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Quantum error correction, and the number that actually matters

Press releases count physical qubits. The figure that decides when quantum computing becomes useful is how many of them it takes to make one that works.

8 min read

Every quantum computer announcement leads with a qubit count. It is close to the least informative number available, because those qubits are noisy, and noisy qubits do not compose into long computations.

A useful algorithm may need millions of reliable operations in sequence. Current hardware fails roughly once in a thousand. Nothing survives that gap without error correction.

Why the classical answer does not work

Classical error correction copies a bit and takes a majority vote. Neither half of that is available here. The no-cloning theorem forbids copying an unknown quantum state, and measuring a qubit to check it destroys the superposition the computation depends on.

25 physical qubits = 1 logical qubitthe flagged qubit is corrected without ever being measured directly
A surface code. One logical qubit is spread across a two-dimensional lattice of physical ones; repeated stabiliser measurements flag where an error occurred without ever reading the encoded value.

The threshold theorem

The result that makes the whole field plausible is this: if the physical error rate is below some threshold, adding more physical qubits per logical qubit suppresses the logical error rate exponentially. Above the threshold, adding qubits makes things worse, because the correction machinery introduces more errors than it removes.

For the surface code the threshold sits near one percent, which current hardware has reached. That is why the field's tone changed: the question stopped being whether error correction can work and became how expensive it is.

physical qubits per logical qubitlogical reliabilitybelow thresholdabove thresholdbelow threshold, more qubits help exponentially
Two regimes. Below the threshold every additional layer of encoding buys reliability; above it, the same additions cost you.

The overhead

Estimates for a cryptographically relevant machine have fallen substantially and remain large: on the order of a thousand physical qubits per logical qubit, and thousands of logical qubits. That multiplies to roughly a million physical qubits for a machine that could factor a 2048-bit key, against devices with hundreds to low thousands today.

  • The gap is closing from both ends: better codes reduce the ratio, and better hardware reduces the error rate that sets it.
  • Not every operation is equally cheap once encoded — some gates require expensive distillation procedures that dominate the runtime.
  • Decoding must run in real time. The classical computer that interprets the error syndromes has become a serious engineering problem of its own.

What to watch instead of qubit counts

Three numbers are informative. The physical two-qubit gate error rate. Whether a logical qubit has been demonstrated with a lower error rate than its constituent physical qubits — the break-even point, now achieved. And whether that advantage improves as the code grows, which is the real evidence that the exponential suppression is working.

One logical qubit that outlives its physical parts is worth more than a thousand that do not.

For everyone else the practical implication is unchanged: migrate anything that must stay confidential for a decade to post-quantum cryptography now, and treat the rest as a research programme to follow rather than to act on.