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Quantum computers need error-correcting codes because physical qubits and the operations performed on them are imperfect. A code spreads one logical qubit across multiple physical qubits, checks the encoded state indirectly, and uses those check results to guide a recovery. If the decoder chooses the wrong recovery, the system can end up back in the code’s valid state space—but with the logical information changed.
Why do quantum computers need error-correcting codes?
Quantum information is vulnerable to noise from interactions with the environment and faults in gates, measurements, and other operations. Errors can accumulate while a computation stores and manipulates qubits. A single physical fault may be correctable, but a useful calculation involves many operations, so reliability depends on managing errors throughout the computation.
Quantum error correction encodes information across several physical qubits as a logical qubit. The code defines which combinations of physical-qubit states represent valid logical information. Instead of measuring that information directly, the system measures code checks. Their results, called a syndrome, provide clues about errors while preserving the encoded state. A decoder interprets the syndrome and selects a recovery.
This is not ordinary copying of an unknown quantum state. The code protects information through an encoded subspace and indirect checks; it does not make independent readable copies of the state.
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What is a logical qubit, and how does a correction cycle work?
- Encode: Represent the information in a logical qubit using a code spread across physical qubits.
- Check: Measure stabilizers or other code checks. The resulting syndrome indicates which error patterns are plausible without directly reading the logical state.
- Decode: Use a decoder to infer a likely error pattern from the syndrome and the assumed noise model.
- Recover: Apply a correction, or account for it in later operations, to restore the intended logical information.
The syndrome is evidence about an error, not necessarily a unique identification of the microscopic fault. Different physical error patterns can produce the same syndrome, so the decoder chooses a recovery that is likely to work under the code and noise assumptions.
What happens when quantum error correction fails?
Let E represent the physical error and R the recovery chosen by the decoder. A logical decoding failure occurs when their combined effect, R E, is a logical operator that changes the encoded information. The recovery may put the system back into the code space, so the checks can look valid even though the logical state has been altered. A later measurement or computation can then yield the wrong logical result.
A syndrome event by itself is not a logical failure: many physical errors are detected and corrected successfully. Failures can arise in several ways:
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- The error exceeds the code’s capability: Too many errors, or an especially damaging pattern, can leave no recovery that restores the logical information.
- The noise differs from the decoder’s assumptions: Correlated faults or other noise patterns not well represented by the model can make the decoder’s choice less reliable.
- The checks are faulty: Syndrome measurements use physical operations too, and errors in those operations can mislead the decoder. Noisy check measurements may require repeated rounds of syndrome extraction.
- The decoder chooses the wrong recovery: Because a syndrome can be consistent with multiple underlying faults, the most likely recovery under the model is not guaranteed to be the right one for a particular run.
These mechanisms are distinct. A logical failure is the residual error in the encoded information after decoding and recovery, not simply any physical-qubit fault.
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1Clear out junk files and repair common Windows errors2Fix the driver behind crashes, sound loss and screen glitches3Repair Windows errors before they cause bigger problemsWhat does code distance mean?
Code distance, usually written d, describes a code’s ability to distinguish and protect logical information. For a code of distance d, the standard guarantee is correction of up to ⌊(d − 1)/2⌋ errors under the code’s assumptions. That relation is a capability statement, not a promise that every larger error fails or every smaller error is harmless in a real device with faulty operations.
Increasing distance generally requires more physical resources. It improves logical reliability only when the code, device noise, syndrome-extraction process, and decoder work together so that scaling the code actually reduces the logical error rate.
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What does a threshold mean?
A threshold is conditional on a code family, noise model, implementation, and decoder. Below the relevant threshold, increasing code size can reduce logical error; above it, adding resources may not help and can make performance worse. There is no single threshold percentage that applies to all quantum computers.
When comparing a threshold or error rate, check whether the number describes physical errors, logical errors, or an end-to-end computation; also check the code, noise assumptions, decoder, and experimental setup. A code’s performance under one model does not establish the same performance on different hardware or for another kind of noise.
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Correcting data-qubit errors is not enough if gates, ancilla qubits, measurements, or syndrome processing introduce faults that spread through the computation. Fault-tolerant protocols are designed to limit that spread and keep correction effective while logical operations are performed. They therefore use additional operations and often extra ancilla qubits.
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Resources are also needed to process syndrome data quickly enough and to implement the logical gates and circuit depth a computation requires. A code that can preserve a logical state is not automatically sufficient for a large computation: the full circuit must be executable with an acceptable logical error rate.
One scale estimate illustrates why overhead is code-specific. IBM’s Quantum Computing Blog reports that researchers benchmarking a honeycomb code estimated 7,000 physical qubits for one logical qubit at a logical error rate of one in a trillion. This is a reported estimate for that code and target, not a universal requirement for every logical qubit or architecture. IBM Quantum Computing Blog: Building the future of quantum error correction.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.How do error correction, detection, mitigation, and suppression differ?
| Approach | What it does | Main trade-off |
|---|---|---|
| Error detection | Uses checks to identify evidence of an error or an invalid run. | Detection alone does not restore the encoded information. |
| Error correction | Uses syndrome information and a decoder to choose a recovery intended to preserve logical information. | Requires encoding and additional operations; it can still fail. |
| Error mitigation | Uses strategies to reduce or estimate the effect of errors in results without necessarily correcting errors during the computation. | Does not by itself provide fault-tolerant protection for arbitrarily long computations. |
| Error suppression | Reduces the occurrence or impact of errors through device or circuit techniques. | Suppression helps but is not the same as encoding and correcting logical information. |
Some approaches use post-selection: they reject runs that fail specified checks. That can improve the reliability of retained results, but discarded runs increase sampling cost, and errors that evade the checks can remain. Post-selection is therefore a trade-off between run rejection and reliability, not proof that all errors have been removed.
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Are today’s quantum computers fault tolerant?
As of October 2026, the cited demonstrations should be described with their device, code, metric, and conditions—not as evidence that arbitrary long quantum computations are already fault tolerant. Google Quantum AI describes its result as a logical-qubit prototype in which increasing the number of qubits in an error-correction scheme reduced errors. That is a meaningful prototype claim, but it does not establish error-free operation or fault tolerance for every workload.
A separate IBM Research study published on November 28, 2024, examined exclusive decoders that abort on decoding instances judged too difficult, combining post-selection with surface-code correction. Its abstract reports up to a quadratic improvement in logical failure rates below threshold. The study also reports thresholds of 50% under depolarizing noise and 32(1)% in its fault-tolerant case for the most discriminating exclusive decoders. These figures belong to that study’s defined setup; they are not general hardware thresholds or a universal result for post-selection.
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