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Characterizing Quantum Gates via Randomized Benchmarking (1109.6887v2)

Published 30 Sep 2011 in quant-ph

Abstract: We describe and expand upon the scalable randomized benchmarking protocol proposed in Phys. Rev. Lett. 106, 180504 (2011) which provides a method for benchmarking quantum gates and estimating the gate-dependence of the noise. The protocol allows the noise to have weak time and gate-dependence, and we provide a sufficient condition for the applicability of the protocol in terms of the average variation of the noise. We discuss how state preparation and measurement errors are taken into account and provide a complete proof of the scalability of the protocol. We establish a connection in special cases between the error rate provided by this protocol and the error strength measured using the diamond norm distance.

Citations (358)

Summary

  • The paper introduces a scalable protocol for characterizing quantum gate errors using randomized benchmarking.
  • It details both zeroth and first-order models to quantify fidelity decay and establish error bounds.
  • The work links the protocol to fault-tolerant quantum computing by benchmarking Clifford gates and relating error metrics to the diamond norm.

Overview and Implications of "Characterizing Quantum Gates via Randomized Benchmarking"

The paper "Characterizing Quantum Gates via Randomized Benchmarking" by Easwar Magesan, Jay M. Gambetta, and Joseph Emerson offers a comprehensive analysis of a protocol developed for evaluating the performance of quantum gates in quantum computing. The authors aim to extend and solidify the methods initially proposed by providing a scalable solution for assessing the error rates of quantum gates through randomized benchmarking (RB), a technique that combines theoretical rigor with experimental adaptability.

Scalable Protocol Development

The authors address significant challenges in quantum process characterization, providing a sophisticated solution by leveraging the scalable randomized benchmarking protocol. One of the main strengths of their work is the detailed presentation of both zeroth and first-order models for quantifying and understanding the flux of fidelity decay in quantum gate operations. They robustly justify the use of a simplistic exponential model for noise estimation under conditions where noise is independent of gate choice and timing—situations that are rare but significant in building a theoretical foundation.

Error Characterization

The authors bridge the gap between theoretical development and practical implementation by offering a thorough exposition on benchmarking the full set of Clifford gates. They derive bounds and conditions, particularly utilizing a perturbative analysis, to evaluate when higher-order terms in noise can be safely ignored. Furthermore, the comparison between the average error characterized by their protocol and measures from fault-tolerant quantum computing, such as the diamond norm, gives vital insights for understanding limitations and operational contexts.

Implications for Fault-Tolerant Quantum Computing

The paper discusses the relevance of this benchmarking procedure in the wider landscape of fault-tolerant quantum computation. The Clifford group, integral to stabilizer codes key to quantum error correction, is effectively assessed by their protocol, thus providing a platform for implementing fault-tolerant quantum operations. The linkage between diamond norm and infidelity measures also offers a deeper understanding of error boundaries essential in achieving robust quantum computation.

Scalability and Practicality

The authors further demonstrate that their approach is computationally feasible by detailing its scalability concerning the number of qubits. They tackle the challenges of implementing complete characterizations under resource limitations by suggesting efficient ways to sample and decompose quantum operations. Their exposition on randomizing Clifford operations, particularly utilizing symplectic geometry to streamline decomposition, provides an operational backbone for real-world quantum computing tasks.

Future Directions

The insights of this paper have profound theoretical and practical implications. It opens avenues for further research on evaluating noise effects more holistically, including multi-qubit correlations and non-Pauli noise, given their protocol primarily centers around the Clifford group. Additionally, potential investigations into refining the diamond norm relationship could deepen our understanding of quantum error correction paradigms, particularly for more computationally accessible algorithms.

In conclusion, Magesan et al. have contributed a sophisticated methodology to the quantum computing toolbox—one that expertly balances the constraints of current quantum systems with the demands for operational accuracy and fault tolerance. Their work sets a high benchmark for others in the field to follow, providing the clarity needed to design and evaluate next-generation quantum computational resources.