Benchmark single-qubit speed and fidelity as two related measurements, not one score. Record the calibrated duration of a specific native gate such as X, SX, or RX, then run single-qubit randomized benchmarking (RB) with identical sequence lengths, randomizations, shots, compilation, and calibration context for every qubit or processor you compare. Report duration in nanoseconds, RB error with its unit (error per Clifford or error per gate), T1 and T2 coherence, readout error, timestamps, and uncertainty.
A short pulse is not automatically a high-fidelity gate. Control error, leakage, crosstalk, calibration drift, and readout can dominate the result. The protocol below separates those effects as far as RB allows and identifies when interleaved randomized benchmarking or gate-set tomography is needed.
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What this benchmark actually measures
A single-qubit gate benchmark answers two different questions:
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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 problems- Speed: how long the processor applies a defined native operation, normally the calibrated pulse or compiled instruction duration in nanoseconds.
- Operational fidelity: how often a gate sequence produces the expected computational result under the selected operating conditions, estimated from randomized benchmarking.
Use a fixed qubit and a named gate. An X gate, SX (square-root of X), RX rotation, and virtual RZ rotation are not interchangeable. A virtual RZ is a software frame update with no physical pulse duration and a reported error of zero in the relevant backend fields; comparing it directly with a finite-duration driven gate produces a meaningless speed ranking.
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IBM’s QPU information guide exposes single-qubit gate-length and randomized-benchmarking error fields for ID, SX, X, and RX. Its reported SX, ID, and X errors come from an RB sequence, while virtual RZ operations are treated as software operations. Treat those fields as calibration snapshots rather than permanent specifications.
Fix the comparison before collecting data
Choose the operation and qubit
Write down the qubit identifier, native gate, rotation angle and direction, and the exact pulse schedule or compiled instruction. If an RX gate can be implemented with different amplitudes, durations, or virtual-frame conventions, each implementation is a separate benchmark target.
Control the surrounding circuit
State whether spectator qubits are idle, reset, driven simultaneously, or executing another circuit. Crosstalk can make an isolated gate look better than the same gate in a real circuit layer. Also record whether the benchmark uses active reset, passive relaxation, dynamical decoupling, barriers, inserted delays, and compiler scheduling.
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For a fair qubit-to-qubit or generation-to-generation comparison, keep the sequence-length grid, number of random Clifford sequences per length, shots per sequence, fitting model, outlier policy, and uncertainty calculation fixed. A different compiler decomposition or shot budget can change the reported error even when the hardware is unchanged.
Capture calibration and timing context
Save the following metadata with every result. Calibration-dependent values can drift during a day, and a recalibration or compiler update can change both duration and error.
| Field | What to record | Why it matters |
|---|---|---|
| Backend and revision | Processor name, backend revision or configuration, and qubit ID | Hardware and calibration namespaces change over time. |
| Gate definition | Native gate name, angle, direction, pulse or instruction identifier | “X” or “RX” can refer to different compiled implementations. |
| Single-qubit gate duration | Calibrated duration in nanoseconds | Provides the physical speed metric. |
| RB error | Fitted error labeled as error per Clifford (EPC) or error per primitive gate (EPG) | The unit determines what can be compared. |
| T1 and T2 | Measured relaxation and dephasing times, with units and timestamp | Shows available coherence headroom. |
| Readout error | Measurement error or measurement fidelity, reported separately | Readout contamination is not gate error. |
| Software context | Compiler/transpiler version, basis gates, optimization level, and scheduling options | Compilation can alter the physical sequence. |
| Experiment timing | Calibration timestamp, experiment start and end, and any recalibration event | Allows drift and repeatability analysis. |
Daily benchmarking commonly reports T1, T2, measurement-fidelity, and gate-error metrics. Preserve the timestamp for each metric instead of combining values collected at different times.
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Measure single-qubit gate duration
Use the calibrated physical duration
Read the duration of the selected finite-duration native instruction from the backend’s calibration or pulse schedule. Report it as nanoseconds per gate. If the duration is 35 ns, for example, the physical pulse occupies 35 ns; that number does not include queueing, measurement, reset, classical processing, or an inter-gate wait unless you explicitly add those components.
Calculate an idealized pulse-rate figure only when useful
You may also report the reciprocal, 1 / duration, as idealized gates per second. Label it clearly as a pulse-duration rate. It is not end-to-end processor throughput because real circuits include scheduling gaps, two-qubit operations, readout, reset, control latency, and classical handling.
Report application-level speed separately
For a system-level comparison, measure circuit-layer time or wall-clock throughput in a separate metric. State whether it includes queueing, compilation, data transfer, readout, reset, and post-processing. Never substitute that value for single-qubit gate duration.
Run single-qubit randomized benchmarking
Randomized benchmarking estimates an average operational error while reducing sensitivity to state-preparation and measurement (SPAM) errors. The standard experiment uses random Clifford operations and a mathematically compensating inverse so that an ideal sequence returns the qubit to the prepared reference state.
- Prepare the reference state. Usually initialize the qubit in computational basis state |0⟩ using the processor’s documented reset or initialization procedure.
- Select sequence lengths. Choose several values of
m, the number of random Clifford operations. Use the same grid for every qubit and device in the comparison. - Generate random Clifford strings. For each length, generate many independent random sequences. Fix the random-seed policy if reproducibility is important, but do not reuse one sequence as if it represented all randomizations.
- Append the inverse Clifford. Compute the Clifford that ideally inverts the preceding product and append it. The complete sequence should return |0⟩ in the absence of errors.
- Compile consistently. Decompose each Clifford into the same native basis and apply the same optimization and scheduling rules. Record the average number of primitive gates per Clifford if you will report EPG.
- Execute repeated shots. Run enough shots for each random sequence to estimate its survival probability. Keep shot count and readout settings constant across comparisons.
- Measure survival. Count the fraction of shots measured in the prepared reference state. Average over random sequences at each length, retaining the per-sequence data for uncertainty analysis.
- Fit the decay. Fit survival probability against sequence length with an exponential-with-offset model such as
A p^m + B, wherepis the fitted decay parameter andAandBabsorb preparation and measurement offsets.
Use the same randomization count, shot count, length grid, and fit procedure for every comparison. A fit that fails to converge, has strongly correlated parameters, or leaves structured residuals should be reported as a diagnostic problem rather than silently converted into a fidelity number.
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Separate EPC, EPG, and fidelity
For a one-qubit depolarizing interpretation, the average gate fidelity is one minus the average gate error. RB software commonly reports error per Clifford (EPC), which describes the average error of the compiled Clifford operation. If the decay parameter is p and the depolarizing dimension is d = 2, a common convention is:
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EPC = (d - 1) / d × (1 - p) = (1 - p) / 2
Call this an average Clifford error, not the error of the target primitive gate. The corresponding average Clifford fidelity under that convention is 1 - EPC.
Convert to error per primitive gate carefully
Error per gate (EPG) attempts to assign error to a primitive basis operation such as X, SX, or RX. A rough conversion divides EPC by the average number of primitive gates in a Clifford, but the exact conversion depends on the decomposition, gate mix, error model, and convention. Use the documented one-qubit EPC/EPG conversion helper for your software stack, and publish the decomposition and assumptions alongside the number.
Never write “fidelity” without its definition. State whether the value is average Clifford fidelity, primitive-gate fidelity inferred from EPG, or a backend-reported RB metric. Include the unit and the conversion convention in the table or sentence containing the result.
Quantify uncertainty
Report a confidence interval or standard uncertainty for the fitted decay and converted error. Suitable approaches include fit-covariance propagation, bootstrap resampling of random sequences, or a hierarchical model that retains shot noise and sequence-to-sequence variation. The uncertainty should include the conversion step, not only the curve-fit parameter.
Isolate a target gate with interleaved randomized benchmarking
Standard RB averages the behavior of the Clifford set. If the question is specifically “how good is this X or SX gate?”, use interleaved randomized benchmarking (IRB). Run a reference RB experiment, then a second experiment in which the target gate is inserted between reference Cliffords. Compare the two fitted decay parameters to estimate the target gate’s error.
IRB requires assumptions about gate-independence, Markovian behavior, and the relationship between the reference and interleaved decay. Those assumptions can fail with coherent errors, leakage, drift, or crosstalk. Report the reference and interleaved fits, uncertainty, sequence lengths, randomization count, and the method used to bound or estimate the target error. Do not present an IRB estimate as exact when the confidence interval or assumptions make it inconclusive.
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Check coherence, readout, and drift
Compare with T1 and T2 coherence
Record T1 and T2 coherence for the same qubit and calibration window. Compare the gate duration with those times to estimate whether relaxation or dephasing could plausibly explain the measured error. This is a coherence-limit diagnostic, not a substitute for RB: control imperfections, leakage, and calibration error can dominate even when T1 and T2 are long.
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Keep readout error separate
Readout error affects the measured survival probability and is partly absorbed by the RB offset terms, but it is not gate error. Report measurement fidelity or readout error independently. A device with better gates but worse readout can show a misleadingly poor raw success rate if the two quantities are mixed.
Repeat across time and calibration cycles
Run the same protocol after a defined interval, after recalibration, and after meaningful compiler or pulse changes. Plot duration, EPC or EPG, T1, T2, and readout error against timestamp. A fast gate that degrades between calibration cycles may be less useful than a slightly slower gate with stable performance.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Know what RB cannot tell you
RB is an average operational metric. It can hide gate-dependent errors, time-correlated noise, coherent over-rotations, leakage outside the computational subspace, and crosstalk from simultaneous spectators. A good exponential fit does not prove that errors are independent or identically distributed.
When you need a predictive model of the complete implemented gate set, supplement RB with gate-set tomography (GST). GST characterizes state preparation, measurement, and individual operations together and can expose coherent, gate-dependent, and leakage-related effects that an average RB number conceals. Cycle-level or layer-level methods are also appropriate when the target is a parallel circuit layer rather than an isolated gate.
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Compare qubits or processors on the same axes
| Axis | Required report | Interpretation |
|---|---|---|
| Duration | Calibrated nanoseconds per finite-duration native gate | Physical pulse speed, excluding any components you did not include. |
| Operational fidelity | RB-derived EPC or EPG, with uncertainty and convention | Average sequence performance under the stated conditions. |
| Coherence headroom | T1 and T2, their timestamps, and duration-to-coherence ratios | Indicates whether relaxation or dephasing may limit the gate. |
| Measurement contribution | Readout error or measurement fidelity | Allows readout quality to be judged independently. |
| Stability | Repeated values across calibration cycles and time intervals | Shows whether a headline result persists. |
| Execution context | Isolated or simultaneous operation, spectators, compiler, pulse schedule, and waits | Defines what workload the number represents. |
Do not rank a virtual RZ against a driven X by duration, and do not rank EPC from one Clifford decomposition against EPG from another without normalizing the definitions.
Historical reference: the NIST trapped-ion result
A National Institute of Standards and Technology randomized-benchmarking demonstration reported a one-qubit error probability of 0.00482(17) per randomized pi/2 pulse in 2007. The parenthetical value denotes the stated uncertainty in the final digits. This is historical context from a trapped-ion experiment, not a universal present-day target and not a direct prediction for another processor technology.
Troubleshoot an unusable benchmark
The fit is unstable or non-exponential
- Increase the number of random sequences and shots, then inspect per-sequence variance.
- Check that the inverse Clifford was generated and compiled correctly.
- Verify that sequence lengths are long enough to reveal decay but not so long that survival reaches the noise floor immediately.
- Inspect residuals for drift, leakage, or time-correlated behavior; split the run by time if calibration changed during execution.
EPC changes when only the compiler changes
- Compare the primitive-gate count and basis decomposition for each Clifford.
- Record optimization and scheduling settings, barriers, inserted delays, and dynamical decoupling.
- Report both the compiled Clifford result and, when possible, a target-gate IRB result.
The gate is fast but the application performs poorly
- Measure circuit-layer or wall-clock throughput separately from pulse duration.
- Check simultaneous spectator activity and crosstalk.
- Include reset, readout, inter-gate waits, and classical latency in the application-level measurement.
Results disagree with backend properties
- Confirm that your experiment used the same qubit, gate definition, and calibration epoch as the published property.
- Check whether the backend value is EPC, EPG, or another averaged metric.
- Rerun after recalibration and preserve both timestamps; a time-sensitive value is not necessarily an error in either measurement.
Reporting checklist
A publication-quality result should let another team reproduce the comparison without guessing:
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- Processor, backend revision, qubit ID, and experiment dates.
- Native gate name, angle, direction, pulse or instruction definition, and calibrated duration in nanoseconds.
- Whether spectators were idle or active, and whether operation was isolated or simultaneous.
- Initialization, reset, readout basis, shot count, randomization count, and sequence-length grid.
- Compiler/transpiler version, basis gates, optimization level, scheduling, barriers, delays, and average primitive gates per Clifford.
- RB model, fitted decay parameter, offset treatment, fit residuals, and uncertainty method.
- Error labeled explicitly as EPC or EPG, with the dimension and conversion convention.
- Readout error, T1, T2, calibration timestamp, and any recalibration during the run.
- For IRB, the reference and interleaved protocols, target gate, assumptions, and confidence interval.
- For GST or layer studies, the additional model scope and why RB alone was insufficient.
How to state the final result
Use a sentence that keeps speed and fidelity distinct: “On qubit Q, the calibrated SX duration was reported in nanoseconds under calibration C; single-qubit randomized benchmarking produced an EPC of the stated value with its uncertainty, while T1, T2, readout error, compiler version, and timestamp were recorded separately.” Then state whether the result came from isolated or simultaneous operation and whether it remained stable across repeats.
The defensible conclusion is not simply “the fastest gate wins.” Select the gate or processor that offers the needed duration, operational fidelity, coherence headroom, readout quality, and stability under the workload you actually intend to run.
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