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Friday, June 12, 2026

Fault Tolerance: Computing Right Through the Noise

A quantum computer built entirely from unreliable parts can still run a flawless calculation. That is the audacious claim of fault toleranceThe milestone where a quantum computer can run long calculations correctly despite ongoing errors. It is the field's holy grail., and it sounds impossible right up until you see how a single threshold makes it true.

More than error correction

The thing fault tolerance is, is the ability to run a long computation correctly even though every part of the machine, the qubitsThe basic unit of a quantum computer. Like a 'bit' in a normal computer, but instead of being only 0 or 1 it can be 0, 1, or a blend of both at once., the gates, the measurementsReading a quantum system, which forces it out of its blend of possibilities into a single definite 0 or 1 and ends its quantum behaviour., is itself unreliable, constantly leaking its state to the environment through decoherenceThe loss of a qubit's quantum information as it interacts with the outside world. The main reason qubits are fragile..1 It is a steeper demand than error correctionTechniques that combine many shaky physical qubits into fewer reliable ones, so a long calculation stays correct.: storing a logical qubitA reliable 'qubit' built by bundling many error-prone physical qubits together with error correction. These are the units that actually matter for useful computing. safely is one thing, computing on it is another.

An error-corrected memory only has to hold still. A fault-tolerant computer has to keep working while it corrects itself.

Every operation has to be built so that a single physical slip stays contained, never cascading through the entanglementA quantum link where two qubits' states become tied together, so acting on or measuring one affects the other. It is a key resource for quantum computing. into a failure too large to fix.2 An error-corrected memory only has to hold still; a fault-tolerant computer has to keep working while it corrects itself.

A conceptual graph of the fault-tolerance threshold. As the code grows, the logical error rate falls if the physical error rate is below the threshold, but rises if it is above. The threshold sits near one percent.
Figure 1: The threshold theorem in one picture. Below a critical physical error rate (near 1 percent), making the code bigger drives the logical error rate down; above it, scaling only makes things worse.

The threshold theorem

Why believe this is even possible? Because of one of the deepest results in the field, the threshold theorem, proved in the late 1990s.3 It says something almost too good to be true: if the error rate of your physical hardware sits below a certain critical value, you can make a computation as reliable as you like, of any length, by spending only a modest and slowly growing amount of extra hardware.2 Below the line, scaling up rescues you; above it, scaling up buries you, piling on errors faster than the code can remove them. For the leading surface codeThe leading error-correction scheme for superconducting qubits. It needs many physical qubits to protect one logical qubit. approach, that line sits near 1 percent.1 It is the result that turns “the noise always wins” into a budget you can actually hit.

The dividing line

This is the Rubicon of quantum computing. On one side sit today's machines, still noisy enough that their encoded qubitsThe basic unit of a quantum computer. Like a 'bit' in a normal computer, but instead of being only 0 or 1 it can be 0, 1, or a blend of both at once. often decay faster than their best raw ones; no device has yet crossed the line for a full computation. On the other sits a computer that can run for as long as a problem demands.4 The gap matters because the real prizes are long: Shor's factoring algorithm needs millions of operations in a row, and at a physical error rate of even a tenth of a percent an unprotected machine would collapseThe instant a measurement forces a qubit from a blend of possibilities into one definite classical value. almost immediately.

The honest question is not whether a press release says “fault-tolerant,” but whether the logical qubits beat the physical ones, and keep improving as the machine grows.

I will be honest about the price. Fault toleranceThe milestone where a quantum computer can run long calculations correctly despite ongoing errors. It is the field's holy grail. is not free, and it is not close. It demands enormous overhead, thousands of physical qubitsAn actual piece of qubit hardware. On its own it is fragile and makes frequent errors. for every logical one, plus special tricks like magic state distillationSpending many noisy magic states to purify a few clean ones, needed for the gates that error correction cannot perform directly. to build the gates error correctionTechniques that combine many shaky physical qubits into fewer reliable ones, so a long calculation stays correct. cannot make directly.1 But it is the only known road from a fascinating prototype to a real tool, and every gain in the underlying qubit lowers the bill. Recent experiments have just crossed below the threshold for the first time,4 which is why the honest question about any machine is not whether its press release says “fault-tolerant,” but whether its logical qubitsA reliable 'qubit' built by bundling many error-prone physical qubits together with error correction. These are the units that actually matter for useful computing. truly beat its physical ones and keep improving as it grows.

Sources

  1. Terhal, B. M. “Quantum Error Correction for Quantum Memories.” Reviews of Modern Physics 87, 307–346 (2015). DOI: 10.1103/RevModPhys.87.307.
  2. Preskill, J. “Reliable Quantum Computers.” Proceedings of the Royal Society A 454, 385–410 (1998). DOI: 10.1098/rspa.1998.0167. Preprint: arXiv:quant-ph/9705031.
  3. Aharonov, D. & Ben-Or, M. “Fault-Tolerant Quantum Computation with Constant Error Rate.” SIAM Journal on Computing 38, 1207–1282 (2008). DOI: 10.1137/S0097539799359385. Preprint: arXiv:quant-ph/9906129.
  4. Google Quantum AI. “Quantum Error Correction Below the Surface Code Threshold.” Nature 638, 920–926 (2025). DOI: 10.1038/s41586-024-08449-y. Preprint: arXiv:2408.13687.