{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T13:36:18Z","timestamp":1769088978314,"version":"3.49.0"},"reference-count":77,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T00:00:00Z","timestamp":1642982400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Moonshot R&D","award":["JPMJMS2061"],"award-info":[{"award-number":["JPMJMS2061"]}]},{"name":"The Centers of Research Excellence in Science and Technology","award":["JPMJCR1676"],"award-info":[{"award-number":["JPMJCR1676"]}]},{"DOI":"10.13039\/501100001691","name":"The Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["JP20H00134"],"award-info":[{"award-number":["JP20H00134"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001691","name":"The Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["JPJSBP120194828"],"award-info":[{"award-number":["JPJSBP120194828"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000183","name":"The Army Research Office","doi-asserted-by":"crossref","award":["W911NF-18-1-0358"],"award-info":[{"award-number":["W911NF-18-1-0358"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"crossref"}]},{"name":"The Asian Office of Aerospace Research and Development","award":["FA2386-20- 1-4069"],"award-info":[{"award-number":["FA2386-20- 1-4069"]}]},{"name":"The Foundational Questions Institute Fund","award":["FQXi-IAF19-06"],"award-info":[{"award-number":["FQXi-IAF19-06"]}]},{"name":"Accelerated Research in Quantum Computing","award":["de-sc0020266"],"award-info":[{"award-number":["de-sc0020266"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mtext mathvariant=\"monospace\">qutip-qip<\/mml:mtext><\/mml:mrow><\/mml:math>, QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad density-matrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce experimental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.<\/jats:p>","DOI":"10.22331\/q-2022-01-24-630","type":"journal-article","created":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T13:27:12Z","timestamp":1643030832000},"page":"630","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":44,"title":["Pulse-level noisy quantum circuits with QuTiP"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2733-7186","authenticated-orcid":false,"given":"Boxi","family":"Li","sequence":"first","affiliation":[{"name":"Peter Gr\u00fcnberg Institute - Quantum Control (PGI-8), Forschungszentrum J\u00fclich GmbH, D-52425 J\u00fclich, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1145-7279","authenticated-orcid":false,"given":"Shahnawaz","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of Microtechnology and Nanoscience, Chalmers University of Technology, 412 96 Gothenburg, Sweden"}]},{"given":"Sidhant","family":"Saraogi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Georgetown University, 3700 O St NW, Washington, DC 20057, United States"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7873-0773","authenticated-orcid":false,"given":"Neill","family":"Lambert","sequence":"additional","affiliation":[{"name":"Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3682-7432","authenticated-orcid":false,"given":"Franco","family":"Nori","sequence":"additional","affiliation":[{"name":"Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan"},{"name":"RIKEN Center for Quantum Computing (RQC), 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan"},{"name":"Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4717-2921","authenticated-orcid":false,"given":"Alexander","family":"Pitchford","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aberystwyth University, Penglais Campus, Aberystwyth, SY23 3BZ, Wales, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8775-3667","authenticated-orcid":false,"given":"Nathan","family":"Shammah","sequence":"additional","affiliation":[{"name":"Unitary Fund, Walnut, California 91789, USA"}]}],"member":"9598","published-online":{"date-parts":[[2022,1,24]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).","DOI":"10.22331\/q-2018-08-06-79"},{"key":"1","doi-asserted-by":"publisher","unstructured":"M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).","DOI":"10.1017\/CBO9780511976667"},{"key":"2","doi-asserted-by":"publisher","unstructured":"I. Buluta, S. Ashhab, and F. Nori, Natural and artificial atoms for quantum computation, Rep. Prog. Phys. 74, 104401 (2011).","DOI":"10.1088\/0034-4885\/74\/10\/104401"},{"key":"3","unstructured":"K. Bharti, A. Cervera-Lierta, T. H. Kyaw, T. Haug, S. Alperin-Lea, A. Anand, M. Degroote, H. Heimonen, J. S. Kottmann, T. Menke, W.-K. Mok, S. Sim, L.-C. Kwek, and A. Aspuru-Guzik, Noisy intermediate-scale quantum (NISQ) algorithms, arXiv preprint (2021), arXiv:2101.08448."},{"key":"4","unstructured":"R. S. Smith, M. J. Curtis, and W. J. Zeng, A Practical Quantum Instruction Set Architecture, arXiv preprint (2016), arXiv:1608.03355."},{"key":"5","doi-asserted-by":"publisher","unstructured":"P. J. Karalekas, N. A. Tezak, E. C. Peterson, C. A. Ryan, M. P. da Silva, and R. S. Smith, A quantum-classical cloud platform optimized for variational hybrid algorithms, Quantum Sci. Technol. 5, 024003 (2020).","DOI":"10.1088\/2058-9565\/ab7559"},{"key":"6","doi-asserted-by":"publisher","unstructured":"G. Aleksandrowicz, T. Alexander, P. Barkoutsos, L. Bello, Y. Ben-Haim, D. Bucher, F. J. Cabrera-Hern\u00e1ndez, J. Carballo-Franquis, A. Chen, C.-F. Chen, J. M. Chow, et al., Qiskit: An Open-source Framework for Quantum Computing (2019).","DOI":"10.5281\/zenodo.2562111"},{"key":"7","doi-asserted-by":"publisher","unstructured":"C. Developers, Cirq (2021), See full list of authors on Github: https:\/\/github.com\/quantumlib\/Cirq\/graphs\/contributors.","DOI":"10.5281\/zenodo.5182845"},{"key":"8","doi-asserted-by":"publisher","unstructured":"D. S. Steiger, T. H\u00e4ner, and M. Troyer, ProjectQ: an open source software framework for quantum computing, Quantum 2, 49 (2018).","DOI":"10.22331\/q-2018-01-31-49"},{"key":"9","unstructured":"V. Bergholm, J. Izaac, M. Schuld, C. Gogolin, M. S. Alam, S. Ahmed, J. M. Arrazola, C. Blank, A. Delgado, S. Jahangiri, et al., PennyLane: Automatic differentiation of hybrid quantum-classical computations, arXiv preprint (2018), arXiv:1811.04968."},{"key":"10","doi-asserted-by":"publisher","unstructured":"M. Fingerhuth, T. Babej, and P. Wittek, Open source software in quantum computing, PLOS ONE 13, e0208561 (2018).","DOI":"10.1371\/journal.pone.0208561"},{"key":"11","doi-asserted-by":"publisher","unstructured":"B. Heim, M. Soeken, S. Marshall, C. Granade, M. Roetteler, A. Geller, M. Troyer, and K. Svore, Quantum programming languages, Nat. Rev. Phys. 2, 709 (2020).","DOI":"10.1038\/s42254-020-00245-7"},{"key":"12","doi-asserted-by":"publisher","unstructured":"T. Alexander, N. Kanazawa, D. J. Egger, L. Capelluto, C. J. Wood, A. Javadi-Abhari, and D. C McKay, Qiskit pulse: Programming quantum computers through the cloud with pulses, Quantum Sci. Technol. 5, 044006 (2020).","DOI":"10.1088\/2058-9565\/aba404"},{"key":"13","doi-asserted-by":"publisher","unstructured":"H. Ball, M. J. Biercuk, A. R. R. Carvalho, J. Chen, M. Hush, L. A. D. Castro, L. Li, P. J. Liebermann, H. J. Slatyer, C. Edmunds, V. Frey, C. Hempel, and A. Milne, Software tools for quantum control: improving quantum computer performance through noise and error suppression, Quantum Sci. Technol. 6, 044011 (2021).","DOI":"10.1088\/2058-9565\/abdca6"},{"key":"14","doi-asserted-by":"publisher","unstructured":"H. Silv\u00e9rio, S. Grijalva, C. Dalyac, L. Leclerc, P. J. Karalekas, N. Shammah, M. Beji, L.-P. Henry, and L. Henriet, Pulser: An open-source package for the design of pulse sequences in programmable neutral-atom arrays, arXiv preprint (2021), arXiv:2104.15044.","DOI":"10.22331\/q-2022-01-24-629"},{"key":"15","doi-asserted-by":"publisher","unstructured":"J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open-source python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).","DOI":"10.1016\/j.cpc.2012.02.021"},{"key":"16","doi-asserted-by":"publisher","unstructured":"J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184, 1234 (2013).","DOI":"10.1016\/j.cpc.2012.11.019"},{"key":"17","doi-asserted-by":"publisher","unstructured":"N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Open quantum systems with local and collective incoherent processes: Efficient numerical simulations using permutational invariance, Phys. Rev. A 98, 063815 (2018).","DOI":"10.1103\/PhysRevA.98.063815"},{"key":"18","doi-asserted-by":"publisher","unstructured":"M. H. Goerz, D. Basilewitsch, F. Gago-Encinas, M. G. Krauss, K. P. Horn, D. M. Reich, and C. P. Koch, Krotov: A Python implementation of Krotov&apos;s method for quantum optimal control, SciPost Phys. 7, 80 (2019).","DOI":"10.21468\/SciPostPhys.7.6.080"},{"key":"19","doi-asserted-by":"publisher","unstructured":"N. Lambert, S. Ahmed, M. Cirio, and F. Nori, Modelling the ultra-strongly coupled spin-boson model with unphysical modes, Nat. Commun. 10, 3721 (2019).","DOI":"10.1038\/s41467-019-11656-1"},{"key":"20","unstructured":"N. Lambert, T. Raheja, S. Ahmed, A. Pitchford, and F. Nori, BoFiN-HEOM: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics, arXiv preprint (2020), arXiv:2010.10806."},{"key":"21","doi-asserted-by":"publisher","unstructured":"J. D. Teske and H. Bluhm, qopt: An experiment-oriented qubit simulation and quantum optimal control package, in IEEE Int. Conf. Quantum Comput. Eng. (QCE) (2021) p. 441.","DOI":"10.1109\/QCE52317.2021.00069"},{"key":"22","doi-asserted-by":"publisher","unstructured":"N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbr\u00fcggen, and S. J. Glaser, Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms, J. Magn. Reson. 172, 296 (2005).","DOI":"10.1016\/j.jmr.2004.11.004"},{"key":"23","doi-asserted-by":"publisher","unstructured":"L. B.-V. Horn, sequencing-dev\/sequencing: v1.1.3 (2021).","DOI":"10.5281\/zenodo.4515635"},{"key":"24","doi-asserted-by":"publisher","unstructured":"P. Groszkowski and J. Koch, Scqubits: a Python package for superconducting qubits, Quantum 5, 583 (2021).","DOI":"10.22331\/q-2021-11-17-583"},{"key":"25","doi-asserted-by":"publisher","unstructured":"C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, et al., Array programming with NumPy, Nature 585, 357 (2020).","DOI":"10.1038\/s41586-020-2649-2"},{"key":"26","doi-asserted-by":"publisher","unstructured":"P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, et al., SciPy 1.0: fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).","DOI":"10.1038\/s41592-019-0686-2"},{"key":"27","doi-asserted-by":"publisher","unstructured":"J. D. Hunter, Matplotlib: A 2D graphics environment, Comput. Sci. Eng. 9, 90 (2007).","DOI":"10.1109\/MCSE.2007.55"},{"key":"28","doi-asserted-by":"publisher","unstructured":"S. Behnel, R. Bradshaw, C. Citro, L. Dalcin, D. S. Seljebotn, and K. Smith, Cython: The best of both worlds, Computing in Science & Engineering 13, 31 (2011).","DOI":"10.1109\/mcse.2010.118"},{"key":"29","unstructured":"The full list of qutip-qip contributors, https:\/\/github.com\/qutip\/qutip-qip\/graphs\/contributors."},{"key":"30","unstructured":"A. W. Cross, L. S. Bishop, J. A. Smolin, and J. M. Gambetta, Open Quantum Assembly Language, arXiv preprint (2017), arXiv:1707.03429."},{"key":"31","unstructured":"A. W. Cross, A. Javadi-Abhari, T. Alexander, N. de Beaudrap, L. S. Bishop, S. Heidel, C. A. Ryan, J. Smolin, J. M. Gambetta, and B. R. Johnson, OpenQASM 3: A broader and deeper quantum assembly language, arXiv preprint (2021), arXiv:2104.14722."},{"key":"32","unstructured":"T. Nguyen, A. Santana, T. Kharazi, D. Claudino, H. Finkel, and A. McCaskey, Extending C++ for Heterogeneous Quantum-Classical Computing, arXiv preprint (2020), arXiv:2010.03935."},{"key":"33","doi-asserted-by":"publisher","unstructured":"H.-P. Breuer and F. Petruccione, The theory of open quantum systems (Oxford University Press, 2002).","DOI":"10.1093\/acprof:oso\/9780199213900.001.0001"},{"key":"34","unstructured":"D. A. Lidar, Lecture Notes on the Theory of Open Quantum Systems, arXiv preprint (2019), arXiv:1902.00967."},{"key":"35","doi-asserted-by":"publisher","unstructured":"H. J. Carmichael, Statistical methods in quantum optics 2: Non-classical fields (Springer Science & Business Media, 2009).","DOI":"10.1007\/978-3-540-71320-3"},{"key":"36","doi-asserted-by":"publisher","unstructured":"F. Minganti, N. Bartolo, J. Lolli, W. Casteels, and C. Ciuti, Exact results for Schr\u00f6dinger cats in driven-dissipative systems and their feedback control, Sci. Rep. 6, 26987 (2016).","DOI":"10.1038\/srep26987"},{"key":"37","doi-asserted-by":"publisher","unstructured":"Y. Tanimura and R. Kubo, Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath, J. Phys. Soc. Jpn. 58, 101 (1989).","DOI":"10.1143\/jpsj.58.101"},{"key":"38","doi-asserted-by":"publisher","unstructured":"D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57, 120 (1998).","DOI":"10.1103\/PhysRevA.57.120"},{"key":"39","doi-asserted-by":"publisher","unstructured":"B. E. Kane, A silicon-based nuclear spin quantum computer, Nature 393, 133 (1998).","DOI":"10.1038\/30156"},{"key":"40","doi-asserted-by":"publisher","unstructured":"M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339, 1169 (2013).","DOI":"10.1126\/science.1231930"},{"key":"41","doi-asserted-by":"publisher","unstructured":"P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A quantum engineer&apos;s guide to superconducting qubits, Appl. Phys. Rev. 6, 021318 (2019).","DOI":"10.1063\/1.5089550"},{"key":"42","doi-asserted-by":"publisher","unstructured":"X. Gu, A. F. Kockum, A. Miranowicz, Y.-X. Liu, and F. Nori, Microwave photonics with superconducting quantum circuits, Phys. Rep. 718-719, 1 (2017).","DOI":"10.1016\/j.physrep.2017.10.002"},{"key":"43","doi-asserted-by":"publisher","unstructured":"A. F. Kockum and F. Nori, Quantum bits with Josephson junctions, in Fundamentals and Frontiers of the Josephson Effect, edited by F. Tafuri (Springer, 2019) p. 703.","DOI":"10.1007\/978-3-030-20726-7_17"},{"key":"44","doi-asserted-by":"publisher","unstructured":"E. Magesan and J. M. Gambetta, Effective Hamiltonian models of the cross-resonance gate, Phys. Rev. A 101, 052308 (2020).","DOI":"10.1103\/PhysRevA.101.052308"},{"key":"45","doi-asserted-by":"publisher","unstructured":"C. Rigetti and M. Devoret, Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies, Phys. Rev. B 81, 134507 (2010).","DOI":"10.1103\/PhysRevB.81.134507"},{"key":"46","doi-asserted-by":"publisher","unstructured":"D. Maslov, G. Dueck, D. Miller, and C. Negrevergne, Quantum circuit simplification and level compaction, IEEE Trans. Comput. Des. Integr. Circuits Syst. 27, 436 (2008).","DOI":"10.1109\/tcad.2007.911334"},{"key":"47","doi-asserted-by":"publisher","unstructured":"A. Javadi-Abhari, S. Patil, D. Kudrow, J. Heckey, A. Lvov, F. T. Chong, and M. Martonosi, ScaffCC: Scalable compilation and analysis of quantum programs, Parallel Comput. 45, 2 (2015).","DOI":"10.1016\/j.parco.2014.12.001"},{"key":"48","doi-asserted-by":"publisher","unstructured":"T. H\u00e4ner, D. S. Steiger, K. Svore, and M. Troyer, A software methodology for compiling quantum programs, Quantum Sci. Technol. 3, 020501 (2018).","DOI":"10.1088\/2058-9565\/aaa5cc"},{"key":"49","unstructured":"T. F\u00f6sel, M. Y. Niu, F. Marquardt, and L. Li, Quantum circuit optimization with deep reinforcement learning, arXiv preprint (2021), arXiv:2103.07585."},{"key":"50","doi-asserted-by":"publisher","unstructured":"T. S. Metodi, D. D. Thaker, A. W. Cross, F. T. Chong, and I. L. Chuang, Scheduling physical operations in a quantum information processor, in Quantum Information and Computation IV, edited by E. J. Donkor, A. R. Pirich, and H. E. Brandt (2006) p. 62440T.","DOI":"10.1117\/12.666419"},{"key":"51","doi-asserted-by":"publisher","unstructured":"S. Sargaran and N. Mohammadzadeh, SAQIP: A Scalable Architecture for Quantum Information Processors, ACM Trans. Archit. Code Optim. 16 (2019).","DOI":"10.1145\/3311879"},{"key":"52","doi-asserted-by":"publisher","unstructured":"P. Murali, J. M. Baker, A. Javadi-Abhari, F. T. Chong, and M. Martonosi, Noise-adaptive compiler mappings for noisy intermediate-scale quantum computers, in Proc. 24th Int. Conf. Archit. Support Program. Lang. Oper. Syst. (ACM, 2019) p. 1015.","DOI":"10.1145\/3297858.3304075"},{"key":"53","doi-asserted-by":"publisher","unstructured":"G. G. Guerreschi and J. Park, Two-step approach to scheduling quantum circuits, Quantum Sci. Technol. 3, 045003 (2018).","DOI":"10.1088\/2058-9565\/aacf0b"},{"key":"54","doi-asserted-by":"publisher","unstructured":"D. D&apos;Alessandro, Introduction to Quantum Control and Dynamics (Chapman & Hall\/CRC, 2007).","DOI":"10.1201\/9781584888833"},{"key":"55","doi-asserted-by":"publisher","unstructured":"S. Machnes, U. Sander, S. J. Glaser, P. de Fouqui\u00e8res, A. Gruslys, S. Schirmer, and T. Schulte-Herbr\u00fcggen, Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework, Phys. Rev. A 84, 022305 (2011).","DOI":"10.1103\/PhysRevA.84.022305"},{"key":"56","doi-asserted-by":"publisher","unstructured":"T. Caneva, T. Calarco, and S. Montangero, Chopped random-basis quantum optimization, Phys. Rev. A 84, 022326 (2011).","DOI":"10.1103\/PhysRevA.84.022326"},{"key":"57","doi-asserted-by":"publisher","unstructured":"P. Doria, T. Calarco, and S. Montangero, Optimal control technique for many-body quantum dynamics, Phys. Rev. Lett. 106, 190501 (2011).","DOI":"10.1103\/PhysRevLett.106.190501"},{"key":"58","doi-asserted-by":"publisher","unstructured":"P. Mundada, G. Zhang, T. Hazard, and A. Houck, Suppression of qubit crosstalk in a tunable coupling superconducting circuit, Phys. Rev. Appl. 12, 054023 (2019).","DOI":"10.1103\/physrevapplied.12.054023"},{"key":"59","doi-asserted-by":"publisher","unstructured":"C. Piltz, T. Sriarunothai, A. Var\u00f3n, and C. Wunderlich, A trapped-ion-based quantum byte with $10^{-5}$ next-neighbour cross-talk, Nat. Commun. 5, 4679 (2014).","DOI":"10.1038\/ncomms5679"},{"key":"60","unstructured":"N. Khammassi, G. G. Guerreschi, I. Ashraf, J. W. Hogaboam, C. G. Almudever, and K. Bertels, cqasm v1. 0: Towards a common quantum assembly language, arXiv preprint (2018), arXiv:1805.09607."},{"key":"61","doi-asserted-by":"publisher","unstructured":"M. Alam, A. Ash-Saki, and S. Ghosh, Accelerating quantum approximate optimization algorithm using machine learning, in 2020 Des. Autom. Test Eur. Conf. Exhib. (DATE) (2020) p. 686.","DOI":"10.23919\/DATE48585.2020.9116348"},{"key":"62","unstructured":"T. Haug and M. S. Kim, Optimal training of variational quantum algorithms without barren plateaus, arXiv preprint (2021), arXiv:2104.14543."},{"key":"63","doi-asserted-by":"publisher","unstructured":"A. B. Magann, C. Arenz, M. D. Grace, T.-S. Ho, R. L. Kosut, J. R. McClean, H. A. Rabitz, and M. Sarovar, From pulses to circuits and back again: A quantum optimal control perspective on variational quantum algorithms, PRX Quantum 2, 010101 (2021).","DOI":"10.1103\/PRXQuantum.2.010101"},{"key":"64","doi-asserted-by":"publisher","unstructured":"Erik, L. Saldyt, Rob, tjproct, J. Gross, sserita, kmrudin, T. L. Scholten, colibri-coruscans, kevincyoung, msarovar, coreyostrove, jordanh6, D. Nadlinger, L. N. Maurer, pyIonControl, and R. Blume-Kohout, pyGSTio\/pyGSTi: Version 0.9.10 (2021).","DOI":"10.5281\/zenodo.5546759"},{"key":"65","doi-asserted-by":"publisher","unstructured":"A. Kandala, K. Temme, A. D. C\u00f3rcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Error mitigation extends the computational reach of a noisy quantum processor, Nature 567, 491 (2019).","DOI":"10.1038\/s41586-019-1040-7"},{"key":"66","doi-asserted-by":"publisher","unstructured":"T. Giurgica-Tiron, Y. Hindy, R. LaRose, A. Mari, and W. J. Zeng, Digital zero noise extrapolation for quantum error mitigation, in IEEE Int. Conf. Quantum Comput. Eng. (QCE) (2020) p. 306.","DOI":"10.1109\/QCE49297.2020.00045"},{"key":"67","unstructured":"R. LaRose, A. Mari, S. Kaiser, P. J. Karalekas, A. A. Alves, P. Czarnik, M. E. Mandouh, M. H. Gordon, Y. Hindy, A. Robertson, P. Thakre, N. Shammah, and W. J. Zeng, Mitiq: A software package for error mitigation on noisy quantum computers, arXiv preprint (2021), arXiv:2009.04417."},{"key":"68","doi-asserted-by":"publisher","unstructured":"M. L. Dahlhauser and T. S. Humble, Modeling noisy quantum circuits using experimental characterization, Phys. Rev. A 103, 042603 (2021).","DOI":"10.1103\/PhysRevA.103.042603"},{"key":"69","doi-asserted-by":"publisher","unstructured":"K. Schultz, G. Quiroz, P. Titum, and B. D. Clader, SchWARMA: A model-based approach for time-correlated noise in quantum circuits, Phys. Rev. Research 3, 033229 (2021).","DOI":"10.1103\/PhysRevResearch.3.033229"},{"key":"70","doi-asserted-by":"publisher","unstructured":"S. Humpohl, L. Prediger, pcerf, P. Bethke, A. Willmes, J. Bergmann, M. Meyer, P. Eendebak, E. Kammerloher, T. Hangleiter, qutech-lab, L. Lankes, m-kreutz, bpapajewski, and P. Eendebak, qutech\/qupulse: qupulse 0.6 (2021).","DOI":"10.5281\/zenodo.5082282"},{"key":"71","doi-asserted-by":"publisher","unstructured":"N. Wittler, F. Roy, K. Pack, M. Werninghaus, A. S. Roy, D. J. Egger, S. Filipp, F. K. Wilhelm, and S. Machnes, Integrated Tool Set for Control, Calibration, and Characterization of Quantum Devices Applied to Superconducting Qubits, Phys. Rev. Appl. 15, 034080 (2021).","DOI":"10.1103\/PhysRevApplied.15.034080"},{"key":"72","doi-asserted-by":"publisher","unstructured":"B. Skinner, J. Ruhman, and A. Nahum, Measurement-induced phase transitions in the dynamics of entanglement, Phys. Rev. X 9, 031009 (2019).","DOI":"10.1103\/PhysRevX.9.031009"},{"key":"73","doi-asserted-by":"publisher","unstructured":"M. S. Blok, V. V. Ramasesh, T. Schuster, K. O&apos;Brien, J. M. Kreikebaum, D. Dahlen, A. Morvan, B. Yoshida, N. Y. Yao, and I. Siddiqi, Quantum information scrambling on a superconducting qutrit processor, Phys. Rev. X 11, 021010 (2021).","DOI":"10.1103\/PhysRevX.11.021010"},{"key":"74","doi-asserted-by":"publisher","unstructured":"S. Machnes, E. Ass\u00e9mat, D. Tannor, and F. K. Wilhelm, Tunable, Flexible, and Efficient Optimization of Control Pulses for Practical Qubits, Phys. Rev. Lett. 120, 150401 (2018).","DOI":"10.1103\/PhysRevLett.120.150401"},{"key":"75","doi-asserted-by":"publisher","unstructured":"D. Dong, C. Chen, B. Qi, I. R. Petersen, and F. Nori, Robust manipulation of superconducting qubits in the presence of fluctuations, Sci. Rep. 5, 7873 (2015).","DOI":"10.1038\/srep07873"},{"key":"76","doi-asserted-by":"publisher","unstructured":"D. Dong, C. Wu, C. Chen, B. Qi, I. R. Petersen, and F. Nori, Learning robust pulses for generating universal quantum gates, Sci. Rep. 6, 36090 (2016).","DOI":"10.1038\/srep36090"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-01-24-630\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T13:56:52Z","timestamp":1643032612000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-01-24-630\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,24]]},"references-count":77,"URL":"https:\/\/doi.org\/10.22331\/q-2022-01-24-630","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,24]]},"article-number":"630"}}