Applications of quantum error correction

Quantum computing can facilitate the fast solution of certain applications that are intractable using classical computers. However, the performance of quantum processors is limited by the inevitable noise from the environment. Circumventing this problem, we can develop new quantum algorithms that achieve quantum advantage already at present-day quantum processors or use redundancy in the algorithm of interest to monitor physical errors and reconstruct the outcome of the error-free calculation by means of quantum error correcting (QEC) codes.

In QEC codes carefully designed (stabilizer) measurements ensure that errors do not go unnoticed, while the encoded information remains undisturbed. Stabilizer measurement outcomes are then used by a classical algorithm, the decoder, to infer the correction for the occurred errors.

In this talk I will present different benchmarking techniques that characterize how well the quantum device performs at executing QEC codes. An important figure of merit to gauge the hardware improvement necessary for practical quantum error correction is the detector likelihood, which tells us how often the code detects an error [1]. Further analysis of the stabilizer measurement process unveils additional details about the errors and tells us how to improve the hardware to excel in error correction.

Finally, I will talk about applications of QEC codes in practice. Using the direct output of quantum measurements, we show that higher error suppression can be achieved when the decoder is supplied with this richer, yet easily available, information [2]. Error suppression is helpful only if quantum algorithms can be applied within the framework of the QEC code. Therefore, we study how to implement operations on the encoded qubits and test their performance on a real device [3].

[1] I. Hesner, B. Hetenyi, and J.R. Wootton, arXiv: 2408.02082 [2] M. Hanisch, B. Hetenyi, and J.R. Wootton, in preparation [3] B. Hetenyi and J.R. Wootton, arXiv: 2404.15989