Alladi Ramakrishnan Hall

Quantum error correction: verifying theoretical guarantees on experimental hardware

Pavithran Iyer

Xanadu Quantum Technologies Inc,, Toronto, Canada

A large-scale quantum computer is envisioned to leverage the theoretical
guarantees of the fault tolerance accuracy threshold theorem to ensure that
long computations are carried out reliably, even in the presence of noise.
Quantum Error Correction (QEC) is an integral part of an fault tolerant
protocol that enables noise-resilient quantum information storage. The
conventional approach to fault tolerance using stabilizer codes assumes a
simplistic model for errors: probabilistic application of Pauli operations.
However, Pauli matrices are an oversimplified model for understanding all
the intricaies in a real-world quantum hardware. For instance, they fail to
capture coherent errors that arise from miscalibration. So, a disparity
exists between (quantum) physical noise and the oversimplified mathematical
models for proving the threshold theorems. In this talk, I aim to integrate
theoretical and experimental efforts in QEC by addressing the following
question. For an n−qubit hardware device, can we efficiently compute a
figure of merit that can accurately predict the quality of the logical
qubit? Recalling the findings from [1], I will demonstrate that standard
error metrics, such as Fidelity, Diamond Distance, and Operator Norms, are
not good candidates. Through this discussion, I will also point out some
nuances in extending standard techniques to benchmarking QEC methods beyond
the Pauli paradigm, which are also discussed in [2]. Then, I will show some
efforts for constructing new measures using machine learning
techniques. Our outstanding conclusion: Single parameter figures of merit
are not good predictors of the efficacy of a QEC scheme. I will discuss a
twofold approach detailed in [3] to address our central question. First,
leveraging Randomized Compiling (RC): a method to render complex physics
effects on hardware into simple, effective Pauli noise. Second, tricks that
exploit the structure of concatenated codes to approximate the average
logical fidelity of the encoded qubit accurately. The twofold approach
provides an efficient and accurate way of benchmarking quantum error
correction schemes. Finally, with the aid of a recent result in [4], I will
demonstrate that besides helping in efficient diagnostics for quantum error
correction, RC can also enhance the error correcting capabilities of the
underlying code itself. These results constitute the need to incorporate RC
as an important tool for building fault tolerant quantum computers in
practice.

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, Aditya Jain, Stephen D. Bartlett, and Joseph Emerson.
Efficient diagnostics for quantum error correction. Phys. Rev. Res.,
4:043218, Dec 2022.
[4]: Aditya Jain, Pavithran Iyer, Stephen D Bartlett, and Joseph Emerson.
Improved quantum error correction with randomized compiling. Phys. Rev.
Res., 5, 033049 (2023).

Other related references:
[5]: Pavithran Iyer and David Poulin. chflow: Quantum error correction for
realistic noise. github.com/paviudes/chflow, 2018.