Generative Data Intelligence

Coherent errors and readout errors in the surface code


Áron Márton1 and János K. Asbóth1,2

1Department of Theoretical Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
2Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49., Hungary

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


We consider the combined effect of readout errors and coherent errors, i.e., deterministic phase rotations, on the surface code. We use a recently developed numerical approach, via a mapping of the physical qubits to Majorana fermions. We show how to use this approach in the presence of readout errors, treated on the phenomenological level: perfect projective measurements with potentially incorrectly recorded outcomes, and multiple repeated measurement rounds. We find a threshold for this combination of errors, with an error rate close to the threshold of the corresponding incoherent error channel (random Pauli-Z and readout errors). The value of the threshold error rate, using the worst case fidelity as the measure of logical errors, is 2.6%. Below the threshold, scaling up the code leads to the rapid loss of coherence in the logical-level errors, but error rates that are greater than those of the corresponding incoherent error channel. We also vary the coherent and readout error rates independently, and find that the surface code is more sensitive to coherent errors than to readout errors. Our work extends the recent results on coherent errors with perfect readout to the experimentally more realistic situation where readout errors also occur.

To perform long computations, the quantum information that quantum computers work on has to be protected against environmental noise. This requires quantum error correction (QEC), whereby each logical qubit is encoded into collective quantum states of many physical qubits. We studied, using numerical simulation, how well the most promising quantum error correcting code, the so-called Surface Code can protect quantum information against a combination of so-called coherent errors (a type of calibration errors) and readout errors. We found that the Surface Code provides better protection as the code is scaled up, as long as the error levels are below a threshold. This threshold is close to the well-known threshold of another combination of errors: incoherent errors (a type of error arising from entanglement with a quantum environment) and readout errors. We also found (as shown in the accompanying image) that the Surface Code is more robust against readout errors than coherent errors. Note that we used the so-called phenomenological error model: we modeled the noise channels very precisely, but did not do a modeling of the code on the quantum circuit level.

► BibTeX data

► References

[1] Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill. “Topological quantum memory”. Journal of Mathematical Physics 43, 4452–4505 (2002).

[2] Austin G Fowler, Matteo Mariantoni, John M Martinis, and Andrew N Cleland. “Surface codes: Towards practical large-scale quantum computation”. Physical Review A 86, 032324 (2012).

[3] Chenyang Wang, Jim Harrington, and John Preskill. “Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory”. Annals of Physics 303, 31–58 (2003).

[4] Héctor Bombin, Ruben S Andrist, Masayuki Ohzeki, Helmut G Katzgraber, and Miguel A Martin-Delgado. “Strong resilience of topological codes to depolarization”. Physical Review X 2, 021004 (2012).

[5] Christopher T Chubb and Steven T Flammia. “Statistical mechanical models for quantum codes with correlated noise”. Annales de l’Institut Henri Poincaré D 8, 269–321 (2021).

[6] Scott Aaronson and Daniel Gottesman. “Improved simulation of stabilizer circuits”. Physical Review A 70, 052328 (2004).

[7] Craig Gidney. “Stim: a fast stabilizer circuit simulator”. Quantum 5, 497 (2021).

[8] Sebastian Krinner, Nathan Lacroix, Ants Remm, Agustin Di Paolo, Elie Genois, Catherine Leroux, Christoph Hellings, Stefania Lazar, Francois Swiadek, Johannes Herrmann, et al. “Realizing repeated quantum error correction in a distance-three surface code”. Nature 605, 669–674 (2022).

[9] Rajeev Acharya et al. “Suppressing quantum errors by scaling a surface code logical qubit”. Nature 614, 676 – 681 (2022).

[10] Yu Tomita and Krysta M Svore. “Low-distance surface codes under realistic quantum noise”. Physical Review A 90, 062320 (2014).

[11] Daniel Greenbaum and Zachary Dutton. “Modeling coherent errors in quantum error correction”. Quantum Science and Technology 3, 015007 (2017).

[12] Andrew S Darmawan and David Poulin. “Tensor-network simulations of the surface code under realistic noise”. Physical Review Letters 119, 040502 (2017).

[13] Shigeo Hakkaku, Kosuke Mitarai, and Keisuke Fujii. “Sampling-based quasiprobability simulation for fault-tolerant quantum error correction on the surface codes under coherent noise”. Physical Review Research 3, 043130 (2021).

[14] Florian Venn, Jan Behrends, and Benjamin Béri. “Coherent-error threshold for surface codes from majorana delocalization”. Physical Review Letters 131, 060603 (2023).

[15] Stefanie J Beale, Joel J Wallman, Mauricio Gutiérrez, Kenneth R Brown, and Raymond Laflamme. “Quantum error correction decoheres noise”. Physical Review Letters 121, 190501 (2018).

[16] Joseph K Iverson and John Preskill. “Coherence in logical quantum channels”. New Journal of Physics 22, 073066 (2020).

[17] Mauricio Gutiérrez, Conor Smith, Livia Lulushi, Smitha Janardan, and Kenneth R Brown. “Errors and pseudothresholds for incoherent and coherent noise”. Physical Review A 94, 042338 (2016).

[18] Sergey Bravyi, Matthias Englbrecht, Robert König, and Nolan Peard. “Correcting coherent errors with surface codes”. npj Quantum Information 4 (2018).

[19] F Venn and B Béri. “Error-correction and noise-decoherence thresholds for coherent errors in planar-graph surface codes”. Physical Review Research 2, 043412 (2020).

[20] Héctor Bombín and Miguel A Martin-Delgado. “Optimal resources for topological two-dimensional stabilizer codes: Comparative study”. Physical Review A 76, 012305 (2007).

[21] Nicolas Delfosse and Naomi H Nickerson. “Almost-linear time decoding algorithm for topological codes”. Quantum 5, 595 (2021).

[22] Sergey Bravyi, Martin Suchara, and Alexander Vargo. “Efficient algorithms for maximum likelihood decoding in the surface code”. Physical Review A 90, 032326 (2014).

[23] Austin G. Fowler. “Minimum weight perfect matching of fault-tolerant topological quantum error correction in average o(1) parallel time”. Quantum Info. Comput. 15, 145–158 (2015).

[24] Eric Huang, Andrew C. Doherty, and Steven Flammia. “Performance of quantum error correction with coherent errors”. Physical Review A 99, 022313 (2019).

[25] Alexei Gilchrist, Nathan K. Langford, and Michael A. Nielsen. “Distance measures to compare real and ideal quantum processes”. Physical Review A 71, 062310 (2005).

[26] Christopher A Pattison, Michael E Beverland, Marcus P da Silva, and Nicolas Delfosse. “Improved quantum error correction using soft information”. preprint (2021).

[27] Oscar Higgott. “Pymatching: A python package for decoding quantum codes with minimum-weight perfect matching”. ACM Transactions on Quantum Computing 3, 1–16 (2022).

[28] Alexei Kitaev. “Anyons in an exactly solved model and beyond”. Annals of Physics 321, 2–111 (2006).

[29] “FLO simulation of the surface code – python script”. https:/​/​​martonaron88/​Surface_code_FLO.git.

[30] Yuanchen Zhao and Dong E Liu. “Lattice gauge theory and topological quantum error correction with quantum deviations in the state preparation and error detection”. preprint (2023).

[31] Jingzhen Hu, Qingzhong Liang, Narayanan Rengaswamy, and Robert Calderbank. “Mitigating coherent noise by balancing weight-2 z-stabilizers”. IEEE Transactions on Information Theory 68, 1795–1808 (2021).

[32] Yingkai Ouyang. “Avoiding coherent errors with rotated concatenated stabilizer codes”. npj Quantum Information 7, 87 (2021).

[33] Dripto M Debroy, Laird Egan, Crystal Noel, Andrew Risinger, Daiwei Zhu, Debopriyo Biswas, Marko Cetina, Chris Monroe, and Kenneth R Brown. “Optimizing stabilizer parities for improved logical qubit memories”. Physical Review Letters 127, 240501 (2021).

[34] S Bravyi and R König. “Classical simulation of dissipative fermionic linear optics”. Quantum Information and Computation 12, 1–19 (2012).

[35] Barbara M Terhal and David P DiVincenzo. “Classical simulation of noninteracting-fermion quantum circuits”. Physical Review A 65, 032325 (2002).

[36] Sergey Bravyi. “Lagrangian representation for fermionic linear optics”. Quantum Information and Computation 5, 216–238 (2005).

Cited by

Could not fetch Crossref cited-by data during last attempt 2023-09-21 12:13:51: Could not fetch cited-by data for 10.22331/q-2023-09-21-1116 from Crossref. This is normal if the DOI was registered recently. On SAO/NASA ADS no data on citing works was found (last attempt 2023-09-21 12:13:53).


Latest Intelligence


Chat with us

Hi there! How can I help you?