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Logical quantum circuits can still produce wrong results because quantum error correction suppresses faults; it does not make the physical gates, measurements, resets, and idle periods perfect. A reported logical error rate describes a particular code, processor, decoder, circuit, and analysis—not a universal guarantee that every encoded computation will work. To judge a result, first identify exactly what was measured and what the number’s denominator is.
Why do logical qubits still have errors?
A logical qubit stores quantum information across multiple physical qubits rather than in one device element. In a surface code, repeated stabilizer or parity checks reveal information about errors without directly measuring the encoded logical state. The changing pattern of check outcomes—the syndrome—gives a decoder evidence about which faults may have occurred. The decoder can use that evidence to choose a correction or to interpret the final logical measurement.
That protection is not a shield around perfect components. The physical qubits and the operations that extract their syndromes remain noisy. Gates can fail; measurements can be misread; resets may leave a qubit in the wrong state; and a qubit can lose its quantum information while waiting. Leakage, unwanted interactions, and faults in the decoding process or its inputs can also matter. Because the syndrome-extraction circuit itself uses noisy operations, the act of checking for errors creates further opportunities for faults.
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There is a scaling trade-off. A larger code uses more physical qubits and typically more operations and correction rounds. That gives it more redundancy with which to identify and correct faults, but it also creates more chances for something to go wrong. Google Research’s 2024 explanation calls the dividing point the threshold: below the threshold relevant to the system, increasing code size can reduce logical errors; above it, the additional faults can outweigh the protection. The threshold depends on the code, noise model, syndrome circuit, and decoder. It is not one universal number for every processor.
So “logical” means encoded and protected, not error-free. A circuit’s output remains probabilistic, and even a well-protected logical state can suffer a logical fault that changes the encoded information. Error correction is a process that limits the risk over a specified experiment; it is not a promise that each individual run will produce the intended answer.
What does “logical error rate per cycle” mean?
A logical error rate per cycle describes failures relative to a defined unit of error-correction operation—often one round of syndrome extraction and decoding under a particular experiment’s protocol. It is not automatically an error probability per logical gate, per complete circuit, or per application. Papers may define the cycle, observable, and counting method differently, so use the authors’ definition rather than assuming all “cycles” are equivalent.
Other common outcomes answer different questions. A memory lifetime characterizes how long encoded information is retained under a specified sequence of operations. A logical-gate error concerns the performance of a particular encoded operation. Circuit fidelity or an output-fidelity bound concerns a circuit or measured output under its own verification procedure. These quantities cannot be substituted for one another without a model that connects them.
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When checking a denominator, look for what counts as one trial and one failure, whether the estimate is conditioned on successful detection or acceptance, and how many rounds or repetitions contributed. A paper may report a rate fitted from repeated measurements rather than a simple count of failures divided by a total. Those details affect how the number should be interpreted and whether another experiment measures the same thing.
What do the published demonstrations actually show?
The figures below come from different experiments, metrics, and analysis protocols. They illustrate what has been reported; they are not a leaderboard. Direct numerical comparisons require the underlying definitions and conditions to match.
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| Source and experiment | Reported result | What the result describes |
|---|---|---|
| Google Quantum AI authors, Nature, 2023, “Suppressing quantum errors by scaling a surface code logical qubit” | 2.914% ± 0.016% logical error per cycle for distance 5, compared with 3.028% ± 0.023% for the average of four selected distance-3 subcodes; about a 4% relative reduction in that comparison. | A fitted, experiment-specific distance-5 versus average distance-3 comparison using the reported decoder. The distance-5 result was slightly worse than two individual distance-3 codes. The paper describes this as the first experimental demonstration in which error correction began to improve performance as qubit number increased. |
| Google Research, 2024, Willow surface-code result | 2.14-fold encoded-error suppression at each increase from a 3×3 to 5×5 to 7×7 lattice; the reported logical-qubit lifetime exceeded twice that of the best constituent physical qubit. | A separate scaling experiment with its own device, code, and protocol. Its figures should not be compared directly with the 2023 per-cycle results without reconciling the metrics and conditions. |
| IBM and University of Chicago, announcement dated July 30, 2026 | 70 logical qubits, 2,415 logical two-qubit operations, and 468 logical T gates; the organizations report effective logical error rates ten times lower than physical error rates. | A company-announced encoded-circuit demonstration. The figures should be attributed to IBM and the University of Chicago unless the underlying paper and verification method have been independently examined. |
| Smith, Brown, and Bartlett, as summarized by IBM Research, 2024 | A 50% threshold under depolarizing noise for the most discriminating exclusive decoder, and 32(1)% for the fault-tolerant case. | Thresholds for particular decoder designs and stated conditions, not a general threshold for quantum hardware. |
The 2023 Google/Nature paper’s authors concluded that their result marked the first experimental demonstration where quantum error correction began to improve performance with increasing qubit number. That is a bounded claim about their experiment, not proof that any larger logical circuit will outperform any smaller one. The later Willow result is evidence from a separate experiment, not an extension of the 2023 rate on a common scale.
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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 problemsThe IBM and University of Chicago announcement describes a circuit-level demonstration with substantial logical-operation counts. Bill Fefferman, an 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 concerns characterization and confidence in the demonstrated computation; it does not turn an announcement’s effective-error comparison into a universal guarantee about other circuits.
These examples answer different questions. The 2023 and 2024 Google results concern surface-code scaling under their respective protocols, while the IBM and University of Chicago announcement describes a multi-operation encoded circuit and an effective-error comparison. The exclusive-decoder figures concern thresholds under specified noise assumptions. A reader comparing them should first align the metric, code family and distance, number of correction rounds, decoder, physical baseline, and data treatment. Where those do not align, the figures are evidence about separate experiments, not a ranking.
How should you evaluate a logical-error claim?
Start with the measured quantity and its denominator, then read the experimental context around it. A point estimate without that context is not enough to compare processors or predict application performance.
- Identify the observable and unit. Is the figure an error per correction round, per logical gate, per completed circuit, a memory lifetime, or a fidelity estimate? Check how the paper defines a cycle and what counts as failure.
- Record the code and scale. Note the code family and distance, the number of logical and physical qubits, and the number of correction rounds. A distance label alone does not specify all of the experiment’s resources or behavior.
- Check the operating regime. Find the stated physical error conditions and the applicable threshold assumptions. A below-threshold result is meaningful only for the code, noise model, syndrome circuit, and decoder under discussion.
- Inspect the decoder and data treatment. Find out which decoder was used, whether runs or difficult decoder instances were rejected, which events were excluded, and how many repetitions contributed to the estimate.
- Look at the comparison design. Ask whether the comparison uses the same device and matched conditions, one code instance or an average across subcodes, and a physical baseline measured in a comparable way.
- Read uncertainty and analysis details. Check the uncertainty interval, fit range, and stated exclusions alongside the central estimate. A small numerical difference may be difficult to interpret without these details.
- Match the scope to your conclusion. A memory result tests storage under its protocol. A multi-gate circuit tests a different collection of operations. Neither alone establishes the performance of every fault-tolerant application.
For a useful comparison, keep a compact record of these fields for each result rather than collecting only the headline percentage. Note whether the result is from one code instance or an average over several subcodes, and whether both sides of the comparison were measured on the same device. Device inhomogeneity matters: an average can be a sensible baseline, but it can also conceal that some smaller subcodes performed better than the larger code.
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Uncertainty and analysis choices deserve the same attention as the central value. In the 2023 Nature study, the distance-5 figure was a fitted result with a reported range of uncertainty, and the paper discusses a high-energy event affecting its repetition-code result. The fit window, excluded events, and number of repetitions help explain what evidence supports the estimate. They are not peripheral details: changing which data are retained can change the apparent rate.
Why can code scaling look modest or uneven?
More redundancy helps only when the physical system and correction process are sufficiently reliable. A code uses additional qubits and rounds to make errors more identifiable, but these additions bring more noisy operations and idle time. If the resulting fault burden is too high, increasing code size can fail to improve the logical result.
Even within a single device, not all qubits or subcodes behave alike. In the 2023 Nature experiment, the distance-5 code’s 2.914% ± 0.016% fitted logical error per cycle was compared with 3.028% ± 0.023% for the average of four selected distance-3 subcodes. The larger code was slightly worse than two individual distance-3 codes. The average comparison therefore supports a modest improvement in that defined comparison, not a claim that every larger code instance beat every smaller one.
Noise can also vary over time. The 2023 paper reports that a high-energy event affected its repetition-code result. That is one reason to read the paper’s exclusions and fit choices rather than treating a headline rate as independent of the experiment’s history. A single anomalous event or a nonuniform physical-qubit set can affect what a particular code-size comparison says.
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Repair common Windows errors and clear accumulated junk for a smoother, more stable PC - no reinstall needed.Free scan · no reinstallThe threshold concept is therefore best read as a conditional scaling statement. Google Research puts it this way: “The critical error rate that divides these two cases, below which quantum error correction transforms from harmful to helpful, is called the threshold.” The phrase “these two cases” matters: the dividing point belongs to a specified setup. Even a result below the relevant threshold does not mean the logical error vanishes; it means code growth can move performance in a beneficial direction under the applicable assumptions.
Which physical faults matter?
Error budgets are experiment-specific. In the 2023 Nature study of Google’s Sycamore device, the modeled dominant contributors included controlled-Z gate errors and data-qubit decoherence while qubits waited through measurement and reset. The authors also discussed measurement and reset error, leakage, unwanted interactions, and high-energy events. This is a useful illustration of how faults can enter a surface-code experiment, not a universal ranking of error sources across quantum architectures.
The practical lesson is to look for the device and protocol’s own error budget. A processor with a different gate set, qubit technology, syndrome circuit, or timing may have a different dominant limitation. “The logical error rate” is the combined outcome of those physical processes and the way the code and decoder handle them, not a direct reading of one isolated component’s quality.
It is also useful to distinguish a fault that affects one physical operation from the logical failure counted at the end of an experiment. Error correction may detect and compensate for some physical faults, while a pattern of faults that defeats the code can alter the encoded result. The reported logical metric summarizes the experiment’s outcome after its specified checks and decoding; it does not reveal, by itself, which component caused each failure. For that, consult the study’s error budget and protocol-specific diagnostics.
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How can decoding and post-selection change the result?
A decoder infers likely faults from noisy syndrome data. Different decoding methods can trade accuracy against speed, computational resources, and the fraction of data accepted. A decoder’s result therefore belongs in the description of a logical-error measurement, not in a footnote readers can ignore.
Some exclusive-decoder approaches abort on difficult instances rather than returning an answer for every run. Rejecting those cases can improve the fidelity of retained data, but it is not a free reduction in error: fewer runs are accepted, and more repetitions or additional resources may be needed to obtain a desired amount of usable data. IBM Research’s 2024 summary of work by Smith, Brown, and Bartlett reports decoder-specific thresholds under stated conditions, including a 50% threshold under depolarizing noise for the most discriminating exclusive decoder and 32(1)% for the fault-tolerant case. Those values should not be presented as device thresholds outside those conditions.
IBM’s 2026 Qiskit Paulice article discusses an open-source research toolkit for experimenting with syndrome post-selection and resource trade-offs. Its relevance is methodological: it provides a way to study choices that affect the accepted-data rate and resource use, not a guarantee that post-selection will improve every experiment.
When a result uses post-selection, ask what was rejected, how often rejection occurred, and whether the reported error rate applies only to retained runs. Then consider the practical cost: the experiment may need more attempts to collect a given amount of accepted data. If two results use different rejection rules or accepted-data rates, their retained-run fidelities are not a like-for-like measure of the cost of producing a usable answer.
Does a below-threshold result mean the computer is fault tolerant?
No. It means that, for a particular code and experimental regime, increasing code size may reduce the logical error under the stated noise and decoding assumptions. It does not establish that arbitrary logical gates, long circuits, or full applications will run reliably. Fault tolerance concerns whether errors can be controlled throughout a computation using appropriate encoded operations and resources; a memory-scaling result alone answers a narrower question.
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When a study reports improvement with code size, ask what was scaled and what was held fixed. A memory experiment can show that encoded information lasts longer as the code grows. To assess a computation, you also need evidence about the logical operations and circuit structure that computation requires, as well as how errors and resource overhead accumulate across them.
The question is not only whether a logical state survives, but whether the required sequence of logical operations can be implemented with errors and overhead low enough for the task. Circuit depth, operation mix, correlations, and verification method all shape that answer. A claim about a particular encoded-circuit demonstration should stay within its measured circuit and stated analysis; it should not silently become a claim about every workload.
What does not make a fair comparison?
- Comparing different metrics as if they were the same: a memory lifetime, error per cycle, logical-gate error, and circuit fidelity describe different quantities.
- Comparing figures from different experiments without protocol context: the 2023 Google/Nature and 2024 Willow results use separate experiments and should not be placed on one numerical scale without reconciling definitions and conditions.
- Ignoring a decoder or rejected data: a post-selected result must be read together with its rejection and resource costs.
- Equating a threshold with zero errors: below-threshold scaling indicates a possible direction of improvement under specific conditions, not error-free operation.
- Turning a per-cycle rate into an application success probability without a model: circuit depth, correlations, gate mix, and independence assumptions matter.
- Reading an organization’s announcement as a universal performance guarantee: the 2026 IBM and University of Chicago figures are announcement-reported, experiment-specific claims.
Frequently Asked Questions
Why do logical qubits still have errors?
A logical qubit is encoded across physical qubits, but its gates, measurements, resets, and idle periods remain noisy. Syndrome checks and decoding suppress many faults, yet faults in the operations or a pattern of faults that defeats the code can still produce a logical error.
What does logical error rate per cycle mean?
It is a failure rate for a defined error-correction cycle or round under a particular experiment’s protocol. Check the paper’s definition of a cycle, what counts as failure, the decoder, and whether the figure is conditioned on accepted data; it is not automatically an error per gate or per full circuit.
Does a below-threshold result mean the quantum computer is fault tolerant?
No. It means code scaling may reduce errors under the specified code, noise model, syndrome circuit, and decoder. It does not establish that arbitrary logical gates or long application circuits will run reliably.
How do I compare logical qubit error rates?
Compare like with like: metric and denominator, code family and distance, logical and physical qubit counts, correction rounds, decoder, operating conditions, data rejection, comparison design, and uncertainty. A memory lifetime, per-cycle error rate, and circuit-fidelity result are different measures.
Can a lower error rate after post-selection be treated as a free improvement?
No. Post-selection can improve the fidelity of retained runs, but rejected runs reduce the accepted-data rate and may require more repetitions or resources. Read the reported error together with the rejection conditions and overhead.
The Bottom Line
Logical quantum circuits still err because encoding and error correction reduce risk rather than eliminate noisy physical operations. Interpret any reported rate through its metric, code, decoder, data treatment, and uncertainty—and do not confuse a memory or scaling result with a guarantee about a full application.
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