling in under five minutes, a task it estimated would take one of the fastest supercomputers 10 septillion (10 to the power 25) years. The benchmark was chosen because it is hard for classical computers, not because its answer is useful.

In October 2025 Google followed with Quantum Echoes, published in Nature. Willow measured a quantity physicists call an out-of-time-order correlator, which tracks how information spreads and scrambles inside a quantum system, in about two hours; Google estimated that the best classical algorithm on a leading supercomputer would take some 13,000 times longer. Google calls the result verifiable because it is a measurable number that another quantum computer should reproduce. The practical payoff is not here yet. A companion demonstration applying the technique to molecules, of the kind studied with nuclear magnetic resonance, was in Google’s own words “not yet beyond classical”.

IBM Nighthawk and the Path to Fault Tolerance

IBM has pursued systematic scaling against a public roadmap. In November 2025 it announced Nighthawk, a 120-qubit processor with 218 tunable couplers, up from 176 on its predecessor Heron, able to run circuits of about 5,000 two-qubit gates, with 7,500 targeted by the end of 2026. Alongside it came Loon, an experimental chip that IBM says demonstrates every key processor component fault tolerance needs, and a decoding milestone: classical hardware that identifies errors in IBM’s codes in under 480 nanoseconds, ten times faster than the previous leading approach and a year ahead of schedule. In August 2026 IBM released Nighthawk r2, which adds a reset element to every qubit and runs more than 100,000 circuits a second, and joined two of its cryogenic modules, cooled below 15 millikelvin, into a single environment. Its roadmap names Kookaburra for 2026; Starling for 2029, which IBM expects to be the first fault-tolerant quantum computer, running 100 million gates on 200 qubits; and Blue Jay, with a billion gates on 2,000 qubits, from 2033.

Microsoft and the Majorana Connection

Microsoft has taken a fundamentally different route, based on the Majorana fermion — a particle that is its own antiparticle, first theorised by the physicist whose haunting story we tell in our article on Ettore Majorana. In February 2025 Microsoft announced Majorana 1, which it described as the first processor built on topological qubits, in which information would be stored in the shape of an exotic quantum state rather than in any one particle and so be naturally shielded from noise. The peer-reviewed paper published alongside it in Nature is more careful. It reports a fast, single-shot measurement of a property called fermion parity in a nanowire device, a necessary step towards such a qubit, and its authors discuss both ordinary and topological explanations for what they measured. On its own it does not establish that the Majorana states a topological qubit needs are present.

The July 2026 Advantage Claim, and the 37-Minute Reply

IBM had promised quantum advantage by the end of 2026 and defined it strictly: a computation beyond what classical computing can do alone, with a result that can be rigorously checked. On 30 July 2026 it said the bar had been met, pointing to three papers. The headline one, written with researchers at the University of Chicago, introduced doped Clifford sampling: circuits built mostly from operations a classical computer handles easily, seeded with a few hundred harder operations called T gates that make the whole circuit hard to simulate. The structure lets the experiment carry its own error checks and certify, from the hardware’s own measurements, a lower bound on how faithfully it ran.

The checking problem is the heart of the matter. If a quantum computer really does something no classical computer can, then no classical computer can confirm the answer directly. Earlier demonstrations leaned on smaller or simplified circuits that could be simulated, and assumed the large version behaved the same way. IBM’s approach tries to build the check into the experiment itself, so that the machine’s own error measurements set a floor on how trustworthy its output is. As the reply below showed, that cannot stop a cleverer classical algorithm from catching up; it means everyone can agree on what the quantum computer actually did.

The first version of the paper described a 70-qubit circuit, 70 layers deep, with 468 T gates, encoded in 97 physical qubits, with a certified fidelity of at least 0.284. Sixteen days later, researchers at the Singapore University of Technology and Design and NVIDIA posted a reply. By exploiting the circuit’s one-dimensional layout, they computed the exact probabilities of all 2,051 output bitstrings IBM had published, using 256 NVIDIA H100 graphics processors for 37.3 minutes. Their classical estimate of the fidelity, about 0.35, agreed with IBM’s certified bound.

That result cut both ways. It removed the advantage for that particular circuit, and at the same time it independently confirmed that the quantum hardware had performed as well as IBM said. By early September IBM had revised the paper around a different 64-qubit circuit, 73 layers deep with 314 T gates on 76 physical qubits and a certified fidelity of at least 0.349, and the three classical researchers had joined it as co-authors. Two further papers, a 74-qubit simulation of a periodically driven magnet by Qedma, RIKEN and BlueQubit, and a 56-qubit study led by Algorithmiq, argue that leading classical methods gave inconsistent answers where the quantum results held steady. Whether the revised claims survive the same scrutiny is the open question at the time of writing.

Where the field stands today

Real quantum computers exist and are improving quickly, but they remain in an early era. Today’s machines have limited numbers of qubits and are noisy, useful mainly for research and for narrow demonstrations rather than everyday problems. They are a long way from the large, error-corrected computers the field is aiming for.

It is important to be accurate about where things stand, because the field has a long history of overpromising. Today’s processors are what researchers call NISQ devices — Noisy Intermediate-Scale Quantum machines, a label introduced by the physicist John Preskill in 2018. They are real quantum computers, but imperfect ones. The largest fault-tolerant tasks are expected to need far more: Gidney’s estimate for breaking RSA assumes almost a million physical qubits. The leading superconducting processors have around a hundred high-quality qubits (Willow has 105, Nighthawk 120), and a Caltech neutral-atom array has trapped more than 6,100 atoms with record coherence, though without yet running computations across all of them.

There have been genuine milestones. In 2019 a team at Google reported that its quantum processor had performed a specific, narrowly defined task faster than the best classical supercomputers of the day could match. The claim was debated, but it marked a symbolic moment: quantum hardware doing something classical hardware could not.

That 2019 claim is also a lesson in how the field argues. In 2022 three researchers used 512 graphics processors for about 15 hours to generate a million samples from the same circuits on ordinary computers. The pattern repeated in 2026, as described above. Each round of claim and reply is how the boundary between quantum and classical computing gets mapped.

Governments and technology companies now invest heavily, treating quantum computing as strategically important. Progress is real and steady. But anyone promising a quantum computer on your desk, or the imminent collapse of all encryption, is running ahead of the evidence. The realistic timeline is measured in years and probably decades for the most demanding applications.

The 2025 and 2026 milestones are genuine and significant. They prove the physics works and the engineering path is tractable. They do not mean quantum computers will replace classical ones, or that they are ready for general commercial use. For most everyday computing, classical machines remain far superior. The realistic near-term future is hybrid: quantum processors handling the specific subroutines where they offer a true advantage, wired into classical infrastructure that handles everything else.

You will also hear two phrases used loosely in coverage: “quantum supremacy” and “quantum advantage”. Supremacy refers to a quantum computer performing any task, even a useless one, that a classical computer effectively cannot — a scientific milestone. Advantage is the more meaningful goal: solving a genuinely useful problem better than a classical machine could.

The distinction is easy to blur but important. A demonstration of supremacy proves the physics scales; it does not, by itself, produce anything commercially useful. Reaching practical quantum advantage — and doing so reliably, on problems people care about — is the milestone that would truly mark the technology’s coming of age, and it has not yet been convincingly achieved.

Quantum computing and artificial intelligence

Two of the most hyped technologies of the moment are quantum computing and artificial intelligence, and they are often mentioned in the same breath. It is worth being careful about how they actually relate, because the popular picture tends to overstate the link.

Today’s artificial intelligence, including the large language models behind modern chatbots, runs on classical computers — vast banks of conventional processors, not qubits. Quantum machines play no part in the AI systems people use now, and will not for the foreseeable future.

Researchers are exploring whether quantum computers might one day help with certain machine-learning tasks, an emerging field sometimes called quantum machine learning. The possibilities are intriguing but speculative, and no clear, practical advantage has yet been demonstrated. For now the two revolutions are running on separate tracks, however often they are bundled together in headlines.

How to Read a Quantum Headline

With the ideas above, you can read quantum news better than most. Five questions do most of the work.

First, is the task useful, or a benchmark chosen because it is hard for classical computers? Google itself says random circuit sampling, behind its most famous speed records, has yet to demonstrate practical commercial applications. Second, has anyone tried to match it on an ordinary computer? Google’s 2019 claim was matched in 2022, and IBM’s first 2026 test case within weeks. Third, are the qubits physical or logical? A thousand noisy qubits and a thousand error-corrected ones are very different machines. Fourth, what are the error rates? A qubit count without them says little. Fifth, is the claim in a peer-reviewed paper, a preprint or a press release? Each can be useful, but they carry different weight.

Three myths worth clearing up

The first myth is that a quantum computer will replace your laptop. It will not. It is a specialised tool for particular problems, and the two kinds of machine will work alongside each other, most likely with quantum processors accessed remotely over the internet when a task actually needs one.

The second myth is that quantum computers work by simply trying all answers simultaneously and reading off the right one. As we saw, measurement destroys the superposition; the real mechanism is the subtle interference that makes the correct answer probable. The distinction is the whole reason quantum programming is hard.

The third myth is that quantum computing is finished science waiting to be switched on. In reality it is a young, fast-moving field wrestling with deep engineering problems. The physics is sound; turning it into large, dependable machines is the unfinished work of a generation of scientists and engineers.

The bottom line

Strip away the hype and quantum computing rests on three ideas: superposition, which lets a qubit be 0 and 1 at once; entanglement, which links qubits into a single system; and interference, which sculpts probability so the right answer emerges. Everything else is engineering in service of those three.

It is neither the magic wand of the headlines nor an empty promise. It is a genuinely new way of computing, powerful for a narrow set of profoundly important problems, and still early in its development. If you understand those three core ideas and their limits, you understand quantum computing better than most of the people talking about it.

Forty-five years later, the machines Feynman imagined exist. They are imperfect and limited against the field’s long-term roadmaps, but they are real, operational, and already producing results that the best classical methods struggle, and sometimes fail, to match. The idea has become engineering, and the engineering is becoming technology. Boston Consulting Group estimated in July 2024 that quantum computing could create 450 to 850 billion dollars of economic value by 2040, sustaining a market of 90 to 170 billion dollars for the companies that build the hardware and software. It is a forecast, and quantum timelines have slipped before.

There is something quietly astonishing in all of this. To compute with a quantum machine is to press the strangest features of reality — a coin that is both heads and tails, particles linked across space, waves that cancel and reinforce — into practical service. Feynman’s provocation was that nature is not classical, so if we truly want to understand it, our machines had better not be either. Four decades on, that bet is paying off, one fragile, frozen qubit at a time.

Frequently asked questions

Sources

Primary institutional sources:

• NobelPrize.org — Physics 2025: quantum properties on a human scale (superconducting qubits)
• Preskill — Quantum Computing in the NISQ era and beyond, arXiv:1801.00862 (2018)
• Google Quantum AI — Quantum error correction below the surface code threshold, Nature (2024)

Foundational science:

• Shor, P. W. (1997). Polynomial-time algorithms for prime factorization on a quantum computer. SIAM Journal on Computing, 26(5), 1484–1509. doi.org/10.1137/S0097539795293172
• Bravyi, S. et al. (2024) — High-threshold and low-overhead fault-tolerant quantum memory. Nature 627:778-782.
• Gidney, C. (May 2025) — How to factor 2048 bit RSA integers with less than a million noisy qubits, arXiv:2505.15917.
• Pan, F., Chen, K. & Zhang, P. (2022) — Solving the sampling problem of the Sycamore quantum circuits. Physical Review Letters 129:090502.
• Manabe, H., Gu, H. & Pan, F. (13 August 2026) — Classical simulation and design frontiers for IBM’s doped Clifford sampling experiment, arXiv:2608.13110.
• IBM (30 July 2026) — Quantum advantage through trusted quantum computation.
• IBM (19 August 2026) — IBM connects its first modular cryogenic systems.
• IBM — Quantum roadmap.
• Google (9 December 2024) — Meet Willow, our state-of-the-art quantum chip.
• NIST (13 August 2024) — First three finalised post-quantum encryption standards.

2025–2026 results and announcements:

• IBM Quantum — Roadmap and processor announcements
• Microsoft — Majorana 1 topological quantum chip (Feb 2025)
• NIST — Post-Quantum Cryptography Standards (2024)
• DiVincenzo — The Physical Implementation of Quantum Computation, arXiv:quant-ph/0002077 (2000)
• Google Quantum AI and collaborators (22 October 2025) — Observation of constructive interference at the edge of quantum ergodicity. Nature 646:825-830.
• Google Research (22 October 2025) — A verifiable quantum advantage.
• IBM (12 November 2025) — New quantum processors, software and algorithm breakthroughs on path to advantage and fault tolerance.
• Martiel, S. et al. (2026) — Sampling hard circuits with verifiably high fidelity, arXiv:2607.25941 (v1 28 July, v3 2 September).
• Leviatan, E. et al. (2026) — Resolving structure in prethermal Floquet dynamics with precision quantum computation, arXiv:2607.24937.
• Barron, S. V. et al. (2026) — Observable estimation in the absence of classical verification, arXiv:2607.25998.
• IBM (31 August 2026) — IBM Quantum Nighthawk r2.
• IBM (November 2025) — Scaling for quantum advantage and beyond (Nighthawk: 218 couplers, up from Heron’s 176).
• Microsoft Azure Quantum (19 February 2025) — Interferometric single-shot parity measurement in InAs–Al hybrid devices. Nature 638:651-655.
• Manetsch, H. J. et al. (2025) — A tweezer array with 6,100 highly coherent atomic qubits. Nature 647:60-67.
• NIST IR 8547 (initial public draft) — Transition to post-quantum cryptography standards.
• Boston Consulting Group (18 July 2024) — The long-term forecast for quantum computing still looks bright.