Evaluating fault-tolerant schemes for noisy hardware (On Zoom)

A large-scale quantum computer is envisioned to leverage the theoretical guarantees of the fault-tolerant accuracy threshold theorem, to ensure that long computations be carried out reliably even in the presence of noise. The conventional approach to fault tolerance using stabilizer codes assumes a simplistic model for errors: probabilistic application of Pauli operations. However, real-world noise is rarely as straightforward as Pauli matrices, e.g., coherent errors that arise from miscalibration. So, a disparity exists between physical noise and oversimplified models for proving the threshold theorems. Quantum Error Correction (QEC) is an integral part of an FT protocol specifying noise-resilient quantum information storage. The theory of open quantum systems prescribes that the time evolution of a quantum system is specified by a Completely Positive Trace Preserving (CPTP) map. Unlike the phenomenological model of Depolarizing noise used in fault tolerance proofs, a single qubit CPTP map is completely specified using twelve independent parameters. In this talk, I aim to integrate theoretical and experimental efforts in QEC by addressing the following question. For n−qubit hardware device (CPTP map), can we efficiently compute a figure of merit that can accurate predict of   the quality of the logical qubit? Recalling the findings from [1], I will demonstrate that standard error metrics such as Fidelity, Diamond Distance, Operator Norms, are not good candidates. Then, I will show some  efforts for constructing new measures using machine learning techniques. Through this discussion, I will also point out some nuances in benchmarking QEC methods beyond the Pauli paradigm, which are discussed in [2]. Additionally, I will highlight sampling issues in analyzing QEC schemes, and our attempts to overcome them. Our outstanding conclusion: Single parameter figures of merit are not good predictors of the efficacy of a QEC scheme. All of these numerical tools can be found online at [3]. To overcome these issues, I will discuss a twofold approach detailed in [4]. First, leveraging Randomized Compiling (RC): a method to render complex physics effects on hardware into simple effective Pauli noise. The microscopic details of the Pauli noise process can also be efficiently extracted using experimental techniques known as Cycle Error Reconstruction. Second, tricks that exploit the structure of concatenated codes to accurately approximate the average logical fidelity of the encoded qubit.

Besides yielding an efficient diagnostic tool for QEC, I will also discuss the impact of RC on error correcting capabilities of concatenated codes which was studied in [5]. Under some classes of coherent error processes, I will demonstrate that if errors rates are below a certain threshold then RC can enhance the performance of QEC schemes to an unlimited extent.

Related works:
[1]: Pavithran Iyer and David Poulin. A small quantum computer is needed to optimize fault-tolerant protocols. Quantum Science and Technology, 3(3):030504, 2018.
[2]: Pavithran Iyer. Une analyse critique de la correction d’erreurs quantiques pour du bruit realiste. PhD thesis, Universite de Sherbrooke, November 2018.
[3]: Pavithran Iyer and David Poulin. chflow: Quantum error correction for realistic noise. https://github.com/paviudes/chflow, 2018.
[4]: Pavithran Iyer, Aditya Jain, Stephen D. Bartlett, and Joseph Emerson. Efficient diagnostics for quantum error correction. Phys. Rev. Res., 4:043218, Dec 2022.
[5]: Aditya Jain, Pavithran Iyer, Stephen D Bartlett, and Joseph Emerson. Improved quantum error correction with randomized compiling. arXiv preprint arXiv:2303.06846, 2023.