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Logical quantum circuits still produce errors because error correction suppresses faults; it does not make the physical gates, measurements, resets or idle periods perfect. A reported logical error rate is meaningful only alongside its code, hardware conditions, decoder, circuit and data-analysis method. The same phrase can describe measurements that are not directly comparable.
What a logical qubit protects—and what it cannot prevent
A logical qubit is encoded across multiple physical qubits so that information is stored nonlocally rather than in one fragile device. In a surface code, the processor repeatedly measures stabilizers, or parity checks. Those measurements produce a syndrome: clues about faults that may have occurred, without directly measuring the encoded quantum state.
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A decoder analyzes the syndrome, often including its history across repeated rounds, and infers which physical faults are most likely. The system can use that inference to select a correction, or use it when decoding the final logical measurement. The process makes certain errors detectable and correctable, but it is itself implemented with imperfect physical operations. A bad gate, measurement, reset or idle period can introduce faults; the syndrome-extraction process can also fail, and the decoder can infer the wrong correction.
Encoding therefore changes the way errors affect information; it does not guarantee that every output is right. A circuit may produce a logical error if physical faults accumulate into an error pattern the code cannot correct, or if the decoder misinterprets the observed syndrome. More physical qubits and more correction rounds can improve protection in the right operating regime, but they also create more operations and more opportunities for faults.
Why a larger code can help—or hurt
Code distance is a measure of how many physical errors must combine before an undetectable logical error can occur. Increasing distance can make a logical fault less likely when the physical operations are sufficiently reliable and the code, syndrome circuit and decoder work well together. But a larger lattice requires more qubits and operations. If physical error rates are too high, the extra faults can outweigh the added protection.
The dividing point is called a threshold, but it is not one universal error-rate limit for every processor. It depends on the code, noise model, syndrome-extraction circuit and decoder. Google Research’s 2024 explanation describes the threshold as the critical rate below which error correction changes from harmful to helpful. A result below one threshold under one model does not establish that another code or device is below its own relevant threshold.
Why logical circuits still fail
There is no single universal error budget. The dominant causes depend on the hardware and protocol being tested. A 2023 Nature study of a Google surface-code experiment identified controlled-Z gate errors and data-qubit decoherence while qubits waited through measurement and reset as dominant modeled contributors for that device and protocol. Its analysis also considered measurement and reset errors, leakage, unwanted interactions and high-energy events. That is an illustrative experiment-specific budget, not a ranking that can automatically be applied to every quantum architecture.
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Entangling gates, single-qubit operations, measurements and resets can all be imperfect. A fault can affect the data qubits, the ancillas used for checks, or the recorded syndrome. If the syndrome is wrong, the decoder is reasoning from faulty evidence as well as from a potentially faulty quantum state.
Errors during waiting and repeated checks
Qubits can lose coherence while idle, including while the device performs measurement and reset elsewhere in the syndrome cycle. Repeating checks is necessary to track errors over time, but each round takes operations and time. A memory measured over many rounds and a computation containing logical gates therefore expose the encoded state to different combinations of risks.
Leakage, correlations and unusual events
Some faults do not behave like the simple error models often used to explain a code. Leakage can move a physical qubit outside the computational states the code expects; unwanted interactions can correlate faults; and high-energy events can affect multiple qubits or rounds. Correlated or poorly modeled faults can make the observed performance differ from a prediction based on independent, identical errors.
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Decoder limits and data selection
Decoding is an inference step, not a direct view of the true fault history. Decoders can trade accuracy against speed, and their choices affect the result. Some approaches post-select: they reject runs or difficult decoder instances rather than returning an answer for every attempt. The accepted data may then look more accurate, but the cost includes discarded runs, additional repetitions or other resource overhead.
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IBM Research’s 2024 discussion of exclusive decoders reports a 50% threshold under depolarizing noise for its most discriminating exclusive decoder and 32(1)% for the fault-tolerant case. Those figures belong to the stated decoder and conditions; they are not a general physical-error threshold for quantum computers. The decoder and rejection policy are part of what the reported performance means.
Post-selection also changes the operational question. If a decoder aborts when it encounters a difficult syndrome, the reported error rate can describe only the answers it accepts. To assess the tradeoff, ask how often it aborts, how many extra attempts are needed to obtain accepted data, and whether the reported resource cost includes that overhead. IBM’s 2026 Qiskit Paulice article describes an open-source research toolkit for exploring syndrome post-selection and its resource tradeoffs; it is a way to investigate these choices, not a consumer product or a guarantee that post-selection is cost-free.
What “logical error rate per cycle” means
A logical error per cycle is an estimate of how often a logical error occurs per unit of the experiment’s repeated error-correction process. The precise definition depends on the study’s protocol and analysis. It is not automatically the probability that a complete application circuit will return a wrong answer, nor is it interchangeable with a logical-gate error rate, a memory lifetime, circuit fidelity or a lower bound on output fidelity.
These metrics answer different questions. A memory experiment asks how reliably encoded information persists under repeated checks. A logical-gate experiment asks how an operation transforms encoded information. A circuit-level experiment combines operations into a particular sequence and measures a circuit-level outcome. A fidelity estimate describes agreement with a target state or output under the study’s chosen definition. The metric’s denominator and measured observable determine what can be inferred.
Even if cycles were independent—which a real device need not guarantee—a per-cycle rate alone would not predict application performance. An application depends on its gate sequence, depth, correlations, fault-tolerant operations and other details. Multiplying a per-cycle rate into an application forecast is justified only if the study supports the assumed noise and independence model.
How to read a published logical-error result
Read the protocol before treating a headline number as a comparison. A useful result identifies the quantity measured, how it was normalized, the code and decoder, the physical-qubit set, and the number of correction rounds. It also explains how the data were selected and what uncertainty accompanies the estimate.
- Identify the metric and denominator. Determine whether the figure is per correction cycle, per logical gate, per completed circuit, a memory lifetime or a fidelity estimate. Check what counts as an error and which outcomes were measured.
- Identify the code and scale. Look for the code family and distance, the number of logical and physical qubits, and how many syndrome rounds were run. A code-distance label alone does not describe the whole experiment.
- Check the operating conditions. Find the stated physical error rates and the noise assumptions. If the paper discusses a threshold, establish that it applies to the experiment’s code, syndrome circuit and decoder.
- Read the decoder and data treatment. Check whether the decoder returns an answer for all runs or rejects some; look for post-selection, rejection rates, excluded events and the number of repetitions. A lower error among retained data can come with a cost in accepted data or resources.
- Inspect the comparison design. Ask whether results come from the same device under matched conditions, or from different devices or code instances. If the authors compare an average across subcodes, do not treat it as the performance of every subcode.
- Read uncertainty and fitting choices. Review error bars or confidence intervals, the fitting window, and any stated analysis choices that affect the estimate. A point estimate without this context is not enough for a clean comparison.
- Match the conclusion to the experiment’s scope. A memory result supports a claim about that memory protocol. It does not, by itself, establish low error for arbitrary logical gates or a useful full application circuit.
Analysis decisions are not footnotes to ignore. In its 2023 Nature report, the Google team specified a fitted range, and discussed a high-energy event that affected its repetition-code result. Such details help explain how a headline estimate was obtained and whether an unusual event or a chosen fit changes its interpretation. Compare like with like: a fitted rate over a specified range is not automatically the same quantity as a raw count over all observations.
What recent demonstrations actually show
Published numbers illustrate why the protocol and metric must travel with the headline. These results are not a simple league table: they use distinct experiments, and the 2023 and 2024 Google results should not be compared numerically without reconciling their metrics and protocols.
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| Demonstration | Reported result | How to interpret it |
|---|---|---|
| Google Quantum AI authors, Nature, 2023 | 2.914% ± 0.016% logical error per cycle for distance 5, versus 3.028% ± 0.023% for the average of selected distance-3 subcodes | The reported fitted comparison corresponds to about a 4% relative reduction using the study’s decoder and fit. The distance-5 code was slightly worse than two individual distance-3 codes, so the average does not mean it beat every smaller code. |
| Google Research, 2024 | 2.14-fold encoded-error suppression at each increase from a 3×3 to 5×5 to 7×7 lattice | Google also reported that the resulting logical-qubit lifetime exceeded twice that of its best constituent physical qubit. This is a separate experiment from the 2023 comparison. |
| IBM and University of Chicago announcement, July 30, 2026 | 70 logical qubits, 2,415 logical two-qubit operations and 468 logical T gates | The organizations said the encoded-circuit demonstration achieved effective logical error rates ten times lower than physical error rates. This is an announcement-level claim; its numbers should be attributed to IBM and the University of Chicago unless the underlying paper and verification method have also been examined. |
The 2023 Nature authors described their work as the first experimental demonstration in which quantum error correction began to improve performance as qubit number increased. That conclusion is specific to the result and comparison they reported. The modest average improvement—and the fact that two individual distance-3 subcodes performed better than distance 5—shows why “larger code” is not synonymous with “lower error in every comparison.”
The 2024 Google result is notable for a different reason: it reports suppression as the lattice grows from 3×3 to 5×5 to 7×7, alongside a logical lifetime more than twice that of the best constituent physical qubit. It should be read on its own terms rather than treated as a continuation of the 2023 result on a shared scale. Different protocols and definitions can make numerical rankings invalid even when both experiments demonstrate progress.
The IBM and University of Chicago figures likewise describe a circuit-level demonstration rather than a memory-only result. Bill Fefferman, associate professor at the University of Chicago, said the experiment “develops techniques to better characterize the fidelity of hard quantum states under noise, increasing confidence that the quantum computer is solving a computationally hard problem.” That statement explains the organizations’ stated motivation; it is not a substitute for examining how the circuit was verified or what its effective error measure covers.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Does a below-threshold result mean a computer is fault tolerant?
No. A below-threshold result means that, under the study’s specified conditions and model, increasing code size can improve protection. It does not by itself prove that every logical operation is reliable, that a large circuit will finish correctly, or that the machine can run a useful application at scale.
Fault tolerance is a circuit-level property: the system must control errors while carrying out the operations needed for a computation. A logical memory that lasts longer as its code is scaled is important evidence about memory protection, but it does not establish the error rate of arbitrary logical gates or a complete algorithm. Likewise, a circuit demonstration provides evidence about its tested operations and verification procedure, not every possible workload.
“Below threshold” is therefore a conditional statement, not a finish line. It refers to a relationship between code scaling and error under specified conditions. To judge what it says about a particular processor, look for the threshold’s noise assumptions, the correction circuit and decoder used, and whether the experiment measured a memory, a gate or a circuit. Even a positive scaling trend leaves practical questions about the errors and resources required for longer computations.
How to compare two logical-qubit claims fairly
Before ranking two published error rates, align the conditions that give those rates meaning. If the studies report different observables or use different selection rules, a single numerical comparison can mislead even when both numbers are accurately reported.
- Metric: compare per-cycle rates with per-cycle rates, or circuit fidelities with circuit fidelities; do not substitute one for another.
- Code and scale: compare code family, distance, logical and physical qubit counts, and correction-round count.
- Operating regime: check physical error rates and the relevant threshold assumptions.
- Decoder and data handling: account for decoder type, post-selection, rejected runs, excluded events and repetitions.
- Comparison design: distinguish same-device comparisons from cross-device comparisons and single instances from averages across subcodes.
- Uncertainty and scope: compare stated uncertainty, measured observable, circuit depth and whether the work tests a memory or multi-gate computation.
If these details are missing or substantially different, report the figures as separate experiment-specific results rather than declaring one platform or code categorically better. In particular, an error per cycle cannot stand in for an application success probability, and a selected-data result cannot be compared fairly with an all-runs result without accounting for the selection cost.
Frequently Asked Questions
Why do logical qubits still have errors?
A logical qubit is encoded and protected, not made error-free. Physical gates, measurements, resets and idle periods can still fail; syndrome checks can be noisy, leakage and correlated faults can complicate the error pattern, and a decoder can infer the wrong correction.
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What does logical error rate per cycle mean?
It estimates logical failures per unit of a study’s repeated error-correction process. The exact cycle and failure definition depend on the protocol. It is not automatically a logical-gate error rate or the probability that an entire application returns a wrong answer.
Does a below-threshold result mean the quantum computer is fault tolerant?
No. It means scaling the code can improve protection under the specified code, noise model, syndrome circuit and decoder. It does not establish low error for every logical operation or a useful full application circuit.
How do I compare logical qubit error rates?
First align the metric and denominator, then compare code family and distance, correction rounds, hardware conditions, decoder, post-selection and rejected data, repetitions, uncertainty, and whether the result is for a memory or a circuit. Treat results with different protocols as separate demonstrations rather than a simple ranking.
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Repair common Windows errors and clear accumulated junk for a smoother, more stable PC - no reinstall needed.Free scan · no reinstallCan I estimate an application’s success rate by multiplying a per-cycle error rate?
Not without additional assumptions supported by the experiment. Such a calculation would require an appropriate model of the circuit’s gates and depth, correlations, fault-tolerant operations and cycle independence; real devices do not necessarily have independent errors.
Does post-selection improve logical performance for free?
No. Rejecting difficult runs can improve the apparent accuracy of retained results, but it reduces accepted data and can require additional repetitions or other resources. A fair report includes the rejection policy and its overhead.
The Bottom Line
Logical circuits still fail because encoding and syndrome-based correction suppress errors rather than eliminate noisy operations or decoder mistakes. Treat every logical-error figure as conditional on its metric, code, hardware, decoder, data selection and analysis. A larger code or a below-threshold result is evidence of progress under stated conditions—not proof that arbitrary quantum applications will run without error.
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