quantum 101 · computing with waves

a computer made of waves

Somewhere in California, in a refrigerator colder than deep space, a chip about the size of a postage stamp holds about a hundred tiny circuits. Each one can be a 0, a 1, or a delicate blend of both. Nudge them with precisely timed microwave pulses and they begin to behave less like switches and more like ripples on a pond, spreading, overlapping, cancelling, and reinforcing.

That is the quiet wonder of a quantum computer. It does not try every answer at once, which is the most common myth about it. It does something subtler and stranger: it sets up waves of possibility so that wrong answers cancel out and right answers ring loud. This lesson walks through how that works, why it is so hard to build, and where it could matter, from medicine and materials to the encryption that protects nearly everything online.

No physics degree needed. If you can square a decimal and add two numbers, you can follow every step below.

the story · from a thought experiment to a chip

In May 1981, at a small conference at MIT on the physics of computation, Richard Feynman asked a deceptively simple question. Nature is quantum mechanical, so why are we trying to simulate it on machines that are not? Every time you add a particle to a quantum system, the bookkeeping needed to describe it on an ordinary computer roughly doubles. Feynman suggested turning the problem around: build a computer out of quantum parts and let it imitate nature directly. His talk was published the following year¹.

For more than a decade the idea stayed mostly theoretical. Then in 1994 Peter Shor, a mathematician at Bell Labs, showed that a quantum computer could find the prime factors of huge numbers dramatically faster than any known classical method². That mattered far beyond math departments, since the difficulty of factoring is what keeps a widely used encryption system called RSA secure. Almost overnight, quantum computing went from a curiosity to a question of national interest.

Skeptics raised a fair objection. Quantum states are absurdly fragile, and any real machine would drown in errors. In 1995 Shor answered that too, showing that quantum information can be protected by spreading it across many qubits, an idea called quantum error correction. Physicists began building. In 2001 a team at IBM used a seven-qubit machine made of molecules in a liquid to run Shor’s algorithm on the number 15 and get 3 × 5. It was a tiny result and a huge proof of principle.

The next big moment came in October 2019, when Google reported that its 53-qubit Sycamore chip had finished a carefully chosen sampling task in about 200 seconds, a job its team estimated would take a leading supercomputer around 10,000 years³. IBM quickly argued that a smarter classical approach could do it in about two and a half days⁴. The task itself had no practical use. What it marked was a line: a quantum machine had done something very hard to copy.

The years since have been about quality more than size. In December 2023 a Harvard-led team with QuEra, MIT, and NIST/University of Maryland ran algorithms on up to 48 error-corrected logical qubits built from neutral atoms⁵. In August 2024 NIST finalized the first post-quantum encryption standards, built to resist a future quantum attack⁶. In December 2024 Google’s Willow chip showed that making an error-corrected qubit bigger made it more reliable, a milestone the field had chased for nearly thirty years⁷. In October 2025 the Nobel Prize in Physics went to John Clarke, Michel Devoret, and John Martinis for 1980s experiments showing that a circuit you could hold in your hand could behave quantum mechanically, the physics underneath today’s superconducting qubits⁸. And in July 2026 IBM and the University of Chicago reported running 70 error-corrected logical qubits on a sampling task built to be both hard for classical computers and checkable⁹, a company-reported result the field is still digesting.

bits and qubits

An ordinary computer stores everything as bits, switches that are either 0 or 1. Your laptop has billions of them, and at any instant each one is definitely one or the other.

A qubit is the quantum version. It can be 0, it can be 1, and it can also be in a superposition, a blend of both described by two numbers called amplitudes. The simplest way to picture it: an arrow on a circle. Point the arrow along one axis and the qubit is 0. Point it along the other and the qubit is 1. Anywhere in between is a blend. The amplitudes are just how far the arrow reaches along each axis.

Here is where it gets interesting. One qubit needs 2 amplitudes. Two qubits need 4, one for each of 00, 01, 10, and 11. Every qubit you add doubles the count.

One honest caveat keeps this from becoming hype. A machine with 300 qubits does not give you 2³⁰⁰ answers to read. When you look, you get just 300 ordinary bits. The art of quantum computing is arranging things so the 300 bits you read are the ones you wanted.

measurement · the moment of truth

You cannot peek at a qubit’s amplitudes directly. When you measure it, you get a plain 0 or 1, and the blend is gone. Which one you get is random, with odds set by the amplitudes: square each amplitude to get its chance. This is called the Born rule, after the physicist Max Born, and it is one of the strangest and best-tested ideas in science.

Measurement is both the payoff and the danger. It is how you get an answer out. It is also what the outside world does to a qubit by accident whenever a stray bit of heat, light, or vibration bumps into it. Keep that in mind; it returns in the section on noise.

interference · the real trick

Drop two pebbles in a pond and the ripples cross. Where two crests meet, the water rises higher. Where a crest meets a trough, the water goes flat. That is interference, and it is the true source of quantum computing’s power.

Amplitudes behave like those ripples, with one twist that ordinary probabilities never have: they can be negative. Chances are always positive, so they can only pile up. Amplitudes can cancel. A quantum algorithm is a choreography that steers the amplitudes of wrong answers to cancel each other while the amplitudes of right answers add up.

The simplest demonstration uses one qubit and one operation, the Hadamard gate, written H. Applied to a 0, H makes an even blend: amplitude about 0.71 for 0 and about 0.71 for 1 (0.71 is √½, so each squares to 50%). Applied to a 1, it makes almost the same blend, with one difference: the amplitude for 1 comes out negative. Now apply H twice in a row and watch the paths.

Real algorithms do the same thing on a grand scale. Shor’s algorithm sets up waves across an enormous number of possibilities so that they reinforce only at values that reveal a hidden repeating pattern, and that pattern gives away the factors. This is also why quantum computers are not universally faster. Interference only helps on problems with the right kind of hidden structure, and finding that structure takes real cleverness. Only a modest number of genuinely powerful quantum algorithms are known.

gates and circuits

Ordinary computers are built from logic gates such as AND, OR, and NOT. Quantum computers have gates too, operations that turn the qubit arrows in precise ways. A program is a circuit: a sequence of gates, read left to right, with one horizontal line per qubit, ending in measurement.

A small set of gates like these, repeated and combined, is enough to build any quantum computation, just as a few logic gates are enough to build any classical one. The circuit in the next section uses only two of them, and it produces one of the most famous effects in physics.

entanglement · linked outcomes

Put an H gate on one qubit, then a CNOT from that qubit to a second one, and something remarkable happens. The pair ends up in a shared state where neither qubit has its own answer, and the two answers always match. Measure them and you get 00 half the time and 11 half the time, never 01 or 10. This is entanglement, and the pair is called a Bell pair.

Albert Einstein was famously uneasy with this kind of linkage and called related effects “spooky action at a distance.” Experiments since the 1970s have confirmed it again and again, with entangled particles separated by kilometers and, as you will see later, by a satellite. One thing entanglement does not allow is faster-than-light messaging. Each side, on its own, sees a perfectly random string of 0s and 1s. The matching only shows up when the two sides compare notes over an ordinary channel.

Inside a computer, entanglement is what lets qubits act as one system instead of a row of independent coins. Without it, a quantum computer could be simulated easily on an ordinary one. Entanglement makes the 2ⁿ space truly shared, and interference makes it useful.

noise and decoherence · why this is hard

Everything above assumes the qubits are left alone. In reality, a qubit is constantly being nudged by its surroundings: a little heat, a stray photon, a vibration, a fluctuating magnetic field. Each nudge is like a tiny accidental measurement. The blend leaks away and the delicate amplitudes drift. Physicists call this decoherence, and the time a qubit can hold its state is its coherence time.

This is why superconducting quantum computers live inside dilution refrigerators that reach about a hundredth of a degree above absolute zero, more than a hundred times colder than deep space, which sits around 2.7 degrees. Even there, the best superconducting qubits hold their state for something like a hundred microseconds¹⁰. Gates are imperfect too. The best two-qubit gates today are right around 99.5% to 99.9% accurate (a rough range across leading platforms). That sounds excellent until you multiply.

One more catch makes quantum errors harder than ordinary ones. In a normal computer you can protect data by copying it three times and taking a vote. A basic law of quantum physics, the no-cloning theorem, forbids copying an unknown quantum state. And you cannot simply look to check for errors, since looking is measuring, and measuring destroys the blend.

error correction · logical from physical

The way around both problems is clever and a little magical. Instead of storing one qubit of information in one physical qubit, you spread it across many. The group as a whole acts as one sturdier qubit, called a logical qubit. The individual hardware qubits are physical qubits.

Extra helper qubits then ask the group careful yes-or-no questions, such as whether neighboring qubits agree in a certain way. The answers reveal whether an error happened and where, without ever revealing the stored information itself, so the blend survives. A fast classical computer reads those answers, called the syndrome, and works out the fix. On Google’s Willow chip, this whole cycle repeats about every microsecond⁷.

the surface code

The most studied scheme is the surface code. Picture a checkerboard: data qubits sit on the grid points and measurement qubits sit in the squares between them, each checking its neighbors. A logical qubit is a whole patch of the board. The size of the patch is its distance, written d. A bigger patch can catch more errors before they add up to a mistake in the stored information.

There is a catch, and it is called the threshold. Bigger patches only help if each physical qubit is already good enough. Below the threshold, adding qubits suppresses errors exponentially. Above it, adding qubits just adds more ways to fail. For decades nobody could show a real chip clearly on the good side of that line as the patch grew. Willow’s 2024 result was the first convincing demonstration that it works, which is why it mattered so much more than a raw qubit count.

the ways to build a qubit

Anything that can hold a clean two-level quantum state can, in principle, be a qubit. In practice a handful of families lead the race, and each makes a different trade between speed, accuracy, and how hard it is to scale. Nobody knows yet which will win, and it is quite possible that more than one will, for different jobs.

The scale of these systems already varies a lot. In 2025 a Caltech team held more than 6,100 atoms in a single tweezer array, each a candidate qubit, with coherence lasting over 12 seconds¹³. Superconducting chips hold far fewer qubits, about a hundred on Willow, and run gates much faster. Trapped ions have posted some of the highest gate accuracies of any platform. Each figure on its own tells you little. What matters is how they combine into logical qubits that run long, reliable calculations.

what it’s actually good for

A quantum computer is not a faster laptop. It is a specialized instrument, a bit like a telescope, extraordinary for some jobs and pointless for most. The useful jobs fall into a short list.

chemistry and materials · the original idea

Molecules are quantum systems, so Feynman’s logic applies directly. Designing a better battery material, a catalyst for fertilizer, or a drug that binds just right all depend on how electrons share space, and the hardest cases are exactly the kind of 2ⁿ problem that overwhelms ordinary computers. A famous target is FeMoco, the iron-and-molybdenum core of the enzyme that lets certain bacteria pull nitrogen from the air at room temperature, something industry does with high heat and pressure. A 2021 estimate put a high-quality simulation of it at about four million physical qubits running for under four days¹⁴ (estimate, using the same 0.1% error assumption as below). This is widely seen as the most likely first area of real scientific value.

shor’s algorithm and the great migration

Much of today’s internet security, including RSA and elliptic-curve cryptography, rests on math problems that are hard for ordinary computers and easy for a large, error-corrected quantum computer running Shor’s algorithm. Nobody can do it yet. The estimates of what it would take keep falling.

So why act now? Because of a strategy called harvest now, decrypt later. An adversary can record encrypted traffic today and simply wait until a capable quantum computer exists. Anything that must stay secret for ten or twenty years, such as medical records, state secrets, and trade secrets, is already exposed in that sense. And swapping cryptography across every bank, phone, satellite, and power grid takes many years.

The response is post-quantum cryptography: new math that runs on ordinary computers and resists quantum attack. NIST finalized the first three standards in August 2024, ML-KEM for setting up shared keys and ML-DSA and SLH-DSA for digital signatures⁶. NIST’s draft transition plan proposes deprecating today’s vulnerable algorithms after 2030 and disallowing them after 2035¹⁶. Some of the most widely used messaging apps already use post-quantum key exchange, including Signal¹⁷ and Apple’s iMessage¹⁸.

optimization · hype versus reality

You will hear that quantum computers will optimize delivery routes, financial portfolios, and supply chains. Be careful here. For most optimization and search problems, the known quantum speedups are modest, often a square-root improvement. That sounds big. Searching a million possibilities takes an ordinary computer up to a million checks and a quantum one about a thousand steps. Each quantum step is far slower, and it carries heavy error-correction overhead. Careful analyses suggest square-root speedups alone will struggle to beat classical machines for a long time¹⁹, and classical optimization software keeps getting better. Treat claims of near-term quantum advantage in optimization with polite skepticism until they come with a head-to-head comparison against the best classical method.

what it isn’t for

• everyday computing: email, video, spreadsheets, and games will stay classical. There is no speedup to be had.
• big data: loading huge datasets into qubits is slow, which erases most of the advantage for data-heavy tasks.
• training large AI models: that is massive, repetitive arithmetic, exactly what GPUs are built for. Quantum is not expected to replace them (estimate, based on the algorithms known today).
• trying every answer at once: it never did that. It uses interference on problems with the right hidden structure.

what’s next · a directional roadmap

Forecasting this field is humbling, so everything in this section is an estimate or a stated target. The milestones in the story above are public and checkable. The road ahead is a mix of company targets, standards deadlines, and educated guesses.

The signals worth watching are not raw qubit counts. Watch logical error rates, how many logical qubits run at once, how many logical operations they survive, and whether a quantum result comes with a solid comparison against the best classical method.

space, ai, and infrastructure

Quantum technology reaches well beyond computers, and some of the most practical pieces point straight at the frontier this site follows.

quantum sensing and navigation

The same fragility that makes qubits hard to compute with makes them superb sensors. A cloud of atoms chilled to near absolute zero responds to tiny changes in gravity, rotation, and magnetic fields. You already rely on quantum physics for navigation: every GPS satellite carries atomic clocks, and your phone finds itself by timing their signals. NASA’s Cold Atom Lab, launched to the International Space Station in 2018, has run the first atom interferometer in orbit, an early step toward quantum sensors that could map gravity from space²¹. On Earth, with GPS jamming and spoofing on the rise, companies are flight-testing quantum magnetometers that navigate by matching the planet’s magnetic field, with no satellite signal at all²² (company-reported results).

quantum keys from orbit

Quantum key distribution, or QKD, uses single photons to share a secret key. Any eavesdropper who looks at the photons disturbs them, and the disturbance shows up as errors, so both ends know the line was tapped. Fiber absorbs photons over long distances, so the farthest links go through space. In 2017 China’s Micius satellite delivered quantum keys to ground stations up to about 1,200 km away²³, and then relayed keys for a video call between China and Austria, about 7,600 km apart²⁴.

QKD is promising and also limited. It needs special hardware at every endpoint, works best at night and in clear weather, and today’s long satellite links rely on trusted relays. U.S. security agencies currently favor post-quantum cryptography over QKD for most uses²⁵. The likely future mixes both: post-quantum math almost everywhere, and quantum links where the stakes justify the cost.

compute, energy, and ai

Quantum computers will not live alone. They are being built as accelerators that sit beside classical supercomputers and AI clusters, the way GPUs sit beside CPUs. Error correction itself depends on fast classical computing: a decoder must read the syndrome and decide on a fix every microsecond or so. AI is already helping. In 2024 Google DeepMind’s AlphaQubit, a neural network, decoded errors more accurately than earlier methods on real hardware data²⁶, and the Willow experiment used a neural network decoder too.

Energy looks different than it does in AI. A superconducting quantum computer’s biggest power draw is usually its refrigeration, on the order of tens of kilowatts per system (estimate), while a large AI datacenter can draw hundreds of megawatts (estimate). For the problems quantum computers suit, the energy per answer could be tiny compared with a brute-force classical attempt. The flow could run the other way too: quantum simulations could one day generate high-quality chemistry data to train AI models (estimate, speculative).

And then there is infrastructure that lasts. A satellite launched this year may still be flying in the late 2030s, a power-grid controller may run for decades, and both will likely outlive today’s encryption. Building them so post-quantum algorithms can be swapped in later, sometimes called crypto-agility, is one of the most practical quantum decisions any operator can make right now.

check yourself

Eight quick questions. Think of your answer, then tap to reveal.

glossary

closing rules of thumb

• Feynman proposed quantum computers in 1981 to simulate nature. Shor showed in 1994 they could break common encryption.
• A qubit is an arrow, not a switch. Each added qubit doubles the space the machine works in.
• Square an amplitude to get a chance. Measuring gives one ordinary bit and ends the blend.
• Interference is the real source of speedup: wrong answers cancel, right answers add.
• Entanglement links outcomes, never messages.
• Noise compounds with every gate. Useful machines are counted in logical qubits, each built from hundreds to thousands of physical ones (estimate).
• The biggest expected wins are chemistry, materials, and code-breaking. The encryption fix is already standardized and rolling out.
• Quantum sensing and quantum keys from orbit are already here, in early form.
• Underneath it all, nature keeps its books in amplitudes that can cancel, and that is the wonder of it.