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Logical Qubits Explained: What Willow's Error Correction Proved

What a logical qubit is, why error correction matters, and what Google's Willow and other published milestones do and don't say about quantum risk.

By CyphrQ.ai

Written with AI assistance and human editorial review. Every figure linked to its source.

10 min read

A logical qubit is one reliable unit of quantum information, stored across many error-prone physical qubits so that mistakes can be spotted and corrected. In 2024 Google showed that adding more physical qubits to a logical qubit made it more reliable, not less. That is the milestone called "below threshold". It is a necessary step, not the finish line.

Quantum computer headlines usually count qubits. The number that decides whether a quantum computer is useful is how many of them you can trust.

What is a physical qubit, and why does it make mistakes?

A physical qubit is the actual hardware element, such as a tiny superconducting circuit or a trapped ion. It holds a quantum state, and that state is fragile. Heat, stray electromagnetic noise and imperfect control pulses all disturb it.

Disturbances show up as errors in every operation. A classical bit in your laptop almost never flips by accident. A physical qubit does so often enough that a long calculation would be ruined well before it finished.

You can't fix this by copying the qubit and taking a majority vote, as a classical system might. Quantum states can't be copied, and measuring one directly destroys the information you were trying to protect. Error correction has to work around both problems.

What is a logical qubit?

A logical qubit is a qubit encoded across many physical qubits, together with the ongoing checking that keeps it intact.

The extra qubits don't each store a piece of your answer. Some hold the data. Others are measured over and over, in rounds called cycles, to reveal where an error probably happened without revealing the stored value. A classical program called a decoder reads those measurements and decides which correction to apply.

That is why "logical qubit" is not a hardware count. It is a claim about performance: this encoded qubit fails less often than the physical qubits it is built from.

What is quantum error correction in simple terms?

Quantum error correction is a way of spreading one qubit's information over many qubits so that errors can be detected and undone without reading the information itself.

The idea is old. Google Quantum AI's announcement credits Peter Shor with introducing quantum error correction in 1995. For three decades the catch was the same: encoding adds more qubits, more qubits add more places for errors, and so the encoded qubit could end up worse than a single bare one.

Whether it ends up better depends on one thing: how good the physical qubits are.

What does "below threshold" mean?

"Below threshold" means the physical qubits are good enough that making the code bigger lowers the logical error rate instead of raising it.

Think of it as a tipping point. Above it, every qubit you add to the code brings in more errors than it removes. Below it, each step up in size makes the logical qubit more reliable, and the improvement compounds.

The size of a code is called its distance. A larger distance means more physical qubits and more errors the code can survive. Distance is the dial the experiment turns.

What did Google's Willow actually show?

Google's Willow chip has 105 qubits. The team used it to run a surface code (a common error-correcting layout that arranges qubits in a grid) at three sizes, "from a grid of 3x3 encoded qubits, to a grid of 5x5, to a grid of 7x7", and found that "we were able to cut the error rate in half" with each step (Google, December 2024).

The Nature paper, Quantum error correction below the surface code threshold, gives the precise figures. Its abstract is on arXiv:

Measure Figure in the abstract
Qubits in the distance-7 code 101
Logical error per correction cycle (distance 7) 0.143% ± 0.003%
Suppression per step up in distance (Λ) 2.14 ± 0.02
Logical memory lifetime vs best physical qubit 2.4 ± 0.3 times longer
Decoder latency (distance 5) 63 microseconds on average
Cycle time 1.1 microseconds

Three of those deserve a plain reading.

  • Λ of 2.14 is the "cut in half" in numbers: each time the distance goes up by two, the logical error rate falls by a factor of about 2.14.
  • 2.4 times longer means the encoded qubit lasted longer than the best single qubit on the same chip. That is called going "beyond break-even", and Google's post calls it "an unfakable sign that error correction is improving the system overall."
  • Real-time decoding matters because a decoder that lags behind the hardware is useless. The abstract reports the decoder keeping up for up to a million cycles.

What didn't Willow show?

It showed a good memory, not a computer. The experiment kept a logical qubit alive. It did not run a useful calculation on logical qubits.

The authors are open about a limit. In repetition-code tests up to distance 29, performance was limited by "rare correlated error events occurring approximately once every hour", according to the abstract. That is a floor the field still needs to push below.

Google's own post says the next challenge is a first "useful, beyond-classical" computation. It also notes that its headline random circuit sampling benchmark has no known commercial application so far.

Have other labs reported logical-qubit milestones?

Yes, and they use different hardware, different codes and different yardsticks. Two examples from the companies' own pages:

Quantinuum (trapped ions). On 19 October 2026 the company announced a logical fidelity of 99.9995% on its Helios computer, which it equates to "just five errors in a million operations", using a color code (a different error-correcting layout). It reports logical errors falling by "a record factor of 12" per tested step up in code distance, and says the result is "within the target range for Apollo", a fault-tolerant machine it expects by 2029. The release says nothing about peer review, and its own forward-looking statements warn that results "may not be able to be replicated at a larger scale, in logical computation, or in commercial use."

IBM (superconducting). IBM's technology page describes a planned fault-tolerant system called Starling, due in 2029, that is meant to "run 100 million quantum gates on 200 logical qubits." That is a roadmap target, not a result.

Why can't you compare these results directly?

Because "logical error rate" depends on choices the headline hides: the code, its distance, what is measured, and which baseline is used.

Quantinuum's own comparison with Google is a useful example. It states that its 99.9995% figure is a logical memory fidelity per correction cycle, that gate performance is a separate measurement, and that quoted improvement multipliers change depending on the baseline chosen. Against one earlier color-code result it cites 1,638 times. Against a surface-code result at the same distance it cites 154 times.

None of that makes the claims wrong. It means a single number is never the whole story. Ask what was measured, at what distance, with which code, and whether it has been independently reviewed.

What does this mean for encryption?

Error correction is the gate between today's machines and a computer that could break RSA. It does not move Q-Day to this year.

For a sense of scale, a 2025 paper by Craig Gidney estimated that a 2048-bit RSA integer "could be factored in less than a week by a quantum computer with less than a million noisy qubits". The estimate assumes a square grid of qubits, a 0.1% gate error rate and a 1 microsecond cycle time. It compares with an earlier estimate of 20 million qubits for eight hours of runtime.

Compare that with Willow's 105 qubits. The gap is large, and it explains why the milestones above matter: they are the steps that make a million-qubit machine conceivable. For the plain-language version of the threat, see What Is Q-Day?. For what you can deploy today, see Post-Quantum TLS Is Already Here.

Going deeper: for security and IT teams

This section assumes you track the cryptographic risk timeline and read vendor claims for a living.

What stands between a logical memory and a cryptographically relevant machine

Breaking RSA-2048 or elliptic-curve keys needs a very long computation of logical gate operations, not a stored qubit. So read milestones on three separate axes:

  1. Memory. Does a logical qubit survive many cycles below threshold? Willow's distance 3, 5 and 7 results and Quantinuum's color-code results are on this axis.
  2. Operations. Can you run logical gates, including the expensive non-Clifford gates (usually supplied by "magic states"), with error that also falls as distance grows? Quantinuum's blog says "nobody has yet demonstrated below threshold scaling for magic state preparation", which is a company statement about the field.
  3. Scale and speed. Can you build hundreds of thousands to millions of physical qubits and run the cycle fast enough? Gidney's estimate assumes a 1 microsecond cycle and a 10 microsecond control reaction time.

A milestone changes the cryptographic timeline only when it moves axis 2 or 3. Axis 1 results are necessary and they are good news for the hardware, but they leave the largest uncertainty untouched.

How the 2025 estimate shifted the target

Gidney's paper cut the resource estimate for RSA-2048 from 20 million noisy qubits (Gidney and Ekerå, 2019, eight hours) to under a million (2025, under a week), without any new hardware. The reduction came from algorithm and error-correction improvements. Treat resource estimates as a moving target: the same machine can get more capable on paper as algorithms improve, so threat timelines should be reviewed on a schedule, not set once.

How to read a vendor roadmap claim

Use this checklist when a roadmap or press release arrives:

Question Why it matters
Is it a result or a target? IBM's Starling and Quantinuum's Apollo are 2029 targets, and Quantinuum's release says it "may not achieve its technology roadmap" on time or at all.
Memory, gate, or both? Memory fidelity per cycle is not gate fidelity.
Which code and distance? Color-code and surface-code numbers are not directly comparable.
Peer reviewed or press release? Google's result is a Nature paper. Quantinuum's October 2026 release does not state a review status.
Is there postselection? Discarding failed attempts can improve a headline error rate. Quantinuum's blog discusses this for another group's result.
Which baseline gives the multiplier? The same result can read as 154 times or 1,638 times better.
Physical qubits per logical qubit? This sets the machine size. Quantinuum's release says up to 37 for its color code and 10 for its Helix code.

What to do with this in a risk register

  • Keep the migration deadlines from NIST and the NCSC, listed with sources in What Is Q-Day?, as your planning basis. They are set by policy, not by any one lab milestone.
  • Track long-lived data. Harvest-now-decrypt-later risk exists regardless of when a machine arrives.
  • Add a standing review item: when a lab reports logical operations, not just memory, below threshold at scale, re-read your timeline assumptions.
  • Ask each vendor with a "quantum-safe" claim which standardised algorithms they support, rather than which quantum milestones they cite. Standards, not physics headlines, are what you can deploy.

I haven't found a published result that shows a fault-tolerant machine running cryptographically relevant computations, and I'd treat any claim that says otherwise as needing a primary source.

Learn more

Key takeaways

  • A logical qubit is an encoded qubit that fails less often than the physical qubits it is made from.
  • "Below threshold" means a bigger code gives a more reliable logical qubit. Google's Willow showed this at distances 3, 5 and 7 with a suppression factor of 2.14 per step.
  • Willow showed a stable memory, not a useful computation. Quantinuum's and IBM's claims are company statements and 2029 targets that need the same questions.
  • Compare results by code, distance, memory versus gates, review status and baseline.
  • For your risk plan, rely on NIST and NCSC migration dates and ask vendors about standardised algorithms, not lab milestones.

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