Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions

Pedro Parrado-Rodríguez1, Ciarán Ryan-Anderson1,2, Alejandro Bermudez3, and Markus Müller4,5

1Department of Physics, College of Science, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom
2Honeywell Quantum Solutions, 303 S. Technology Ct., Broomfield, Colorado 80021, USA
3Departamento de Física Teórica, Universidad Complutense, 28040 Madrid, Spain.
4Institute for Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, 52428 Jülich, Germany
5JARA-Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany

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Physical qubits in experimental quantum information processors are inevitably exposed to different sources of noise and imperfections, which lead to errors that typically accumulate hindering our ability to perform long computations reliably. Progress towards scalable and robust quantum computation relies on exploiting quantum error correction (QEC) to actively battle these undesired effects. In this work, we present a comprehensive study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level. Finally, we study the impact of residual crosstalk errors on the performance of fault-tolerant QEC numerically, identifying the experimental target values that need to be achieved in near-term trapped-ion experiments to reach the break-even point for beneficial QEC with low-distance topological codes.

Ion traps are one of the leading platforms for building scalable quantum computers, offering all-to-all connectivity between qubits encoded in ions that belong to same Coulomb crystal and having demonstrated high fidelity gate operations. These quantum processors, however, are susceptible to multiple sources of noise that can corrupt the results of the computations. The development and implementation of quantum error correction (QEC) techniques is thus crucial to allow for reliable and scalable quantum computing. In ion traps, one major source of errors can be crosstalk, a process that can happen when gates applied to a given set of qubits unwantedly affect neighbouring qubits. But how much does this error affect the computations, and how can it be handled?
In this work, we evaluate the effects of crosstalk on QEC protocols implemented on a state-of-the-art ion trap platform. Using realistic error models derived from first principles, and through extensive numerical simulations, we demonstrate the feasibility of beneficial QEC and the efficiency of techniques like refocussing pulse sequences that can greatly suppress the detrimental effects of crosstalk.
The proposed techniques can be extended to other QEC codes, and our work can guide the path towards experimental realizations of error-corrected trapped-ion quantum processors.

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[1] Lukas Postler, Sascha Heuβen, Ivan Pogorelov, Manuel Rispler, Thomas Feldker, Michael Meth, Christian D. Marciniak, Roman Stricker, Martin Ringbauer, Rainer Blatt, Philipp Schindler, Markus Müller, and Thomas Monz, "Demonstration of fault-tolerant universal quantum gate operations", Nature 605 7911, 675 (2022).

[2] Andrea Rodriguez-Blanco, Farid Shahandeh, and Alejandro Bermudez, "Witnessing entanglement in trapped-ion quantum error correction under realistic noise", Physical Review A 109 5, 052417 (2024).

[3] Sascha Heußen, Lukas Postler, Manuel Rispler, Ivan Pogorelov, Christian D. Marciniak, Thomas Monz, Philipp Schindler, and Markus Müller, "Strategies for a practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers", Physical Review A 107 4, 042422 (2023).

[4] J. Hilder, D. Pijn, O. Onishchenko, A. Stahl, M. Orth, B. Lekitsch, A. Rodriguez-Blanco, M. Müller, F. Schmidt-Kaler, and U. G. Poschinger, "Fault-Tolerant Parity Readout on a Shuttling-Based Trapped-Ion Quantum Computer", Physical Review X 12 1, 011032 (2022).

[5] J. A. Montañez-Barrera, R. T. Holladay, G. P. Beretta, and Michael R. von Spakovsky, "Method for generating randomly perturbed density operators subject to different sets of constraints", Quantum Information Processing 21 9, 314 (2022).

[6] Jeremy Flannery, Roland Matt, Luca Huber, Robin Oswald, Kaizhao Wang, and Jonathan Home, 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) 816 (2022) ISBN:978-1-6654-9113-6.

[7] Charles H. Baldwin, Karl Mayer, Natalie C. Brown, Ciarán Ryan-Anderson, and David Hayes, "Re-examining the quantum volume test: Ideal distributions, compiler optimizations, confidence intervals, and scalable resource estimations", Quantum 6, 707 (2022).

[8] Matthew N. H. Chow, Christopher G. Yale, Ashlyn D. Burch, Megan Ivory, Daniel S. Lobser, Melissa C. Revelle, and Susan M. Clark, "First-order crosstalk mitigation in parallel quantum gates driven with multi-photon transitions", Applied Physics Letters 124 4, 044002 (2024).

[9] Chung-You Shih, Sainath Motlakunta, Nikhil Kotibhaskar, Manas Sajjan, Roland Hablützel, and Rajibul Islam, "Reprogrammable and high-precision holographic optical addressing of trapped ions for scalable quantum control", npj Quantum Information 7 1, 57 (2021).

[10] Samudra Dasgupta, Travis S. Humble, and Arshag Danageozian, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 99 (2023) ISBN:979-8-3503-4323-6.

[11] Ye-Hong Chen, Roberto Stassi, Wei Qin, Adam Miranowicz, and Franco Nori, "Fault-Tolerant Multiqubit Geometric Entangling Gates Using Photonic Cat-State Qubits", Physical Review Applied 18 2, 024076 (2022).

[12] C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit, K. Gilmore, J. A. Gerber, B. Neyenhuis, D. Hayes, and R. P. Stutz, "Realization of Real-Time Fault-Tolerant Quantum Error Correction", Physical Review X 11 4, 041058 (2021).

[13] Chao Fang, Ye Wang, Shilin Huang, Kenneth R. Brown, and Jungsang Kim, "Crosstalk Suppression in Individually Addressed Two-Qubit Gates in a Trapped-Ion Quantum Computer", Physical Review Letters 129 24, 240504 (2022).

[14] I. A. Simakov, I. S. Besedin, and A. V. Ustinov, "Simulation of the five-qubit quantum error correction code on superconducting qubits", Physical Review A 105 3, 032409 (2022).

[15] Zhao-Di Liu, Olli Siltanen, Tom Kuusela, Rui-Heng Miao, Chen-Xi Ning, Chuan-Feng Li, Guang-Can Guo, and Jyrki Piilo, "Overcoming noise in quantum teleportation with multipartite hybrid entanglement", Science Advances 10 18, eadj3435 (2024).

[16] Stephen D. Erickson, Jenny J. Wu, Pan-Yu Hou, Daniel C. Cole, Shawn Geller, Alex Kwiatkowski, Scott Glancy, Emanuel Knill, Daniel H. Slichter, Andrew C. Wilson, and Dietrich Leibfried, "High-Fidelity Indirect Readout of Trapped-Ion Hyperfine Qubits", Physical Review Letters 128 16, 160503 (2022).

[17] Mingyu Kang, Hanggai Nuomin, Sutirtha N. Chowdhury, Jonathon L. Yuly, Ke Sun, Jacob Whitlow, Jesús Valdiviezo, Zhendian Zhang, Peng Zhang, David N. Beratan, and Kenneth R. Brown, "Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics", Nature Reviews Chemistry 8 5, 340 (2024).

[18] Martin Ringbauer, Michael Meth, Lukas Postler, Roman Stricker, Rainer Blatt, Philipp Schindler, and Thomas Monz, "A universal qudit quantum processor with trapped ions", Nature Physics 18 9, 1053 (2022).

[19] David Schwerdt, Yotam Shapira, Tom Manovitz, and Roee Ozeri, "Comparing two-qubit and multiqubit gates within the toric code", Physical Review A 105 2, 022612 (2022).

[20] Pedro Figueroa-Romero, Kavan Modi, Robert J. Harris, Thomas M. Stace, and Min-Hsiu Hsieh, "Randomized Benchmarking for Non-Markovian Noise", PRX Quantum 2 4, 040351 (2021).

[21] Bogdan M. Mihalcea, "Quasienergy operators and generalized squeezed states for systems of trapped ions", Annals of Physics 442, 168926 (2022).

[22] Yan Li and Zhihong Ren, "Quantum metrology with an N -qubit W superposition state under noninteracting and interacting operations", Physical Review A 107 1, 012403 (2023).

[23] Mummadi Swathi and Bhawana Rudra, "A Novel Approach for Asymmetric Quantum Error Correction With Syndrome Measurement", IEEE Access 10, 44669 (2022).

[24] Pedro Figueroa-Romero, Kavan Modi, and Min-Hsiu Hsieh, "Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise", Quantum 6, 868 (2022).

[25] Cameron Foreman, Sherilyn Wright, Alec Edgington, Mario Berta, and Florian J. Curchod, "Practical randomness amplification and privatisation with implementations on quantum computers", Quantum 7, 969 (2023).

[26] Ali Binai-Motlagh, Matthew L Day, Nikolay Videnov, Noah Greenberg, Crystal Senko, and Rajibul Islam, "A guided light system for agile individual addressing of Ba+ qubits with 10−4 level intensity crosstalk", Quantum Science and Technology 8 4, 045012 (2023).

[27] Sascha Heußen, Don Winter, Manuel Rispler, and Markus Müller, "Dynamical subset sampling of quantum error-correcting protocols", Physical Review Research 6 1, 013177 (2024).

[28] Mingyu Kang, Ye Wang, Chao Fang, Bichen Zhang, Omid Khosravani, Jungsang Kim, and Kenneth R. Brown, "Designing Filter Functions of Frequency-Modulated Pulses for High-Fidelity Two-Qubit Gates in Ion Chains", Physical Review Applied 19 1, 014014 (2023).

[29] Hila Safi, Karen Wintersperger, and Wolfgang Mauerer, 2023 IEEE International Conference on Quantum Software (QSW) 104 (2023) ISBN:979-8-3503-0479-4.

[30] Roman Stricker, Davide Vodola, Alexander Erhard, Lukas Postler, Michael Meth, Martin Ringbauer, Philipp Schindler, Rainer Blatt, Markus Müller, and Thomas Monz, "Characterizing Quantum Instruments: From Nondemolition Measurements to Quantum Error Correction", PRX Quantum 3 3, 030318 (2022).

[31] Zeyuan Zhou, Ryan Sitler, Yasuo Oda, Kevin Schultz, and Gregory Quiroz, "Quantum Crosstalk Robust Quantum Control", Physical Review Letters 131 21, 210802 (2023).

[32] Cameron Foreman, Sherilyn Wright, Alec Edgington, Mario Berta, and Florian J. Curchod, "Practical randomness amplification and privatisation with implementations on quantum computers", arXiv:2009.06551, (2020).

[33] Hila Safi, Karen Wintersperger, and Wolfgang Mauerer, "Influence of HW-SW-Co-Design on Quantum Computing Scalability", arXiv:2306.04246, (2023).

[34] Seungchan Seo, Jiheon Seong, and Joonwoo Bae, "Mitigation of Crosstalk Errors in a Quantum Measurement and Its Applications", arXiv:2112.10651, (2021).

[35] Benjamin Anker and Milad Marvian, "Flag Gadgets based on Classical Codes", arXiv:2212.10738, (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-26 07:57:50) and SAO/NASA ADS (last updated successfully 2024-05-26 07:57:51). The list may be incomplete as not all publishers provide suitable and complete citation data.