Skip to the content
Kets & Gates homeOpen the app

Lesson D: Where things stand

How qubits are built, why errors are the hard part, and how to read the news

7 partsbest after lesson C

Start the interactive lesson

The interactive version checks every answer, gives hints and saves your progress in this browser. This page is the same lesson on one page, with the answers folded away.

1 / 7 · Learn

Before you start

The last lesson of Part 0 brings the story up to date: how qubits are actually built, what holds today’s machines back and how that might be fixed, and how to read the news about quantum computers. It ends with a map of the rest of the course.

Check yourself

A warm-up: make a guess before reading on. The lesson comes back to it.

As of 2026, the largest quantum machines hold thousands of qubits, and the most reliable have about a hundred. Shor’s algorithm (Lesson C) could break the encryption keys that protect much of the internet. What mainly stops today’s machines from running it on real keys?

  1. ASize alone: with enough qubits of today’s kind, it would simply run
  2. BSoftware: nobody has worked out how to program it yet
  3. CSpeed: each operation takes too long for the calculation to finish
  4. DErrors: each operation sometimes goes wrong, and the mistakes pile up
Show the answer

Answer: D. Errors: each operation sometimes goes wrong, and the mistakes pile up

Errors. Today’s operations go wrong roughly once in every few hundred to few thousand, and running Shor’s algorithm on a real key takes billions of operations. Size matters too, but mostly because correcting errors takes many extra qubits.

Why not the others

  • A. More qubits are needed, but qubits of today’s kind wouldn’t be enough on their own. Each operation goes wrong now and then, and Shor’s algorithm on a real key takes billions of operations, so the mistakes would swamp the answer. Most of the extra qubits are needed to correct errors.
  • B. The algorithm has been known since 1994, and researchers have planned out, step by step, how to run it on real key sizes. What is missing is hardware reliable enough to carry out the plan.
  • C. Speed isn’t the main problem. A 2025 estimate says a large enough machine that corrects its errors could factor a real key in under a week. Today’s machines fall short for another reason: their operations go wrong too often for a calculation that long.

2 / 7 · Learn

Building qubits

Many physical systems can serve as a qubit: anything with two distinct states that can hold amplitudes for both (the numbers from Lesson A that can cancel or add up), and that can be controlled. Five very different kinds are being built: superconducting circuits, trapped ions, neutral atoms, photons and spins in silicon. As of 2026, none has clearly won.

What each kind is like
  • Superconducting circuits: tiny electrical circuits on a chip, cooled to about a hundredth of a degree above absolute zero. Their operations are very fast, and the chips are made with the chip industry’s methods.
  • Trapped ions: single charged atoms held in a vacuum by electric fields and controlled with lasers or microwaves. Every ion of a kind is identical, and their operations are among the most accurate, though slower.
  • Neutral atoms: uncharged atoms held in place by tightly focused laser beams. Thousands can be held at once and moved around, so any two can be brought together.
  • Photons: particles of light, as in Lesson A. They shrug off most noise and travel easily, but they hardly affect each other, and they are easily lost.
  • Spins in silicon: single electrons trapped in structures much like the transistors of ordinary chips, with the electron’s spin, a tiny built-in magnetism, as the qubit. They are very small, which could help in building big machines, but this approach is at an earlier stage.

Every kind faces the same tension. First, a qubit must be isolated. Remember the two-route experiment in Lesson A. With both routes open, the two routes’ amplitudes cancelled at detector B, so B never clicked. Once a watcher recorded which route each photon took, the cancellation disappeared and B started clicking.

A qubit’s surroundings can act as an accidental watcher. A stray bit of heat, light or vibration that touches the qubit carries away a trace of its state, and its amplitudes stop cancelling and adding up as they should. Left like this, a qubit drifts toward behaving like an ordinary random bit. This loss is called decoherence.

Check yourself

A stray atom bumps into a qubit and flies off, carrying a trace of the qubit’s state with it. Which change to Lesson A’s two-route experiment is this most like?

  1. AOpening the second route: the qubit gains a new way to reach an answer
  2. BMaking the source brighter: more photons, same pattern
  3. CBlocking a route: the photon is stopped
  4. DTurning on the watcher: something else now holds a record, so the cancellation is lost
Hint
  1. In Lesson A, which change made B start clicking although no photon was stopped?
Show the answer

Answer: D. Turning on the watcher: something else now holds a record, so the cancellation is lost

Like the watcher, the stray atom ends up holding a record of the qubit’s state. Once a record exists anywhere, the amplitudes stop cancelling as they should: that is decoherence.

Why not the others

  • A. Opening the second route is what created the cancellation; the stray atom destroys it. It acts like the watcher: a record of the state, held by something outside, so the amplitudes stop cancelling.
  • B. A brighter source left B silent, because nothing recorded the routes. The stray atom does carry away a record, as the watcher did, so the pattern changes.
  • C. A block stops photons, but the stray atom doesn’t destroy the qubit: the qubit is still there afterwards. What the atom does is carry off a record of the qubit’s state, which is what the watcher did.

Yet a qubit must also be controllable. You have to reach in to run operations on it (the steps of a calculation, like the splitters in Lesson A), and to measure it at the end. Every wire, laser beam or microwave signal that lets you in also lets noise in.

Check yourself

Shielding a qubit better makes it keep its amplitudes longer. Suppose engineers could seal one off from everything, perfectly. What would be wrong with it?

  1. ANothing: a perfectly sealed qubit is exactly what a quantum computer needs
  2. BNothing could reach it, so nobody could run operations on it or measure it
  3. CIts amplitudes would fade anyway, with nothing to keep them going
Show the answer

Answer: B. Nothing could reach it, so nobody could run operations on it or measure it

Isolation protects the amplitudes; control and measurement need contact. The two demands pull in opposite directions, and every kind of qubit is a compromise between them.

Why not the others

  • A. It would keep its amplitudes, but it would also be useless. A computer has to run operations on its qubits and read them at the end, and every way in for control is also a way in for noise.
  • C. Amplitudes don’t need anything to keep them going: they are lost through contact with the surroundings, which is exactly what sealing would stop. The trouble is that a sealed qubit can’t be controlled or measured.

3 / 7 · Worked example

Errors, and a first fix

Because no qubit is perfectly isolated and no control is perfectly precise, every operation on today’s machines goes wrong now and then: on the best machines, roughly once in every few hundred to few thousand operations. That sounds rare, but the mistakes add up. If each operation goes wrong 1 time in 1,000:

  • a calculation of 100 operations has about 100 ÷ 1,000 = 0.1 errors on average, so it usually runs cleanly;
  • a calculation of 1 million operations has about 1,000,000 ÷ 1,000 = 1,000 errors.

Check yourself

A calculation takes 1 billion operations, and each operation goes wrong 1 time in 1,000. Nothing corrects the errors. About how many errors would one run contain?

  1. AAbout 1,000,000
  2. BNone, if the machine is well built
  3. CAbout 1,000
  4. DAbout 1: errors happen only 1 time in 1,000
Hint
  1. How many groups of 1,000 operations are there in 1 billion?
Show the answer

Answer: A. About 1,000,000

1,000,000,000 operations at 1 error per 1,000 gives about 1,000,000 errors. One error can be enough to spoil the answer, so without error correction the run is hopeless.

Why not the others

  • B. An error rate of 1 in 1,000 already describes a well-built machine: it still goes wrong now and then. Over 1 billion operations that is about 1,000,000 errors.
  • C. That would be right for 1 million operations. A billion is a thousand times more, so the errors are a thousand times more too: 1,000,000,000 ÷ 1,000 = 1,000,000.
  • D. 1 in 1,000 is the rate for each operation, not the total. Over 1 billion operations it adds up: 1,000,000,000 ÷ 1,000 = 1,000,000 errors.

The oldest fix for errors is redundancy: keep several copies and let the majority decide. Here it is for an ordinary bit, with numbers you can check by hand. One rule makes the arithmetic work: when two separate things each happen 1 time in 10, both happen 1 time in 100, since 1 in 10 of 1 in 10 is 1 in 100.

Store a bit as three copies and read it back by majority vote. One flipped copy is outvoted, 2 to 1; two flipped copies outvote the one copy that is still right.

Worked example

Three copies, each flipping 1 time in 10

Each copy flips 1 time in 10, independently of the others. How often does the vote get the bit wrong?

  1. When the vote fails

    One flip is outvoted, as in the figure. The vote fails only when two or more copies flip.

  2. Two copies flip

    A particular pair, say copies 1 and 2, both flip about 1 time in 100. There are three pairs (1 and 2, 1 and 3, 2 and 3), so two flips happen about 3 times in 100. All three flipping is rarer still: 1 time in 1,000.

  3. Compare

    A single copy is wrong 10 times in 100; the vote, about 3 times in 100. With three copies and a vote, errors become about three times rarer.

  4. Your turn

    Your turn

    Now each copy flips only 1 time in 100. Roughly how often is the vote wrong?

    1. AAbout 1 time in 1,000,000: all three copies must flip
    2. BAbout 3 times in 10,000
    3. CAbout 3 times in 100: three copies give three chances to go wrong
    4. DAbout 1 time in 100: a vote can’t beat the copies it counts
    Hints
    1. The vote fails as soon as two copies flip.
    2. A particular pair both flips about 1 in 100 of 1 in 100 times. How many pairs are there?
    Show the answer

    Answer: B. About 3 times in 10,000

    Each pair both flips 1 time in 10,000, and there are three pairs: about 3 in 10,000. A single copy is wrong 100 times in 10,000, so with the vote, errors become over 30 times rarer.

    Why not the others

    • A. Two flips are already enough to win the vote, so it fails when any pair flips: three pairs, each about 1 time in 10,000, so about 3 in 10,000. All three flipping is the rarer, extra case.
    • C. Three copies do give three chances for a flip, but one flip is outvoted. The vote fails only when two copies flip together: three pairs, each about 1 time in 10,000, so about 3 in 10,000.
    • D. A vote can beat its copies, because it fails only when two copies go wrong together. A pair both flips about 1 time in 10,000 (1 in 100 of 1 in 100), and there are three pairs: about 3 in 10,000.
The exact numbers

The worked example rounded a little. For exactly two flips, the third copy must also stay right, which it does 9 times in 10. So with flips 1 time in 10, each pair flips while the third copy stays right 9 times in 1,000 (9 in 10 of 1 in 100). Three pairs make 27 in 1,000, and all three flipping adds 1 in 1,000: 28 in 1,000 in all, a little under 3 in 100. With flips 1 time in 100 the same count gives 298 in a million, just under 3 in 10,000.

The better each copy is, the more the vote gains: errors become about three times rarer at 1 flip in 10, and over 30 times rarer at 1 in 100. It works the other way too. If each copy flips 6 times in 10, most copies are wrong, and the vote is wrong even more often than a single copy: about 65 times in 100.

So redundancy helps only when each part is reliable enough to begin with. The dividing line is called the threshold. For copies and a vote it is 1 flip in 2: below it, more copies make the bit more reliable; above it, they make it worse.

Check yourself

Each copy flips 4 times in 10. Would storing the bit as more copies, say 5 or 7, and taking a majority vote make it more reliable?

  1. AOnly up to 3 copies; beyond that, more copies make it worse
  2. BNo: at 4 in 10 the copies are too unreliable for a vote to help
  3. CYes: each copy is still right more often than wrong
  4. DNo: more copies just add more chances to go wrong
Hint
  1. Compare 4 in 10 with the threshold for a vote, 1 flip in 2.
Show the answer

Answer: C. Yes: each copy is still right more often than wrong

The threshold for a vote is 1 flip in 2. At 4 in 10 each copy is right more often than wrong, so more copies push the chance of a wrong vote down: about 35 in 100 with 3 copies, 32 with 5, 29 with 7. Close to the threshold the gains are slow; far below it they are large, which is why the error rate of each part matters so much.

Why not the others

  • A. Below the threshold every extra pair of copies helps. With flips 4 times in 10, the vote is wrong about 35 times in 100 with 3 copies, about 32 with 5 and about 29 with 7.
  • B. For a vote, the dividing line is 1 flip in 2, and 4 in 10 is below it. Each copy is still right more often than wrong (6 times in 10), so a majority is more likely to be right than any one copy.
  • D. More copies do mean more flips, but also more correct copies to outvote them. Below the threshold the correct copies win more and more often as you add copies.

4 / 7 · Learn

Error correction for qubits

Qubits need the same protection, but two things stop you from simply copying and voting:

  • You can’t copy an unknown qubit. No process can turn one qubit in an unknown state into two copies of it. Lesson 7 proves this; it is called the no-cloning theorem.
  • Looking disturbs it. Reading a qubit gives 0 or 1 and wipes out its amplitudes, just as the watcher in Lesson A wiped out the cancellation. Reading the copies to hold a vote would destroy what you were protecting.

Qubits can also go wrong in more ways than bits. Besides a flip between 0 and 1, the sign of an amplitude can flip (the plus and minus of Lesson A), and a quantum code has to catch both kinds.

The way around both problems is to ask the qubits only whether they agree, never what they hold. Go back to three copies of a bit and run two checks: do copies 1 and 2 agree? Do copies 2 and 3 agree? If one copy has flipped, the pattern of answers says which one, and the pattern is the same whether the stored bit is 0 or 1.

Copy 3 has flipped in both panels. The two checks give the same answers, agree and differ, whether the stored bit was 0 or 1: they say where the error is, never what is stored.

Check yourself

Three copies again. This time both checks say differ: copies 1 and 2 differ, and copies 2 and 3 differ. If only one copy has flipped, which one is it?

  1. ACopy 2
  2. BCopy 1
  3. CCopy 3
  4. DYou can’t tell without reading the copies
Hint
  1. Which copy takes part in both checks?
Show the answer

Answer: A. Copy 2

Copy 2 is in both checks, so its flip makes both say differ. A flip of copy 1 or copy 3 would upset only one check.

Why not the others

  • B. If copy 1 had flipped, copies 2 and 3 would still match, so the second check would say agree. Only a flip of copy 2, the copy in both checks, makes both say differ.
  • C. If copy 3 had flipped, copies 1 and 2 would still match, so the first check would say agree. The copy that sits in both checks, copy 2, is the one that flipped.
  • D. The checks are enough. Each copy upsets a different pattern of checks: copy 1 only the first, copy 3 only the second, copy 2 both. Both say differ, so it is copy 2, found without reading any copy.

A quantum code works this way. It spreads the stored information across several qubits, in a way that copies nothing, and helper qubits carry out agreement checks between them, round after round. The checks reveal where an error happened but nothing about the stored state, so they don’t disturb it, and each error they find is corrected.

A qubit protected like this is called a logical qubit; the qubits that make it up are physical qubits. Real codes use many more than three. The most studied, the surface code, lays physical qubits out in a square grid and checks neighbors against each other, catching both kinds of error.

The threshold rule still holds: a bigger grid fixes more errors, but only if the physical qubits are good enough. For the surface code the threshold is roughly 1 error in 100 operations, far stricter than a vote’s 1 in 2, partly because the checks themselves can go wrong. At today’s error rates one well-protected logical qubit takes hundreds to a thousand or so physical qubits; newer codes aim to need fewer.

Check yourself

In 2024, Google ran the surface code on grids of 3 × 3, 5 × 5 and 7 × 7 qubits (plus helpers for the checks). Each bigger grid cut the logical qubit’s error rate about in half. Why was that the important part of the result?

  1. AIt showed the qubits were below the threshold: bigger codes gave fewer errors, so growing the code can push errors lower still
  2. BIt showed the physical qubits no longer made errors
  3. CIt wasn’t: bigger codes always give fewer errors
  4. DIt meant the chip could now run Shor’s algorithm on real keys
Hint
  1. What happens to a vote among copies that flip 6 times in 10 when you add more copies?
Show the answer

Answer: A. It showed the qubits were below the threshold: bigger codes gave fewer errors, so growing the code can push errors lower still

Errors that fall as the code grows are the sign of being below threshold. Then more qubits buy more protection, which is the road to logical qubits reliable enough for long algorithms.

Why not the others

  • B. The physical qubits still went wrong now and then, about 3 times in 1,000 for two-qubit operations. Error correction worked because the checks caught those errors faster than they built up.
  • C. Only below the threshold. Above it, a bigger code makes things worse, like votes among copies that flip 6 times in 10. Seeing errors fall as the grid grew is how you know the qubits are good enough.
  • D. That would take more than a thousand logical qubits, each far more reliable than this one, running billions of operations. This experiment protected one logical qubit holding stored information. It showed that the method works, a first step.

5 / 7 · Learn

Reading the headlines

News about quantum computers often claims more than the research behind it. Three kinds of story come up again and again.

“Quantum computer beats supercomputer.” These report quantum advantage (once called “quantum supremacy”): a quantum computer does a task that, by its makers’ estimate, the best ordinary computers would take far longer to do. The tasks are chosen to be hard to simulate, not to be useful: typically, running a random sequence of operations and recording the random outputs. And “far longer” is an estimate based on the classical methods known at the time, which can improve.

Check yourself

In 2019 a quantum computer did a random-output task that, by its makers’ estimate, would take a supercomputer 10,000 years. About two years later, other researchers did the same task in about 15 hours on 512 graphics processors. What does that show?

  1. AThe quantum computer’s 2019 result was wrong
  2. BOrdinary computers can simulate any quantum computer cheaply
  3. CA real quantum advantage is impossible
  4. DAn advantage claim is measured against the best classical methods known at the time, and those can improve
Show the answer

Answer: D. An advantage claim is measured against the best classical methods known at the time, and those can improve

The 10,000-year figure was an estimate for the classical methods known then. Better methods cut it to hours. Every advantage claim is a race against improving classical methods.

Why not the others

  • A. The quantum computer did what was claimed. What changed was the other side of the comparison: people found much faster classical methods for that particular task.
  • B. Lesson B showed why that fails in general: an exact simulation doubles in cost with each added qubit. Clever methods can be far cheaper for particular tasks, which is what happened here.
  • C. One claim being matched doesn’t rule out others. It shows that each claim has to hold up against the best classical methods, including ones found later.

“By 2029 …” Companies publish roadmaps: plans for bigger, error-corrected machines by a given year. They show where people are aiming, and they are targets, not results. A US defense research agency, DARPA, is running an independent check of whether any design can reach the point where a machine is worth more than it costs to build and run.

“Quantum computers will break encryption.” On a large enough error-corrected machine, Shor’s algorithm would. The gap is still wide. Real runs of Shor’s algorithm have factored only the tiniest numbers, such as 15 = 3 × 5. Larger reported factoring “records” have used shortcuts, some of which only work if you already know the answer. As Lesson C explained, replacements for today’s encryption are being switched on anyway, because messages recorded now could be decrypted later.

Targets and estimates, as of late 2026
  • Roadmaps. IBM plans a machine with 200 logical qubits running 100 million operations by 2029, and Quantinuum a fault-tolerant machine, one that corrects its errors throughout, the same year. Google aims for useful machines by the end of the decade. DARPA’s check asks whether any design can be worth its cost by 2033.
  • Breaking a 2048-bit RSA key, a widely used kind: under a million physical qubits running for under a week, each operation going wrong at most 1 time in 1,000 (2025 estimate; the 2019 estimate was 20 million). A 2026 preprint claims under 100,000 with newer codes; it has not yet been checked by others.
  • Elliptic-curve keys (256-bit, used by most cryptocurrencies): fewer than 500,000 physical qubits, running for a few minutes (Google, 2026).
  • Chemistry. A flagship problem from Lesson C, the part of an enzyme that lets some bacteria turn nitrogen from the air into ammonia, was estimated in 2021 at about 4 million physical qubits running for under four days, with the same error rate. (Ordinary computers have since settled one part of that problem, as Lesson C told.)
  • Today’s machines have about a hundred high-quality qubits, and logical qubits in the tens.

Check yourself

A company announces a machine with 100,000 qubits, far more than any before. Which question tells you most about whether it brings useful machines closer?

  1. AHow cold does it have to be kept?
  2. BHow often do its operations go wrong, and can it correct its errors?
  3. CWhich kind of qubit does it use?
  4. DIs 100,000 really more than any other machine has?
Show the answer

Answer: B. How often do its operations go wrong, and can it correct its errors?

Below the threshold, more qubits buy more protection; above it, they don’t help. So a qubit count means little without the error rates, and without knowing whether the qubits are physical or logical.

Why not the others

  • A. That is an engineering detail, and not every kind of qubit needs deep cooling. It says little about usefulness, which depends on error rates and error correction.
  • C. Worth knowing, but no kind has clearly won, and any kind can be built well or badly. What decides usefulness is how often operations go wrong and whether errors can be corrected.
  • D. The count says least. Qubits that go wrong too often can’t run long calculations however many there are: error rates, and whether errors can be corrected, decide whether more qubits help.
An example of a disputed claim

Microsoft is developing topological qubits, designed so that the physics of the device itself protects them from errors. It announced chips based on them in February 2025 and June 2026. As of late 2026, many physicists are not convinced that the devices show the effect at all, and the authors of the 2025 paper wrote that their measurements did not, on their own, settle the question. The approach may still work out. The point is that an announcement and an established result are different things.

6 / 7 · Mastery check

Mastery check

Check yourself

A company builds a machine with a million qubits. Each operation goes wrong about 1 time in 1,000, and the machine does not correct its errors. Could it run Shor’s algorithm on a real encryption key?

  1. ANo: over billions of operations, millions of errors would pile up in every run
  2. BYes: run it many times and keep the most common answer
  3. CNo: a million qubits is far too few, whatever their quality
  4. DYes: a million qubits is as many as the published estimates call for
Show the answer

Answer: A. No: over billions of operations, millions of errors would pile up in every run

Billions of operations at 1 error per 1,000 means millions of errors per run. The qubit count would be enough only if the machine used most of its qubits to correct errors.

Why not the others

  • B. Repeating helps only when a good share of runs come out right. With millions of errors in every run, essentially none do, so there is no right answer to collect.
  • C. A 2025 estimate put a real key within reach of under a million qubits that correct their errors. What sinks this machine is the missing error correction, not the number of qubits.
  • D. Those estimates assume the qubits are used for error correction: most of them do nothing but catch errors. Without it, a run of billions of operations at 1 error per 1,000 contains millions of errors.

Check yourself

Why do quantum error-correcting codes rely on checks such as “do these two qubits agree?” instead of reading each qubit and taking a vote?

  1. AAgreement checks are quicker to carry out than reading each qubit, so errors are caught sooner
  2. BQubits can’t be read at all until the computation is over, so checks are the only option
  3. CA vote works only with three copies, and quantum codes use many more qubits than that
  4. DReading them would wipe out their amplitudes; agreement checks find errors without revealing what is stored
Show the answer

Answer: D. Reading them would wipe out their amplitudes; agreement checks find errors without revealing what is stored

Looking disturbs a qubit. Agreement checks reveal where an error happened but nothing about the stored state, so they can be run again and again without destroying it.

Why not the others

  • A. Speed isn’t the reason. Reading a qubit gives 0 or 1 and destroys its amplitudes, which is what the code is there to protect. A check of agreement finds the error without learning the stored state.
  • B. Qubits can be read at any point, and codes do measure their helper qubits during the computation. The trouble is what reading a qubit that holds the data does: it gives 0 or 1 and wipes out the amplitudes.
  • C. A vote works with any odd number of copies. The real obstacles are that an unknown qubit can’t be copied and that reading the qubits would destroy their amplitudes.

Check yourself

A lab spreads each logical qubit over more and more physical qubits, and the logical error rate goes up, not down. What is the most likely explanation?

  1. AThe checks are run too often; running them less often would fix it
  2. BThe code is still too small; making it bigger again will eventually bring the errors down
  3. CError correction can never work for qubits, because an unknown qubit can’t be copied
  4. DIts physical qubits are above the threshold: they go wrong too often for a bigger code to help
Show the answer

Answer: D. Its physical qubits are above the threshold: they go wrong too often for a bigger code to help

Below the threshold, a bigger code gives fewer logical errors; above it, more. Errors that grow with the code mean the physical qubits are not yet good enough.

Why not the others

  • A. Checks must run over and over to catch errors before they pile up, so checking less would let more slip through. Errors that grow with the code size are the sign of physical qubits above the threshold: the qubits themselves must improve.
  • B. Above the threshold, bigger only makes things worse, like votes among copies that flip 6 times in 10. The physical qubits must improve first.
  • C. Codes don’t need copies: they spread the information and use agreement checks. Several labs have run codes below the threshold, where bigger codes give fewer errors.

Check yourself

A headline reads: “Quantum computer does in minutes what would take a supercomputer longer than the age of the universe.” Going by such claims so far, what is the most reasonable reading?

  1. AIt did a task chosen to be hard to simulate, which may not be useful, and the gap may shrink as classical methods improve
  2. BThe claim must be false: nothing can beat a supercomputer by that much
  3. CToday’s encryption is now in danger, since a machine this fast could break it
  4. DQuantum computers are now faster than supercomputers at most kinds of work, not just this one
Show the answer

Answer: A. It did a task chosen to be hard to simulate, which may not be useful, and the gap may shrink as classical methods improve

Advantage demonstrations so far use tasks chosen to be hard to simulate. They show the machine can do something classical computers find very hard, not that it can do useful work, and the classical side of the comparison can improve.

Why not the others

  • B. For such tasks the gap can be real and enormous: an exact simulation doubles in cost with each added qubit. The fair caution is that the task is not useful and that classical methods may improve.
  • C. Breaking encryption needs a large error-corrected machine running billions of operations. A sampling demonstration doesn’t bring that ability with it.
  • D. Such results concern one task, chosen because it is hard to simulate. For most work an ordinary computer is still far better, and is expected to stay so.

7 / 7 · Recap

Recap

Where this course goes

Part 0 gave you the ideas in words. The rest of the course makes them precise, a small step at a time, with notation and short calculations, and you try each idea yourself as you go.

  • Part 1 · The foundations (Lessons 1–10). How a qubit is written down and measured, phase, gates, measuring in different ways, many qubits and entanglement, why an unknown qubit can’t be copied, teleportation, and Deutsch’s algorithm, the simplest case of interference letting a quantum computer use fewer steps than an ordinary one. Lesson 10 draws a map of the field.
  • Part 2 · Circuits, oracles and search (Lessons 11–18). Circuits as programs and as Python code with Qiskit, a widely used free library for programming quantum computers; then the Bernstein–Vazirani and Simon algorithms, Grover search, and how the “oracles” these algorithms consult are built.

By the end of Part 2 you can read and write small quantum circuits, run them as code, and explain how algorithms such as Simon’s and Grover’s use interference, and how much they gain.

Key ideas

  1. Qubits are built from superconducting circuits, trapped ions, neutral atoms, photons and spins in silicon, and none has clearly won. Each must be shielded from its surroundings yet reachable for control; stray contact acts like Lesson A’s watcher and causes decoherence.

  2. Today’s operations go wrong roughly once in every few hundred to few thousand. Useful algorithms need billions of operations, so errors, more than size alone, are the obstacle.

  3. Copies and a majority vote protect a bit only when each copy is reliable enough: below a threshold, more copies help; above it, they hurt.

  4. Qubits can’t be copied or read without disturbing them, so a quantum code spreads one logical qubit over many physical ones and uses agreement checks, which find errors without revealing the stored state. Several labs have now run codes below the threshold.

  5. Advantage demonstrations so far use tasks chosen to be hard to simulate, and classical methods sometimes catch up. Roadmaps are targets. Ask what the task is, what it was compared with, which qubits, whether it is a result or a plan, and who has checked it.

Go further

Free resources for when you want more than this lesson covers.

Start the interactive lesson