ICTS:30952

Video URL

Efficient Syndrome detection for approximate quantum error correction – Road towards the optimal re…

Efficient Syndrome detection for approximate quantum error correction – Road towards the optimal recovery.

(2025). Efficient Syndrome detection for approximate quantum error correction – Road towards the optimal recovery.. SciVideos. https://youtu.be/3xtpZCzWqZc

Efficient Syndrome detection for approximate quantum error correction – Road towards the optimal recovery.. SciVideos, Jan. 20, 2025, https://youtu.be/3xtpZCzWqZc 

          @misc{ scivideos_ICTS:30952,
            doi = {},
            url = {https://youtu.be/3xtpZCzWqZc},
            author = {},
            keywords = {},
            language = {en},
            title = {Efficient Syndrome detection for approximate quantum error correction {\textendash} Road towards the optimal recovery.},
            publisher = {},
            year = {2025},
            month = {jan},
            note = {ICTS:30952 see, \url{https://scivideos.org/icts-tifr/30952}}
          }
Debjyoti Biswas
Talk numberICTS:30952
Source RepositoryICTS-TIFR
Collection

Abstract

Noise in quantum hardware poses the biggest challenge to realizing robust and scalable quantum computing devices. While conventional quantum error correction (QEC) schemes are relatively resource-intensive, approximate QEC (AQEC) promises a comparable degree of protection from specific noise channels using fewer physical qubits [1 ]. However, unlike standard QEC, the AQEC framework faces hurdles in reliable syndrome measurements due to the overlapping syndrome subspaces leading to the violation of the distinguishability criterion of error subspaces. Our work [2 ] provides an algorithm for discriminating overlapping syndrome subspaces based on the Gram-Schmidt-like orthogonalization routine. In the recovery, we map these orthogonal and disjoint subspaces to the code space followed by a recovery like the perfect recovery [1 , 3 ], or the Petz map [4, 5]. We further prove that this evolved recovery utilizing the Petz map (which we call the canonical Petz map ) gives optimal protection on the information regarding the measure of entanglement fidelity. We show that the performance of the canonical Petz map is similar to that of the Fletcher recovery [ 6 ]. 

[1] D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, Approximate quantum error correction can lead to better codes, Physical Review A 56, 2567 (1997).
[2] D. Biswas and P. Mandayam, Efficient syndrome detection for approximate quantum error correction – road towards the optimal recovery, Manuscript is under preparation (2025).
[3] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
[4 ] H. K. Ng and P. Mandayam, Simple approach to approximate quantum error correction based on the transpose channel, Phys. Rev. A 81, 062342 (2010).
[5] H. Barnum and E. Knill, Reversing quantum dynamics with near- optimal quantum and classical fidelity, Journal of Mathematical Physics 43, 2097 (2002).
[6] A. S. Fletcher, P. W. Shor, and M. Z. Win, Channel-adapted quantum error correction for the amplitude damping channel, IEEE Transactions on Information Theory 54, 5705 (2008).