Robust randomized benchmarking of quantum processes (1009.3639v1)

Abstract: We describe a simple randomized benchmarking protocol for quantum information processors and obtain a sequence of models for the observable fidelity decay as a function of a perturbative expansion of the errors. We are able to prove that the protocol provides an efficient and reliable estimate of an average error-rate for a set operations (gates) under a general noise model that allows for both time and gate-dependent errors. We determine the conditions under which this estimate remains valid and illustrate the protocol through numerical examples.

• The paper introduces a robust randomized benchmarking protocol that accurately estimates quantum gate error rates despite time- and gate-dependent noise.
• It develops both zeroth-order and first-order fitting models, with the first-order model addressing edge effects and detailed error dynamics.
• Numerical simulations validate the protocol across various noise models, demonstrating its scalability and practical utility in quantum processor design.

Overview of "Robust Randomized Benchmarking of Quantum Processes"

The paper "Robust Randomized Benchmarking of Quantum Processes" by Easwar Magesan, J. M. Gambetta, and Joseph Emerson introduces a robust, efficient randomized benchmarking (RB) protocol designed to evaluate the average error-rate of quantum gate operations, even in scenarios with noise that is both time and gate-dependent. The significance of this work lies in its ability to overcome the inherent limitations of quantum process tomography (QPT), particularly its requirement for low-error state preparation and measurement and its exponential scaling with the number of qubits.

The protocol established here offers a credible estimate of error-rates while avoiding the prohibitive costs of QPT by utilizing a sequence of randomized quantum operations. The paper articulates conditions under which these estimates hold, offers numerical validation, and exemplifies the protocol's application through simulation.

Major Contributions

1. Randomized Benchmarking Protocol: The protocol involves generating sequences of quantum operations where the first $m$ operations are selected randomly from the Clifford group, followed by a specific operation that ideally returns the sequence to the identity. Measurement involves the survival probability of the system across numerous sequences, allowing for an estimation of the average error-rate. This approach effectively circumvents QPT's scaling issues.
2. Error Modeling: A perturbative expansion framework for the error superoperators is introduced, leading to increasingly precise models for fitting experimental data. This method accommodates a wide range of realistic noise models, including those with time and gate-dependent errors, as well as state preparation and measurement errors.
3. Fitting Models: Two fitting models are derived: a simpler zeroth-order model for cases with minimal variation in noise and a first-order model that accounts for edge effects and gate-dependence in noise, providing a detailed portrayal of error dynamics.
4. Numerical Validation: The paper supports its theoretical claims with numerical simulations across various error models, including unitary errors alone and those combined with depolarizing and amplitude damping noise. Results demonstrate the first-order fitting model's superior accuracy in the presence of significant noise variation.

Implications and Future Work

From a theoretical standpoint, this research provides an essential framework for understanding and quantifying quantum gate error-rates, a critical component in advancing scalable quantum computing. Practically, the protocol could significantly enhance the efficiency of error characterization processes in experimental quantum systems, enabling more precise refinements in quantum processor design.

Future directions could include extending the protocol's applicability to other quantum gate sets beyond the Clifford group, refining error models to more accurately capture device-specific noise characteristics, and exploring techniques to further mitigate the effects of gate-dependence and time-variance in noise profiles.

In conclusion, this work offers a substantive advancement in the field of quantum error characterization, providing a robust, scalable approach that bridges theoretical insights with practical experimental utility. This protocol lays the groundwork for more effective benchmarking of quantum processors, pivotal for the evolution of reliable and efficient quantum computing technologies.