Lesson 7 of 9
Noise, and why the machines are cold
Explain why error correction multiplies the number of qubits a machine needs.
01 · Learn · the idea
The chip sits at a hundredth of a degree above absolute zero, colder than the space between stars. That is not flourish — it is the only way to slow the leak.
How it works
- A qubit's state is a direction, and any nudge rotates it
- Worse, the environment LEARNS about it — which collapses it decoherence
- Every gate is slightly wrong, so long circuits never run clean
- You cannot copy a qubit, and checking one destroys it so no majority vote
- Instead, spread one logical qubit over many and measure their RELATIONSHIPS
- Below a ~1% error threshold this works; above it, more qubits make it worse
In numbers
Chance a whole circuit runs clean, at 1 error per 1,000 gates
The horizontal axis is powers of ten. A useful factoring circuit is far past a million gates, and at any error rate ever measured it never once runs clean.
Side by side
Fixing errors, two ways
The common misread
That the obstacle is building enough qubits. The obstacle is that each one is noisy: below the error threshold the rest is money and patience, and above it no amount of building helps at all.
The words
- decoherence
- the state leaking into its surroundings, which measure it by accident
- logical qubit
- one reliable qubit built out of about a thousand unreliable physical ones
- threshold
- the error rate below which adding more qubits helps and above which it hurts
Carry this
“A 1,000-qubit machine” counts physical qubits. That is headcount, not output — real, and not the number that tells you whether it works.
Full lesson
A machine that has to be colder than space
A quantum computer is mostly refrigerator. The chip itself is a small thing at the bottom of a chandelier of gold-plated plumbing, and the plumbing exists to hold it near absolute zero — a hundredth of a degree above it, colder than the space between stars.
That is not engineering flourish. It follows directly from what a qubit is.
A qubit’s state is a direction, and a direction is a delicate thing. Any nudge from outside rotates it: a passing stray magnetic field, a vibration, a stray photon, the ordinary jostling of warm atoms. Worse, the outside does not merely disturb the state — it learns something about it. And by item 6’s rule, anything that learns about a quantum state collapses it.
So the environment is constantly, accidentally measuring your computer. The name for that leak is decoherence, and cold is how you slow it down.
The clock you are racing
Two numbers set the whole problem.
A qubit holds its direction for something on the order of a fraction of a millisecond. A single gate takes tens of nanoseconds. Divide one by the other and you get a budget: a few thousand operations, maybe tens of thousands, before the state is mush.
Meanwhile every gate is itself slightly wrong. Say the error rate is 1 in 1,000 — a good figure, hard-won. The chance a whole circuit runs clean is (1 − 0.001) raised to the number of gates:
- 100 gates: 90% chance of a clean run
- 10,000 gates: 0.005% — about 1 run in 22,000
- 1,000,000 gates: indistinguishable from zero
A useful factoring circuit is far past a million gates. At any error rate a physicist has ever measured, it never once runs clean. This — not the qubit count in the headline — is the thing standing between the machines that exist and the machines that are promised.
Why you cannot fix it the ordinary way
An ordinary computer handles noise cheaply. Store each bit three times. If two copies say 1 and one says 0, the odd one out is wrong. Majority vote, done.
Neither half of that works here.
You cannot copy. There is a result called the no-cloning theorem which says that an unknown quantum state cannot be duplicated. Not “is hard to”; cannot. It falls straight out of the same mathematics as everything else in this course.
You cannot look. Even if you had copies, checking them means measuring them, and measuring collapses the very state you were protecting.
So error correction here has to do something that sounds impossible: detect an error without learning the value.
The move that works, and what it costs
The answer is to stop asking about individual qubits and ask about relationships between them.
Spread one useful qubit — a logical qubit — across a large patch of physical ones. Then repeatedly measure things like “do these two neighbours still agree?” That question has an answer that does not depend on what the qubits actually are, so asking it reveals an error without revealing the state. Errors show up as a pattern of disagreements, and the pattern says where to correct.
It works. And it is enormously expensive.
At a physical error rate around 1 in 1,000, the leading scheme needs roughly a thousand physical qubits to make one reliable logical qubit. So the arithmetic for a serious task runs like this:
- A useful factoring run: a few thousand logical qubits
- At about a thousand physical each: a few million physical qubits
Set that beside machines built out of a few hundred noisy physical qubits, and the distance is not a matter of tuning. That gap is the subject.
The threshold, which is the real news
There is one genuinely encouraging result underneath all this, and it is worth stating precisely because it is what makes the whole field a serious engineering programme rather than a hope.
If the physical error rate is below a threshold — around 1%, depending on the scheme — then adding more physical qubits per logical qubit drives the logical error rate down exponentially. Below the threshold, the problem is money and patience.
If the error rate is above the threshold, adding more qubits makes things worse: the extra machinery introduces errors faster than it removes them.
So it is not a dial that gets slowly better. It is a cliff with a wrong side and a right side. Getting across it, rather than building something big, has been the real work.
What the number in the headline is doing
You now have the tool to read one of the most misleading figures in technology journalism. “A 1,000-qubit machine” almost always means a thousand physical qubits, uncorrected. In logical terms — qubits you could actually run a long computation on — that may be one, or none.
It is the same shape as a company announcing headcount instead of output, or a country announcing hospital beds instead of treatments. The number is real. It is simply not counting the thing that would tell you whether it works.
02 · Try · the lab
03 · Check · quick quiz
1. Why can't quantum computers use the classical trick of storing each bit three times and taking a majority vote?
- An unknown quantum state cannot be copied, and checking the copies would collapse them
- Three copies is not enough; quantum noise needs at least five
- The copies would decohere at different rates and drift apart
- It works, but the refrigerator cannot hold three times the hardware
Answer
An unknown quantum state cannot be copied, and checking the copies would collapse them — Both halves fail. No-cloning forbids the copies, and measuring to compare them destroys the state you were protecting. Correction instead measures relationships, which reveal an error without revealing the value.
2. A machine's physical error rate sits just above the error-correction threshold. What does adding more physical qubits per logical qubit do?
- Makes it worse — the extra machinery adds errors faster than it removes them
- Improves it, just more slowly than below the threshold
- Has no effect until the rate drops below the threshold
- Improves it exponentially, the same as below the threshold
Answer
Makes it worse — the extra machinery adds errors faster than it removes them — It is a cliff, not a dial. Below the threshold more qubits drive logical errors down exponentially; above it they drive them up. Getting across has been the real work.
3. An announcement says a machine has 1,000 qubits. What does that most likely mean?
- 1,000 physical qubits, uncorrected — which may be one logical qubit, or none
- 1,000 logical qubits, enough for a serious factoring run
- 1,000 qubits that have each been error-corrected individually
- 1,000 simultaneous operations per second
Answer
1,000 physical qubits, uncorrected — which may be one logical qubit, or none — At about a thousand physical qubits per logical one, a thousand physical qubits is roughly one usable qubit. The number is real; it is just not counting the thing that would tell you whether it works.