Alladi Ramakrishnan Hall

Analyzing quantum error correction on realistic hardware

Pavithran Iyer

Xanadu Quantum Technologies Inc,, Toronto, Canada

The aim of this talk is to provide key technical ideas that are used in
analyzing the usefulness of quantum error correcting schemes for noise
quantum hardware. I will show a mathematical framework described in [1,2]
for computing the effective logical channel that describes the composite
effect of physical noise and quantum error correction on the encoded
logical information. The effective logical channel allows us to define a
notion of the logical noise strength. I will show how to compute the
effective channel to approximate the logical error for Steane quantum error
correction schemes under simple coherent errors, described in [4]. I will
discuss a fundamental problem associated to estimating the average logical
channel using Montecarlo sampling: a popular technique used to study Pauli
errors. This naturally leads to outlining the use of importance sampling
methods to sample error syndromes in the case of non-Pauli noise and
efficiently estimating the average logical error rate. In the case of Pauli
errors, I will describe techniques used to efficiently and accurately
approximate the total probability of uncorrectable errors in the
concatenated Steane code. This forms the basis of our twofold approach for
efficient diagnostic techniques for quantum error correction in [3].

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.