| randomized benchmarking | |
|---|---|
| Name | Randomized benchmarking |
| Field | Quantum information science |
randomized benchmarking
Randomized benchmarking is an experimental protocol for assessing the performance of quantum gates by applying sequences of random operations and measuring decay of fidelity. It provides a scalable, statistically robust estimate of average error rates that is less sensitive to state preparation and measurement errors than direct process tomography. Randomized benchmarking matters in Quantum Physics and Quantum computing because it offers a practical method to quantify noise in near-term quantum processors from platforms such as superconducting qubits and trapped ions.
Randomized benchmarking (RB) was developed to address limitations of quantum quantum state tomography and quantum process tomography when characterizing noisy quantum devices. As quantum processors scale beyond a few qubits, full tomography becomes impractical due to exponential resource requirements and susceptibility to systematic bias. RB trades complete reconstruction for scalable metrics: by applying random sequences drawn from a unitary ensemble and measuring survival probabilities, RB extracts an average error parameter that reflects coherent and incoherent noise. It is widely used by groups at institutions like IBM, Google Quantum AI, Rigetti Computing, Honeywell, IonQ, and research labs such as UC Berkeley and MIT.
The theoretical basis of RB relies on properties of unitary groups and twirling channels. Standard RB typically samples from the Clifford group for n-qubit systems because Clifford twirling maps arbitrary errors to a depolarizing channel characterized by a single parameter. The analysis uses group representation theory and average-case error models: composing random unitaries and their inverses converts gate-dependent noise into an effective exponential decay in sequence length. Related mathematical tools include the theory of completely positive trace-preserving maps (CPTP maps), Pauli operators, and techniques from randomized algorithms and statistical estimation. Foundational papers by researchers such as Emerson, Joseph, Knill, Emanuel, and Nielsen, Michael A. formalized the connection between twirling and RB.
The standard RB protocol proceeds by preparing a fixed initial state (typically |0...0>), choosing a random sequence of m Clifford gates, appending the sequence-inverting Clifford that ideally returns the state, and measuring the survival probability. This is repeated over many random sequences and varying m to obtain a decay curve. Fitting the observed average survival probability to an exponential yields an average gate fidelity or an error per gate (EPG). Key analytical steps link the decay parameter to the average fidelity via relations provided by Gate fidelity theory and the notion of average process fidelity introduced in quantum information literature. Implementations often use dedicated compilations of Clifford gates into native gates for hardware such as superconducting qubit circuits or trapped-ion chains.
Multiple extensions address gate-dependent noise, leakage, non-Markovian effects, and multi-qubit systems. Examples include interleaved randomized benchmarking for estimating the fidelity of a specific gate, simultaneous benchmarking for crosstalk evaluation, and leakage benchmarking for population outside the computational subspace. Other variants are cycle benchmarking, randomized compiling, and unitarity benchmarking, which quantify coherence of errors. Advanced protocols incorporate ideas from randomized compiling and randomized benchmarking tomography to combine RB robustness with partial process information. Many variants reference work from groups at NIST, Sandia National Laboratories, and universities such as Yale University and University of Waterloo.
Implementing RB requires efficient random sampling from the chosen gate set, error-aware compilation to native pulses, and control over state preparation and measurement (SPAM) errors. Hardware platforms differ: superconducting devices use microwave pulses and cryogenic control; trapped ions use laser-driven gates; silicon spin qubits and NV centers have other controls. Experimental considerations include choice of sequence lengths, number of randomizations, calibration drift, and mitigating coherent error accumulation via randomized compiling. Laboratories often combine RB with complementary diagnostics such as gate set tomography and error mitigation experiments run in campaigns at facilities like JILA and national quantum centers.
Data analysis fits survival probabilities versus sequence length to models that may include an offset for SPAM. The primary metric extracted is the average error rate or average gate infidelity, often converted to an error per Clifford or error per native gate. Other metrics from RB variants include unitarity (a measure of coherent vs incoherent noise), leakage rates, and gate-dependent error estimates from interleaved RB. Statistical methods used include maximum likelihood estimation, bootstrapping for confidence intervals, and Bayesian approaches. Reported metrics are commonly compared against fault-tolerance thresholds for error-correcting codes such as the surface code.
RB is used in benchmarking devices for quantum supremacy experiments, calibrating quantum error correction experiments, and guiding hardware development by identifying dominant error sources. In metrology contexts, RB-style protocols can characterize decoherence channels relevant to precision sensors. Industry and academic benchmarking efforts inform roadmaps at organizations like Intel, Microsoft Quantum, and government initiatives such as the National Quantum Initiative.
Randomized benchmarking provides average metrics that may obscure worst-case errors relevant to fault-tolerant thresholds. It can be insensitive to some coherent error structures and may require careful interpretation under non-Markovian dynamics or strong gate dependence. Open questions include rigorous connections between RB metrics and logical failure rates in error-corrected systems, improved protocols for correlated noise and multi-qubit architectures, and integrating RB with scalable characterization methods like compressed sensing or selective tomography. Ongoing research is active in academic groups and national labs working to tighten the theoretical guarantees and practical applicability of RB in large-scale quantum processors.