Detecting crosstalk errors in quantum information processors

Mohan Sarovar, Timothy Proctor, Kenneth Rudinger, Kevin Young, Erik Nielsen, and Robin Blume-Kohout

Quantum Performance Laboratory, Sandia National Laboratories, Albuquerque, NM 87185 and Livermore, CA 94550

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Crosstalk occurs in most quantum computing systems with more than one qubit. It can cause a variety of correlated and nonlocal $\textit{crosstalk errors}$ that can be especially harmful to fault-tolerant quantum error correction, which generally relies on errors being local and relatively predictable. Mitigating crosstalk errors requires understanding, modeling, and detecting them. In this paper, we introduce a comprehensive framework for crosstalk errors and a protocol for detecting and localizing them. We give a rigorous definition of crosstalk errors that captures a wide range of disparate physical phenomena that have been called ``crosstalk'', and a concrete model for crosstalk-free quantum processors. Errors that violate this model are crosstalk errors. Next, we give an equivalent but purely operational (model-independent) definition of crosstalk errors. Using this definition, we construct a protocol for detecting a large class of crosstalk errors in a multi-qubit processor by finding conditional dependencies between observed experimental probabilities. It is highly efficient, in the sense that the number of unique experiments required scales at most cubically, and very often quadratically, with the number of qubits. We demonstrate the protocol using simulations of 2-qubit and 6-qubit processors.

Crosstalk is a pressing concern for nearly all quantum computing hardware platforms; characterizing and mitigating errors due to various sources of crosstalk will be essential for achieving fault-tolerant quantum computation. Despite this, there is no general definition of crosstalk in the field and no general-purpose tools for efficiently characterizing, or even detecting, crosstalk. We address these critical needs by (i) formalizing crosstalk errors and developing a framework for characterizing the effects of crosstalk in quantum information processors (QIPs), and (ii) developing an efficient crosstalk error detection protocol for multi-qubit QIPs by adapting techniques from statistical causal inference.

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► References

[1] PyGSTi. A python implementation of Gate Set Tomography. URL: http:/​/​​.

[2] IBM Qiskit/​ibmq-device-information/​tenerife, 2019. URL: https:/​/​​Qiskit/​ibmq-device-information/​tree/​master/​backends/​tenerife/​V1.

[3] Carole Addis, Francesco Ciccarello, Michele Cascio, G Massimo Palma, and Sabrina Maniscalco. Dynamical decoupling efficiency versus quantum non-markovianity. New Journal of Physics, 17(12):123004, 2015. doi:10.1088/​1367-2630/​17/​12/​123004.

[4] D Bacciu, T A Etchells, P J G Lisboa, and J Whittaker. Efficient identification of independence networks using mutual information. Computational Statistics, 28:621, 2013. doi:10.1007/​s00180-012-0320-6.

[5] Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, and Ronald de Wolf. Quantum lower bounds by polynomials. Journal of the ACM, 48(4):778–797, July 2001. doi:10.1145/​502090.502097.

[6] R. C. Bialczak, M. Ansmann, M. Hofheinz, E. Lucero, M. Neeley, A. D. O'Connell, D. Sank, H. Wang, J. Wenner, M. Steffen, A. N. Cleland, and J. M. Martinis. Quantum process tomography of a universal entangling gate implemented with Josephson phase qubits. Nature Physics, 6(6):409–413, 2010. doi:10.1038/​nphys1639.

[7] Robin Blume-Kohout, John King Gamble, Erik Nielsen, Kenneth Rudinger, Jonathan Mizrahi, Kevin Fortier, and Peter Maunz. Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography. Nature Communications, 8:1, 2017. doi:10.1038/​ncomms14485.

[8] Heinz-Peter Breuer, Elsi-Mari Laine, and Jyrki Piilo. Measure for the degree of non-markovian behavior of quantum processes in open systems. Phys. Rev. Lett., 103:210401, 2009. doi:10.1103/​PhysRevLett.103.210401.

[9] Caslav Brukner. Quantum causality. Nature Physics, 10(4):259–263, 2014. doi:10.1038/​nphys2930.

[10] Donovan Buterakos, Robert E. Throckmorton, and S. Das Sarma. Crosstalk error correction through dynamical decoupling of single-qubit gates in capacitively coupled singlet-triplet semiconductor spin qubits. Physical Review B, 97(4):045431, January 2018. doi:10.1103/​PhysRevB.97.045431.

[11] Yanzhu Chen, Maziar Farahzad, Shinjae Yoo, and Tzu-Chieh Wei. Detector tomography on IBM quantum computers and mitigation of an imperfect measurement. Physical Review A, 100(5):052315, November 2019. Publisher: American Physical Society. doi:10.1103/​PhysRevA.100.052315.

[12] W. A. Coish and Daniel Loss. Hyperfine interaction in a quantum dot: Non-markovian electron spin dynamics. Phys. Rev. B, 70:195340, 2004. doi:10.1103/​PhysRevB.70.195340.

[13] Diego Colombo and Marloes H Maathuis. Order-Independent Constraint-Based Causal Structure Learning. J. Machine Learning Research, 15:3921, 2014. URL: http:/​/​​papers/​volume15/​colombo14a/​colombo14a.pdf. https:/​/​​abs/​1211.3295.

[14] Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine. Exact and approximate unitary 2-designs and their application to fidelity estimation. Physical Review A, 80(1):012304, 2009. doi:10.1103/​PhysRevA.80.012304.

[15] E. B. Davies and J. T. Lewis. An operational approach to quantum probability. Communications in Mathematical Physics, 17(3):239–260, 1970. doi:10.1007/​BF01647093.

[16] S. Debnath, N. M. Linke, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe. Demonstration of a small programmable quantum computer with atomic qubits. Nature, 536(7614):63–66, August 2016. doi:10.1038/​nature18648.

[17] Alexander Erhard, Joel J. Wallman, Lukas Postler, Michael Meth, Roman Stricker, Esteban A. Martinez, Philipp Schindler, Thomas Monz, Joseph Emerson, and Rainer Blatt. Characterizing large-scale quantum computers via cycle benchmarking. Nature Communications, 10(1):5347, 2019. doi:10.1038/​s41467-019-13068-7.

[18] Jay M. Gambetta, A D Córcoles, S T Merkel, B R Johnson, John A Smolin, Jerry M Chow, Colm A Ryan, Chad Rigetti, S Poletto, Thomas A Ohki, Mark B Ketchen, and M Steffen. Characterization of Addressability by Simultaneous Randomized Benchmarking. Physical Review Letters, 109(24):240504–5, 2012. doi:10.1103/​PhysRevLett.109.240504.

[19] Ming Gong, Ming-Cheng Chen, Yarui Zheng, Shiyu Wang, Chen Zha, Hui Deng, Zhiguang Yan, Hao Rong, Yulin Wu, Shaowei Li, Fusheng Chen, Youwei Zhao, Futian Liang, Jin Lin, Yu Xu, Cheng Guo, Lihua Sun, Anthony D. Castellano, Haohua Wang, Chengzhi Peng, Chao-Yang Lu, Xiaobo Zhu, and Jian-Wei Pan. Genuine 12-Qubit Entanglement on a Superconducting Quantum Processor. Physical Review Letters, 122(11):110501, 2019. doi:10.1103/​PhysRevLett.122.110501.

[20] D. Gross, K. Audenaert, and J. Eisert. Evenly distributed unitaries: On the structure of unitary designs. Journal of Mathematical Physics, 48(5):052104, 2007. doi:10.1063/​1.2716992.

[21] Vojtech Havlicek, Antonio D. Corcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta. Supervised learning with quantum-enhanced feature spaces. Nature, 567(7747):209–212, 2019. doi:10.1038/​s41586-019-0980-2.

[22] Patrick Hayden, Debbie Leung, and Graeme Smith. Multiparty data hiding of quantum information. Physical Review A, 71(6):062339, 2005. doi:10.1103/​PhysRevA.71.062339.

[23] Johannes Heinsoo, Christian Kraglund Andersen, Ants Remm, Sebastian Krinner, Theodore Walter, Yves Salathe, Simone Gasparinetti, Jean-Claude Besse, Anton Potocnik, Andreas Wallraff, and Christopher Eichler. Rapid High-fidelity Multiplexed Readout of Superconducting Qubits. Physical Review Applied, 10(3), 2018. doi:10.1103/​PhysRevApplied.10.034040.

[24] Miguel A Hernan, David Clayton, and Niels Keiding. The Simpson's paradox unraveled. International Journal of Epidemiology, 40(3):780–785, 2011. doi:10.1093/​ije/​dyr041.

[25] Markus Kalisch and Peter Bühlmann. Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm. Journal of Machine Learning Research, 8(Mar):613–636, January 2007. URL: http:/​/​​papers/​v8/​kalisch07a.html.

[26] Anna Klimova, Caroline Uhler, and Tamás Rudas. Faithfulness and learning hypergraphs from discrete distributions. Computational Statistics & Data Analysis, 87:57–72, 2015. doi:10.1016/​j.csda.2015.01.017.

[27] D Koller and N Friedman. Probabilistic Graphical Models. MIT Press, 2009.

[28] Timo J.T. Koski and John Noble. A Review of Bayesian Networks and Structure Learning. Mathematica Applicanda, 40(1):51–103, 2012. doi:10.14708/​ma.v40i1.278.

[29] T D Ladd, F Jelezko, R Laflamme, Y Nakamura, C Monroe, and J L O'Brien. Quantum computers. Nature, 464:45, 2010. doi:10.1038/​nature08812.

[30] Thuc Duy Le, Tao Hoang, Jiuyong Li, Lin Liu, Huawen Liu, and Shu Hu. A Fast PC Algorithm for High Dimensional Causal Discovery with Multi-Core PCs. IEEE/​ACM Transactions on Computational Biology and Bioinformatics, 16(5):1483–1495, 2019. doi:10.1109/​TCBB.2016.2591526.

[31] Junning Li and Z Jane Wang. Controlling the False Discovery Rate of the Association/​Causality Structure Learned with the PC Algorithm. J. Machine Learning Research, 10:475, 2009. URL: http:/​/​​papers/​v10/​li09a.html.

[32] Li Li, Michael J.W. Hall, and Howard M. Wiseman. Concepts of quantum non-markovianity: A hierarchy. Physics Reports, 759:1 – 51, 2018. doi:10.1016/​j.physrep.2018.07.001.

[33] David Lopez-Paz, Krikamol Muandet, Bernhard Schölkopf, and Ilya Tolstikhin. Towards a learning theory of cause-effect inference. In Proceedings of the 32nd International Conference on International Conference on Machine Learning - Volume 37, ICML'15, pages 1452–1461, 2015. URL: http:/​/​​citation.cfm?id=3045118.3045273.

[34] Ruichao Ma, Brendan Saxberg, Clai Owens, Nelson Leung, Yao Lu, Jonathan Simon, and David I. Schuster. A dissipatively stabilized Mott insulator of photons. Nature, 566(7742):51, February 2019. doi:10.1038/​s41586-019-0897-9.

[35] Filip B. Maciejewski, Zoltán Zimborás, and Michał Oszmaniec. Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography. Quantum, 4:257, April 2020. doi:10.22331/​q-2020-04-24-257.

[36] Rupak Majumdar and Filip Niksic. Why is random testing effective for partition tolerance bugs? Proceedings of the ACM on Programming Languages, 2(POPL):1–24, January 2018. doi:10.1145/​3158134.

[37] S. Mavadia, C. L. Edmunds, C. Hempel, H. Ball, F. Roy, T. M. Stace, and M. J. Biercuk. Experimental quantum verification in the presence of temporally correlated noise. npj Quantum Information, 4(1):7, 2018. doi:10.1038/​s41534-017-0052-0.

[38] F Mazda. Telecommunications Engineer's Reference Book. Elsevier, 1993. doi:10.1016/​C2013-0-06529-2.

[39] David C. McKay, Sarah Sheldon, John A. Smolin, Jerry M. Chow, and Jay M. Gambetta. Three-Qubit Randomized Benchmarking. Physical Review Letters, 122(20):200502, 2019. doi:10.1103/​PhysRevLett.122.200502.

[40] Jovana Mitrovic, Dino Sejdinovic, and Yee Whye Teh. Causal inference via kernel deviance measures. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, NIPS'18, pages 6986–6994, 2018. URL: https:/​/​​doi/​10.5555/​3327757.3327802.

[41] Richard E Neapolitan. Learning Bayesian Networks. Prentice Hall, 2004.

[42] Matthew Neeley, Radoslaw C. Bialczak, M. Lenander, E. Lucero, Matteo Mariantoni, A. D. O'Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and John M. Martinis. Generation of three-qubit entangled states using superconducting phase qubits. Nature, 467(7315):570–573, 2010. doi:10.1038/​nature09418.

[43] C. Neill, P. Roushan, K. Kechedzhi, S. Boixo, S. V. Isakov, V. Smelyanskiy, A. Megrant, B. Chiaro, A. Dunsworth, K. Arya, R. Barends, B. Burkett, Y. Chen, Z. Chen, A. Fowler, B. Foxen, M. Giustina, R. Graff, E. Jeffrey, T. Huang, J. Kelly, P. Klimov, E. Lucero, J. Mutus, M. Neeley, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, H. Neven, and J. M. Martinis. A blueprint for demonstrating quantum supremacy with superconducting qubits. Science, 360(6385):195–199, April 2018. doi:10.1126/​science.aao4309.

[44] C. Piltz, T. Sriarunothai, A.F. Varon, and C. Wunderlich. A trapped-ion-based quantum byte with $10^{-5}$ next-neighbour cross-talk. Nature Communications, 5(1):4679, December 2014. doi:10.1038/​ncomms5679.

[45] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, 2018. doi:10.22331/​q-2018-08-06-79.

[46] Timothy Proctor, Melissa Revelle, Erik Nielsen, Kenneth Rudinger, Daniel Lobser, Peter Maunz, Robin Blume-Kohout, and Kevin Young. Detecting, tracking, and eliminating drift in quantum information processors. July 2019. arXiv: 1907.13608. URL: http:/​/​​abs/​1907.13608.

[47] Timothy Proctor, Kenneth Rudinger, Kevin Young, Mohan Sarovar, and Robin Blume-Kohout. What Randomized Benchmarking Actually Measures. Physical Review Letters, 119(13), 2017. doi:10.1103/​PhysRevLett.119.130502.

[48] Timothy J. Proctor, Arnaud Carignan-Dugas, Kenneth Rudinger, Erik Nielsen, Robin Blume-Kohout, and Kevin Young. Direct Randomized Benchmarking for Multiqubit Devices. Physical Review Letters, 123(3):030503, 2019. doi:10.1103/​PhysRevLett.123.030503.

[49] Matthew Reagor, Christopher B. Osborn, Nikolas Tezak, Alexa Staley, Guenevere Prawiroatmodjo, Michael Scheer, Nasser Alidoust, Eyob A. Sete, Nicolas Didier, Marcus P. da Silva, Ezer Acala, Joel Angeles, Andrew Bestwick, Maxwell Block, Benjamin Bloom, Adam Bradley, Catvu Bui, Shane Caldwell, Lauren Capelluto, Rick Chilcott, Jeff Cordova, Genya Crossman, Michael Curtis, Saniya Deshpande, Tristan El Bouayadi, Daniel Girshovich, Sabrina Hong, Alex Hudson, Peter Karalekas, Kat Kuang, Michael Lenihan, Riccardo Manenti, Thomas Manning, Jayss Marshall, Yuvraj Mohan, William O'Brien, Johannes Otterbach, Alexander Papageorge, Jean-Philip Paquette, Michael Pelstring, Anthony Polloreno, Vijay Rawat, Colm A. Ryan, Russ Renzas, Nick Rubin, Damon Russel, Michael Rust, Diego Scarabelli, Michael Selvanayagam, Rodney Sinclair, Robert Smith, Mark Suska, Ting-Wai To, Mehrnoosh Vahidpour, Nagesh Vodrahalli, Tyler Whyland, Kamal Yadav, William Zeng, and Chad T. Rigetti. Demonstration of universal parametric entangling gates on a multi-qubit lattice. Science Advances, 4(2):eaao3603, 2018. doi:10.1126/​sciadv.aao3603.

[50] Kenneth Rudinger, Timothy Proctor, Dylan Langharst, Mohan Sarovar, Kevin Young, and Robin Blume-Kohout. Probing Context-Dependent Errors in Quantum Processors. Physical Review X, 9(2):021045, 2019. doi:10.1103/​PhysRevX.9.021045.

[51] Sarah Sheldon, Easwar Magesan, Jerry M Chow, and Jay M. Gambetta. Procedure for systematically tuning up cross-talk in the cross-resonance gate. Phys. Rev. A, 93(6):060302, 2016. doi:10.1103/​PhysRevA.93.060302.

[52] Peter Spirtes. Introduction to Causal Inference. Journal of Machine Learning Research, 11:1643, 2010. URL: http:/​/​​papers/​v11/​spirtes10a.html.

[53] Peter Spirtes and Clark Glymour. An Algorithm for Fast Recovery of Sparse Causal Graphs. Social Science Computer Review, 9(1):67, 1991. doi:10.1177/​089443939100900106.

[54] Peter Spirtes, Clark N. Glymour, and Richard Scheines. Causation, prediction, and search. MIT Press, Cambridge, Mass, 2nd ed edition, 2000.

[55] Peter Spirtes and Kun Zhang. Causal discovery and inference: concepts and recent methodological advances. Applied Informatics, 3:3, 2016. doi:10.1186/​s40535-016-0018-x.

[56] Eric V. Strobl, Peter L. Spirtes, and Shyam Visweswaran. Estimating and Controlling the False Discovery Rate of the PC Algorithm Using Edge-specific P-Values. ACM Transactions on Intelligent Systems and Technology, 10(5):1–37, 2019. doi:10.1145/​3351342.

[57] L. M. K. Vandersypen and I. L. Chuang. NMR techniques for quantum control and computation. Reviews of Modern Physics, 76(4):1037–1069, January 2005. doi:10.1103/​RevModPhys.76.1037.

[58] Andrzej Veitia, Marcus P. da Silva, Robin Blume-Kohout, and Steven J. van Enk. Macroscopic instructions vs microscopic operations. 2017. arXiv: 1708.08173. URL: http:/​/​​abs/​1708.08173.

[59] Joel J Wallman and Steven T Flammia. Randomized benchmarking with confidence. New Journal of Physics, 16(10):103032, 2014. doi:10.1088/​1367-2630/​16/​10/​103032.

[60] Adam Winick, Joel J. Wallman, and Joseph Emerson. Phenomenological measure of quantum non-markovianity. 2019. arXiv:1901.00267. URL: http:/​/​​abs/​1901.00267.

[61] Christopher J Wood and Robert W Spekkens. The lesson of causal discovery algorithms for quantum correlations: causal explanations of Bell-inequality violations require fine-tuning. New Journal of Physics, 17(3):033002, 2015. doi:10.1088/​1367-2630/​17/​3/​033002.

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[7] Pedro Parrado-Rodríguez, Ciarán Ryan-Anderson, Alejandro Bermudez, and Markus Müller, "Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions", Quantum 5, 487 (2021).

[8] Peng Duan, Zi-Feng Chen, Qi Zhou, Wei-Cheng Kong, Hai-Feng Zhang, and Guo-Ping Guo, "Mitigating Crosstalk-Induced Qubit Readout Error with Shallow-Neural-Network Discrimination", Physical Review Applied 16 2, 024063 (2021).

[9] Adam Winick, Joel J. Wallman, and Joseph Emerson, "Simulating and Mitigating Crosstalk", Physical Review Letters 126 23, 230502 (2021).

[10] Dominik Hangleiter, "Crosstalk diagnosis for the next generation of quantum processors", Quantum Views 4, 46 (2020).

[11] Lukasz Cincio, Kenneth Rudinger, Mohan Sarovar, and Patrick J. Coles, "Machine Learning of Noise-Resilient Quantum Circuits", arXiv:2007.01210, PRX Quantum 2 1, 010324 (2021).

[12] Gregory A. L. White, "Gate set tomography is not just hyperaccurate, it’s a different way of thinking", Quantum Views 5, 60 (2021).

[13] Xi Cao, Yu-xi Liu, and Re-Bing Wu, "Identification of time-varying signals in quantum systems", Physical Review A 103 2, 022612 (2021).

[14] Gary J. Mooney, Gregory A. L. White, Charles D. Hill, and Lloyd C. L. Hollenberg, "Whole‐Device Entanglement in a 65‐Qubit Superconducting Quantum Computer", Advanced Quantum Technologies 4 10, 2100061 (2021).

[15] G. A. L. White, C. D. Hill, F. A. Pollock, L. C. L. Hollenberg, and K. Modi, "Demonstration of non-Markovian process characterisation and control on a quantum processor", Nature Communications 11 1, 6301 (2020).

[16] Erik Nielsen, John King Gamble, Kenneth Rudinger, Travis Scholten, Kevin Young, and Robin Blume-Kohout, "Gate Set Tomography", Quantum 5, 557 (2021).

[17] Carsten Blank, Daniel K. Park, June-Koo Kevin Rhee, and Francesco Petruccione, "Quantum classifier with tailored quantum kernel", npj Quantum Information 6, 41 (2020).

[18] Erik Nielsen, Kenneth Rudinger, Timothy Proctor, Antonio Russo, Kevin Young, and Robin Blume-Kohout, "Probing quantum processor performance with pyGSTi", Quantum Science and Technology 5 4, 044002 (2020).

[19] David C. McKay, Andrew W. Cross, Christopher J. Wood, and Jay M. Gambetta, "Correlated Randomized Benchmarking", arXiv:2003.02354.

[20] S. Krinner, S. Lazar, A. Remm, C. K. Andersen, N. Lacroix, G. J. Norris, C. Hellings, M. Gabureac, C. Eichler, and A. Wallraff, "Benchmarking Coherent Errors in Controlled-Phase Gates due to Spectator Qubits", Physical Review Applied 14 2, 024042 (2020).

[21] Timothy Proctor, Kenneth Rudinger, Kevin Young, Erik Nielsen, and Robin Blume-Kohout, "Measuring the Capabilities of Quantum Computers", arXiv:2008.11294.

[22] Robin Harper, Wenjun Yu, and Steven T. Flammia, "Fast Estimation of Sparse Quantum Noise", arXiv:2007.07901.

[23] Salonik Resch and Ulya R. Karpuzcu, "Benchmarking Quantum Computers and the Impact of Quantum Noise", arXiv:1912.00546.

[24] Sihao Huang, Benjamin Lienhard, Greg Calusine, Antti Vepsäläinen, Jochen Braumüller, David K. Kim, Alexander J. Melville, Bethany M. Niedzielski, Jonilyn L. Yoder, Bharath Kannan, Terry P. Orlando, Simon Gustavsson, and William D. Oliver, "Microwave Package Design for Superconducting Quantum Processors", PRX Quantum 2 2, 020306 (2021).

[25] Dominik Hangleiter, "Sampling and the complexity of nature", arXiv:2012.07905.

[26] Yvonne Y. Gao, M. Adriaan Rol, Steven Touzard, and Chen Wang, "A practical guide for building superconducting quantum devices", arXiv:2106.06173.

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