{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T12:19:07Z","timestamp":1777983547425,"version":"3.51.4"},"reference-count":66,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T00:00:00Z","timestamp":1777939200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union\u2019s Horizon Europe Framework Programme","award":["101114899"],"award-info":[{"award-number":["101114899"]}]},{"DOI":"10.13039\/501100004359","name":"Swedish Research Council","doi-asserted-by":"crossref","award":["DAIQUIRI"],"award-info":[{"award-number":["DAIQUIRI"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"crossref"}]},{"name":"CREST","award":["JPMJCR23I3"],"award-info":[{"award-number":["JPMJCR23I3"]}]},{"name":"Hybrid Quantum Initiative","award":["ANR-22-PNCQ-0002"],"award-info":[{"award-number":["ANR-22-PNCQ-0002"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"State conversion is a fundamental task in quantum information processing. Quantum resource theories allow for analyzing and bounding conversions that use restricted sets of operations. In the context of continuous-variable systems, state conversions restricted to Gaussian operations are crucial for both fundamental and practical reasons, particularly in state preparation and quantum computing with bosonic codes. However, previous analysis did not consider the relevant case of approximate state conversion. In this work, we introduce a framework for assessing approximate Gaussian state conversion by extending the stellar rank to the approximate stellar rank, which serves as an operational measure of non-Gaussianity. We derive bounds for Gaussian state conversion and distillation under approximate and probabilistic conditions, yielding new no-go results for non-Gaussian state preparation and enabling a reliable assessment of the performance of Gaussian conversion protocols. We also provide an open-source Python library to compute stellar-rank-related quantities and to assess Gaussian conversion.<\/jats:p>","DOI":"10.22331\/q-2026-05-05-2095","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T11:21:29Z","timestamp":1777980089000},"page":"2095","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Assessing non-Gaussian quantum state conversion with the stellar rank"],"prefix":"10.22331","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1677-8696","authenticated-orcid":false,"given":"Oliver","family":"Hahn","sequence":"first","affiliation":[{"name":"Department of Basic Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8902, Japan"},{"name":"Wallenberg Centre for Quantum Technology, Department of Microtechnology and Nanoscience, Chalmers University of Technology, Sweden , SE-412 96 G\u00f6teborg, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maxime","family":"Garnier","sequence":"additional","affiliation":[{"name":"DIENS, \u00c9cole Normale Sup\u00e9rieure, PSL University, CNRS, INRIA, 45 rue d\u2019Ulm, Paris, 75005, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giulia","family":"Ferrini","sequence":"additional","affiliation":[{"name":"Wallenberg Centre for Quantum Technology, Department of Microtechnology and Nanoscience, Chalmers University of Technology, Sweden , SE-412 96 G\u00f6teborg, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Ferraro","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica ``Aldo Pontremoli'', Universit\u00e0 degli Studi di Milano, I-20133 Milano, Italy"},{"name":"Centre for Theoretical Atomic, Molecular and Optical Physics, Queen's University Belfast, Belfast BT7 1NN, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0135-9819","authenticated-orcid":false,"given":"Ulysse","family":"Chabaud","sequence":"additional","affiliation":[{"name":"DIENS, \u00c9cole Normale Sup\u00e9rieure, PSL University, CNRS, INRIA, 45 rue d\u2019Ulm, Paris, 75005, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,5,5]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"E. Chitambar and G. Gour, ``Quantum resource theories,'' Rev. Mod. Phys. 91, 025001 (2019).","DOI":"10.1103\/RevModPhys.91.025001"},{"key":"1","doi-asserted-by":"publisher","unstructured":"S. Lloyd and S. L. Braunstein, ``Quantum computation over continuous variables,'' in Quantum Information with Continuous Variables, pp. 9\u201317. Springer, 1999.","DOI":"10.1007\/978-94-015-1258-9_2"},{"key":"2","doi-asserted-by":"publisher","unstructured":"N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, ``Universal Quantum Computation with Continuous-Variable Cluster States,'' Phys. Rev. Lett. 97, 110501 (2006).","DOI":"10.1103\/PhysRevLett.97.110501"},{"key":"3","doi-asserted-by":"publisher","unstructured":"C. Weedbrook, S. Pirandola, R. Garc\u00eda-Patr\u00f3n, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, ``Gaussian quantum information,'' Rev. Mod. Phys. 84, 621\u2013669 (2012).","DOI":"10.1103\/RevModPhys.84.621"},{"key":"4","doi-asserted-by":"publisher","unstructured":"O. Pfister, ``Continuous-variable quantum computing in the quantum optical frequency comb,'' J. Phys. B 53, 012001 (2019).","DOI":"10.1088\/1361-6455\/ab526f"},{"key":"5","doi-asserted-by":"publisher","unstructured":"K. Fukui and S. Takeda, ``Building a large-scale quantum computer with continuous-variable optical technologies,'' J. Phys. B. 55, 012001 (2022).","DOI":"10.1088\/1361-6455\/ac489c"},{"key":"6","doi-asserted-by":"publisher","unstructured":"B. M. Terhal, J. Conrad, and C. Vuillot, ``Towards scalable bosonic quantum error correction,'' Quantum Sci. Technol. 5, 043001 (2020).","DOI":"10.1088\/2058-9565\/ab98a5"},{"key":"7","doi-asserted-by":"publisher","unstructured":"A. L. Grimsmo and S. Puri, ``Quantum Error Correction with the Gottesman-Kitaev-Preskill Code,'' PRX Quantum 2, 020101 (2021).","DOI":"10.1103\/PRXQuantum.2.020101"},{"key":"8","doi-asserted-by":"publisher","unstructured":"A. Joshi, K. Noh, and Y. Y. Gao, ``Quantum information processing with bosonic qubits in circuit QED,'' Quantum Sci. Technol. 6, 033001 (2021).","DOI":"10.1088\/2058-9565\/abe989"},{"key":"9","doi-asserted-by":"publisher","unstructured":"W. Cai, Y. Ma, W. Wang, C.-L. Zou, and L. Sun, ``Bosonic quantum error correction codes in superconducting quantum circuits,'' Fundam. Res. 1, 50\u201367 (2021).","DOI":"10.1016\/j.fmre.2020.12.006"},{"key":"10","doi-asserted-by":"publisher","unstructured":"V. V. Albert, ``Bosonic coding: introduction and use cases,'', vol. 209 of International School of Physics \u201cEnrico Fermi\u201d. IOS Press, Jan., 2025.","DOI":"10.3254\/ENFI250007"},{"key":"11","doi-asserted-by":"publisher","unstructured":"A. J. Brady, A. Eickbusch, S. Singh, J. Wu, and Q. Zhuang, ``Advances in bosonic quantum error correction with Gottesman\u2013Kitaev\u2013Preskill Codes: Theory, engineering and applications,'' Prog. Quantum Electron. 93, 100496 (2024).","DOI":"10.1016\/j.pquantelec.2023.100496"},{"key":"12","doi-asserted-by":"publisher","unstructured":"A. Ferraro, S. Olivares, and M. G. A. Paris, ``Gaussian States in Continuous Variable Quantum Information,''. Bibliopolis, Napoli, 2005, ISBN 88-7088-483-X.","DOI":"10.48550\/arXiv.quant-ph\/0503237"},{"key":"13","doi-asserted-by":"publisher","unstructured":"G. Adesso, S. Ragy, and A. R. Lee, ``Continuous Variable Quantum Information: Gaussian States and Beyond,'' Open Syst. Inf. Dyn. 21, 1440001 (2014).","DOI":"10.1142\/s1230161214400010"},{"key":"14","doi-asserted-by":"publisher","unstructured":"M. Walschaers, ``Non-Gaussian quantum states and where to find them,'' PRX Quantum 2, 030204 (2021).","DOI":"10.1103\/PRXQuantum.2.030204"},{"key":"15","doi-asserted-by":"publisher","unstructured":"S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, ``Efficient Classical Simulation of Continuous Variable Quantum Information Processes,'' Phys. Rev. Lett. 88, 097904 (2002).","DOI":"10.1103\/PhysRevLett.88.097904"},{"key":"16","doi-asserted-by":"publisher","unstructured":"A. Mari and J. Eisert, ``Positive Wigner Functions Render Classical Simulation of Quantum Computation Efficient,'' Phys. Rev. Lett. 109, 230503 (2012).","DOI":"10.1103\/PhysRevLett.109.230503"},{"key":"17","doi-asserted-by":"publisher","unstructured":"V. Veitch, N. Wiebe, C. Ferrie, and J. Emerson, ``Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation,'' New J. Phys. 15, 013037 (2013).","DOI":"10.1088\/1367-2630\/15\/1\/013037"},{"key":"18","doi-asserted-by":"publisher","unstructured":"S. D. Bartlett, B. C. Sanders, S. L. Braunstein, and K. Nemoto, ``Efficient Classical Simulation of Continuous Variable Quantum Information Processes,'' Phys. Rev. Lett. 88, 097904 (2002).","DOI":"10.1103\/PhysRevLett.88.097904"},{"key":"19","doi-asserted-by":"publisher","unstructured":"S. Rahimi-Keshari, T. C. Ralph, and C. M. Caves, ``Sufficient Conditions for Efficient Classical Simulation of Quantum Optics,'' Phys. Rev. X 6, 021039 (2016).","DOI":"10.1103\/PhysRevX.6.021039"},{"key":"20","doi-asserted-by":"publisher","unstructured":"A. Kenfack and K. \u017byczkowski, ``Negativity of the Wigner function as an indicator of non-classicality,'' J. Opt. B: Quantum Semiclassical Opt.. 6, 396 (2004).","DOI":"10.1088\/1464-4266\/6\/10\/003"},{"key":"21","doi-asserted-by":"publisher","unstructured":"F. Albarelli, M. G. Genoni, M. G. Paris, and A. Ferraro, ``Resource theory of quantum non-Gaussianity and Wigner negativity,'' Phys. Rev. A 98, 052350 (2018).","DOI":"10.1103\/PhysRevA.98.052350"},{"key":"22","doi-asserted-by":"publisher","unstructured":"R. Takagi and Q. Zhuang, ``Convex resource theory of non-Gaussianity,'' Phys. Rev. A 97, 062337 (2018).","DOI":"10.1103\/PhysRevA.97.062337"},{"key":"23","doi-asserted-by":"publisher","unstructured":"U. Chabaud, D. Markham, and F. Grosshans, ``Stellar representation of non-Gaussian quantum states,'' Phys. Rev. Lett. 124, 063605 (2020).","DOI":"10.1103\/PhysRevLett.124.063605"},{"key":"24","doi-asserted-by":"publisher","unstructured":"U. Chabaud and S. Mehraban, ``Holomorphic representation of quantum computations,'' Quantum 6, 831 (2022).","DOI":"10.22331\/q-2022-10-06-831"},{"key":"25","doi-asserted-by":"publisher","unstructured":"L. c. v. Lachman, I. Straka, J. Hlou\u0161ek, M. Je\u017eek, and R. Filip, ``Faithful Hierarchy of Genuine $n$-Photon Quantum Non-Gaussian Light,'' Phys. Rev. Lett. 123, 043601 (2019).","DOI":"10.1103\/PhysRevLett.123.043601"},{"key":"26","doi-asserted-by":"publisher","unstructured":"O. Hahn, R. Takagi, G. Ferrini, and H. Yamasaki, ``Classical simulation and quantum resource theory of non-Gaussian optics,'' Quantum 9, 1881 (2025).","DOI":"10.22331\/q-2025-10-13-1881"},{"key":"27","doi-asserted-by":"publisher","unstructured":"B. Dias and R. K\u00f6nig, ``Classical simulation of non-Gaussian bosonic circuits,'' Phys. Rev. A 110, 042402 (2024).","DOI":"10.1103\/PhysRevA.110.042402"},{"key":"28","unstructured":"M. Garnier, T. Martinez, and U. Chabaud, ``stellar-rank-numerics.'' https:\/\/github.com\/qat-inria\/stellar-numerics, 2026."},{"key":"29","doi-asserted-by":"publisher","unstructured":"U. Chabaud, G. Roeland, M. Walschaers, F. Grosshans, V. Parigi, D. Markham, and N. Treps, ``Certification of Non-Gaussian States with Operational Measurements,'' PRX Quantum 2, 020333 (2021).","DOI":"10.1103\/PRXQuantum.2.020333"},{"key":"30","doi-asserted-by":"publisher","unstructured":"J. Eisert and M. B. Plenio, ``Conditions for the Local Manipulation of Gaussian States,'' Phys. Rev. Lett. 89, 097901 (2002).","DOI":"10.1103\/PhysRevLett.89.097901"},{"key":"31","doi-asserted-by":"publisher","unstructured":"J. Fiur\u00e1\u0161ek, ``Gaussian Transformations and Distillation of Entangled Gaussian States,'' Phys. Rev. Lett. 89, 137904 (2002).","DOI":"10.1103\/PhysRevLett.89.137904"},{"key":"32","doi-asserted-by":"publisher","unstructured":"G. Giedke and J. Ignacio Cirac, ``Characterization of Gaussian operations and distillation of Gaussian states,'' Phys. Rev. A 66, 032316 (2002).","DOI":"10.1103\/PhysRevA.66.032316"},{"key":"33","doi-asserted-by":"publisher","unstructured":"J. Niset, J. Fiur\u00e1\u0161ek, and N. J. Cerf, ``No-Go Theorem for Gaussian Quantum Error Correction,'' Phys. Rev. Lett. 102, 120501 (2009).","DOI":"10.1103\/PhysRevLett.102.120501"},{"key":"34","doi-asserted-by":"publisher","unstructured":"R. I. Booth, U. Chabaud, and P.-E. Emeriau, ``Contextuality and Wigner Negativity Are Equivalent for Continuous-Variable Quantum Measurements,'' Phys. Rev. Lett. 129, 230401 (2022).","DOI":"10.1103\/PhysRevLett.129.230401"},{"key":"35","doi-asserted-by":"publisher","unstructured":"U. Chabaud, G. Ferrini, F. Grosshans, and D. Markham, ``Classical simulation of Gaussian quantum circuits with non-Gaussian input states,'' Phys. Rev. Res. 3, 033018 (2021).","DOI":"10.1103\/PhysRevResearch.3.033018"},{"key":"36","doi-asserted-by":"publisher","unstructured":"Y. Yao, F. Miatto, and N. Quesada, ``Riemannian optimization of photonic quantum circuits in phase and Fock space,'' SciPost Phys. 17, 082 (2024).","DOI":"10.21468\/SciPostPhys.17.3.082"},{"key":"37","unstructured":"I. Segal, ``Mathematical Problems of Relativistic Physics: With an Appendix on Group Representations in Hilbert Space,''. Lectures in applied mathematics. American Mathematical Society, 1967."},{"key":"38","doi-asserted-by":"publisher","unstructured":"V. Bargmann, ``On a Hilbert space of analytic functions and an associated integral transform part I,'' Commun. Pure Appl. Math. 14, 187\u2013214 (1961).","DOI":"10.1002\/cpa.3160140303"},{"key":"39","doi-asserted-by":"publisher","unstructured":"R. Filip and L. Mi\u0161ta Jr, ``Detecting quantum states with a positive Wigner function beyond mixtures of Gaussian states,'' Phys. Rev. Lett. 106, 200401 (2011).","DOI":"10.1103\/PhysRevLett.106.200401"},{"key":"40","doi-asserted-by":"publisher","unstructured":"J. Fiur\u00e1\u0161ek, ``Efficient construction of witnesses of the stellar rank of nonclassical states of light,'' Opt. Express 30, 30630\u201330639 (2022).","DOI":"10.1364\/OE.466175"},{"key":"41","doi-asserted-by":"publisher","unstructured":"U. Chabaud and M. Walschaers, ``Resources for bosonic quantum computational advantage,'' Physical Review Letters 130, 090602 (2023).","DOI":"10.1103\/PhysRevLett.130.090602"},{"key":"42","doi-asserted-by":"publisher","unstructured":"U. Chabaud, G. Roeland, M. Walschaers, F. Grosshans, V. Parigi, D. Markham, and N. Treps, ``Erratum: Certification of non-Gaussian states with operational measurements,'' PRX Quantum 6, 010902 (2025).","DOI":"10.1103\/PRXQuantum.6.010902"},{"key":"43","doi-asserted-by":"publisher","unstructured":"L. Lami, B. Regula, R. Takagi, and G. Ferrari, ``Framework for resource quantification in infinite-dimensional general probabilistic theories,'' Phys, Rev, A 103, 032424 (2021).","DOI":"10.1103\/PhysRevA.103.032424"},{"key":"44","doi-asserted-by":"publisher","unstructured":"A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, ``Generation of optical \u2018Schr\u00f6dinger cats\u2019 from photon number states,'' Nature 448, 784 (2007).","DOI":"10.1038\/nature06054"},{"key":"45","doi-asserted-by":"publisher","unstructured":"J. Etesse, R. Blandino, B. Kanseri, and R. Tualle-Brouri, ``Proposal for a loophole-free violation of Bell's inequalities with a set of single photons and homodyne measurements,'' New J. Phys. 16, 053001 (2014).","DOI":"10.1088\/1367-2630\/16\/5\/053001"},{"key":"46","doi-asserted-by":"publisher","unstructured":"D. J. Weigand and B. M. Terhal, ``Generating grid states from Schr\u00f6dinger-cat states without postselection,'' Phys. Rev. A 97, 022341 (2018).","DOI":"10.1103\/PhysRevA.97.022341"},{"key":"47","doi-asserted-by":"publisher","unstructured":"K. Takase, F. Hanamura, H. Nagayoshi, J. E. Bourassa, R. N. Alexander, A. Kawasaki, W. Asavanant, M. Endo, and A. Furusawa, ``Generation of flying logical qubits using generalized photon subtraction with adaptive Gaussian operations,'' Phys. Rev. A 110, 012436 (2024).","DOI":"10.1103\/PhysRevA.110.012436"},{"key":"48","doi-asserted-by":"publisher","unstructured":"Y. Zheng, O. Hahn, P. Stadler, P. Holmvall, F. Quijandr\u00eda, A. Ferraro, and G. Ferrini, ``Gaussian Conversion Protocols for Cubic Phase State Generation,'' PRX Quantum 2, 010327 (2021).","DOI":"10.1103\/PRXQuantum.2.010327"},{"key":"49","doi-asserted-by":"publisher","unstructured":"O. Hahn, P. Holmvall, P. Stadler, G. Ferrini, and A. Ferraro, ``Deterministic Gaussian conversion protocols for non-Gaussian single-mode resources,'' Phys. Rev. A 105, 062446 (2022).","DOI":"10.1103\/PhysRevA.105.062446"},{"key":"50","doi-asserted-by":"publisher","unstructured":"Y. Zheng, A. Ferraro, A. F. Kockum, and G. Ferrini, ``Gaussian conversion protocol for heralded generation of generalized Gottesman-Kitaev-Preskill states,'' Phys. Rev. A 108, 012603 (2023).","DOI":"10.1103\/PhysRevA.108.012603"},{"key":"51","doi-asserted-by":"publisher","unstructured":"J. Etesse, B. Kanseri, and R. Tualle-Brouri, ``Iterative tailoring of optical quantum states with homodyne measurements,'' Opt. Express 22, 30357\u201330367 (2014).","DOI":"10.1364\/OE.22.030357"},{"key":"52","doi-asserted-by":"publisher","unstructured":"F. Arzani, N. Treps, and G. Ferrini, ``Polynomial approximation of non-Gaussian unitaries by counting one photon at a time,'' Phys. Rev. A 95, 052352 (2017).","DOI":"10.1103\/PhysRevA.95.052352"},{"key":"53","doi-asserted-by":"publisher","unstructured":"P. V. Parellada, V. G. i Garcia, J. J. Moyano-Fern\u00e1ndez, and J. C. Garcia-Escartin, ``No-go theorems for photon state transformations in quantum linear optics,'' Results Phys. 54, 107108 (2023).","DOI":"10.1016\/j.rinp.2023.107108"},{"key":"54","unstructured":"U. Chabaud, ``Continuous Variable Quantum Advantages and Applications in Quantum Optics.'' Phd thesis arXiv:2102.05227 [quant-ph], Sorbonne University, 2021."},{"key":"55","doi-asserted-by":"publisher","unstructured":"A. J. Pizzimenti and D. Soh, ``Optical Gottesman-Kitaev-Preskill qubit generation via approximate squeezed coherent state superposition breeding,'' Phys. Rev. A 110, 062619 (2024).","DOI":"10.1103\/PhysRevA.110.062619"},{"key":"56","doi-asserted-by":"publisher","unstructured":"T. Matsuura, H. Yamasaki, and M. Koashi, ``Equivalence of approximate Gottesman-Kitaev-Preskill codes,'' Phys. Rev. A 102, 032408 (2020).","DOI":"10.1103\/PhysRevA.102.032408"},{"key":"57","doi-asserted-by":"publisher","unstructured":"D. Gottesman, A. Kitaev, and J. Preskill, ``Encoding a qubit in an oscillator,'' Phys. Rev. A 64, 012310 (2001).","DOI":"10.1103\/PhysRevA.64.012310"},{"key":"58","doi-asserted-by":"publisher","unstructured":"S. Aaronson and A. Arkhipov, ``The computational Complexity of Linear Optics,'' Theory Comput. 9, 143 (2013).","DOI":"10.1145\/1993636.1993682"},{"key":"59","doi-asserted-by":"publisher","unstructured":"E. Knill, R. Laflamme, and G. J. Milburn, ``A scheme for efficient quantum computation with linear optics,'' Nature 409, 46\u201352 (2001).","DOI":"10.1038\/35051009"},{"key":"60","doi-asserted-by":"publisher","unstructured":"M. M. Wilde, ``Quantum Information Theory,''. Cambridge University Press, Nov., 2016.","DOI":"10.1017\/9781316809976"},{"key":"61","doi-asserted-by":"publisher","unstructured":"D. S. Mitrinovi\u0107 and P. M. Vasi\u0107, ``Analytic Inequalities,'', vol. 165 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag, Berlin, Heidelberg, 1970.","DOI":"10.1007\/978-3-642-99970-3"},{"key":"62","doi-asserted-by":"publisher","unstructured":"A. Rastegin, ``A lower bound on the relative error of mixed-state cloning and related operations,'' J. Opt. B Quantum Semiclassical Opt. 5, S647 (2003).","DOI":"10.1088\/1464-4266\/5\/6\/017"},{"key":"63","doi-asserted-by":"publisher","unstructured":"U. Chabaud, T. Douce, F. Grosshans, E. Kashefi, and D. Markham, ``Building Trust for Continuous Variable Quantum States,'' LIPIcs, TQC 2020 158, 3:1\u20133:15 (2020).","DOI":"10.4230\/LIPICS.TQC.2020.3"},{"key":"64","doi-asserted-by":"publisher","unstructured":"F. M. Miatto and N. Quesada, ``Fast optimization of parametrized quantum optical circuits,'' Quantum 4, 366 (2020).","DOI":"10.22331\/q-2020-11-30-366"},{"key":"65","unstructured":"XanaduAI, ``Mr Mustard.'' https:\/\/github.com\/XanaduAI\/MrMustard, 2021."}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-05-05-2095\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T11:21:36Z","timestamp":1777980096000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-05-05-2095\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,5]]},"references-count":66,"URL":"https:\/\/doi.org\/10.22331\/q-2026-05-05-2095","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,5]]},"article-number":"2095"}}