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In: Neue Deutsche Biographie Deutschland Online . ; 2024.","mla":"Peckhaus, Volker. “Fraenkel, Abraham A. .” Neue Deutsche Biographie Deutschland Online , 2024.","short":"V. Peckhaus, in: Neue Deutsche Biographie Deutschland Online , 2024."},"publication":"Neue Deutsche Biographie Deutschland Online ","type":"encyclopedia_article"},{"_id":"44860","editor":[{"last_name":"Hermann","first_name":"Kay","full_name":"Hermann, Kay"},{"full_name":"Schwitzer, Boris","first_name":"Boris","last_name":"Schwitzer"}],"author":[{"last_name":"Peckhaus","first_name":"Volker","full_name":"Peckhaus, Volker","id":"391"}],"status":"public","title":"Kritische Mathematik und die Axiomatik Hilberts","type":"book_chapter","publication":"Der Geist der kritischen Schule. Kantisches Denken in der Tradition von Jakob Friedrich Fries und Leonard Nelson im 20. Jahrhundert: Wirkungen und Aktualität","citation":{"bibtex":"@inbook{Peckhaus_2024, place={Berlin}, title={Kritische Mathematik und die Axiomatik Hilberts}, booktitle={Der Geist der kritischen Schule. Kantisches Denken in der Tradition von Jakob Friedrich Fries und Leonard Nelson im 20. Jahrhundert: Wirkungen und Aktualität}, publisher={SpringerNature}, author={Peckhaus, Volker}, editor={Hermann, Kay and Schwitzer, Boris}, year={2024} }","ama":"Peckhaus V. Kritische Mathematik und die Axiomatik Hilberts. In: Hermann K, Schwitzer B, eds. Der Geist der kritischen Schule. Kantisches Denken in der Tradition von Jakob Friedrich Fries und Leonard Nelson im 20. Jahrhundert: Wirkungen und Aktualität. SpringerNature; 2024.","chicago":"Peckhaus, Volker. “Kritische Mathematik und die Axiomatik Hilberts.” In Der Geist der kritischen Schule. Kantisches Denken in der Tradition von Jakob Friedrich Fries und Leonard Nelson im 20. Jahrhundert: Wirkungen und Aktualität, edited by Kay Hermann and Boris Schwitzer. Berlin: SpringerNature, 2024.","ieee":"V. Peckhaus, “Kritische Mathematik und die Axiomatik Hilberts,” in Der Geist der kritischen Schule. Kantisches Denken in der Tradition von Jakob Friedrich Fries und Leonard Nelson im 20. Jahrhundert: Wirkungen und Aktualität, K. Hermann and B. Schwitzer, Eds. Berlin: SpringerNature, 2024.","mla":"Peckhaus, Volker. “Kritische Mathematik und die Axiomatik Hilberts.” Der Geist der kritischen Schule. Kantisches Denken in der Tradition von Jakob Friedrich Fries und Leonard Nelson im 20. Jahrhundert: Wirkungen und Aktualität, edited by Kay Hermann and Boris Schwitzer, SpringerNature, 2024.","short":"V. Peckhaus, in: K. Hermann, B. Schwitzer (Eds.), Der Geist der kritischen Schule. Kantisches Denken in der Tradition von Jakob Friedrich Fries und Leonard Nelson im 20. Jahrhundert: Wirkungen und Aktualität, SpringerNature, Berlin, 2024.","apa":"Peckhaus, V. (2024). Kritische Mathematik und die Axiomatik Hilberts. In K. Hermann & B. Schwitzer (Eds.), Der Geist der kritischen Schule. Kantisches Denken in der Tradition von Jakob Friedrich Fries und Leonard Nelson im 20. Jahrhundert: Wirkungen und Aktualität. SpringerNature."},"date_created":"2023-05-16T10:11:17Z","user_id":"391","department":[{"_id":"520"}],"language":[{"iso":"ger"}],"publisher":"SpringerNature","date_updated":"2023-12-30T22:31:52Z","place":"Berlin","year":"2024"},{"status":"public","title":"Vexierbilder als gegenhegemoniales Moment. Strategien postmigrantischen Erzählens bei Andrea Karimé","_id":"33429","editor":[{"full_name":"Hodaie, Nazli","last_name":"Hodaie","first_name":"Nazli"},{"full_name":"Hofmann, Michael","last_name":"Hofmann","first_name":"Michael"}],"author":[{"id":"86552","full_name":"Kißling, Magdalena","last_name":"Kißling","first_name":"Magdalena"},{"first_name":"Nadine","last_name":"Seidel","full_name":"Seidel, Nadine"}],"page":"i.Dr.","date_updated":"2024-01-05T11:33:50Z","publisher":"Metzler Verlag","year":"2024","place":"Heidelberg","publication_status":"unpublished","type":"book_chapter","publication":"Literatur der Postmigration: Grundzüge, Formen und Vertreter_innen","department":[{"_id":"464"}],"language":[{"iso":"ger"}],"citation":{"apa":"Kißling, M., & Seidel, N. (n.d.). Vexierbilder als gegenhegemoniales Moment. Strategien postmigrantischen Erzählens bei Andrea Karimé. In N. Hodaie & M. Hofmann (Eds.), Literatur der Postmigration: Grundzüge, Formen und Vertreter_innen (p. i.Dr.). Metzler Verlag.","short":"M. Kißling, N. Seidel, in: N. Hodaie, M. Hofmann (Eds.), Literatur der Postmigration: Grundzüge, Formen und Vertreter_innen, Metzler Verlag, Heidelberg, n.d., p. i.Dr.","mla":"Kißling, Magdalena, and Nadine Seidel. “Vexierbilder als gegenhegemoniales Moment. Strategien postmigrantischen Erzählens bei Andrea Karimé.” Literatur der Postmigration: Grundzüge, Formen und Vertreter_innen, edited by Nazli Hodaie and Michael Hofmann, Metzler Verlag, p. i.Dr.","ieee":"M. Kißling and N. Seidel, “Vexierbilder als gegenhegemoniales Moment. Strategien postmigrantischen Erzählens bei Andrea Karimé,” in Literatur der Postmigration: Grundzüge, Formen und Vertreter_innen, N. Hodaie and M. Hofmann, Eds. Heidelberg: Metzler Verlag, p. i.Dr.","chicago":"Kißling, Magdalena, and Nadine Seidel. “Vexierbilder als gegenhegemoniales Moment. Strategien postmigrantischen Erzählens bei Andrea Karimé.” In Literatur der Postmigration: Grundzüge, Formen und Vertreter_innen, edited by Nazli Hodaie and Michael Hofmann, i.Dr. Heidelberg: Metzler Verlag, n.d.","ama":"Kißling M, Seidel N. Vexierbilder als gegenhegemoniales Moment. Strategien postmigrantischen Erzählens bei Andrea Karimé. In: Hodaie N, Hofmann M, eds. Literatur der Postmigration: Grundzüge, Formen und Vertreter_innen. Metzler Verlag; :i.Dr.","bibtex":"@inbook{Kißling_Seidel, place={Heidelberg}, title={Vexierbilder als gegenhegemoniales Moment. Strategien postmigrantischen Erzählens bei Andrea Karimé}, booktitle={Literatur der Postmigration: Grundzüge, Formen und Vertreter_innen}, publisher={Metzler Verlag}, author={Kißling, Magdalena and Seidel, Nadine}, editor={Hodaie, Nazli and Hofmann, Michael}, pages={i.Dr.} }"},"date_created":"2022-09-16T12:41:34Z","user_id":"86552"},{"date_updated":"2024-01-07T20:10:13Z","year":"2024","publication":"arXiv:2401.02368","type":"preprint","external_id":{"arxiv":["2401.02368"]},"user_id":"71541","date_created":"2024-01-07T20:09:13Z","citation":{"bibtex":"@article{Rudolph_Gharibian_Nagaj_2024, title={Quantum 2-SAT on low dimensional systems is $\\mathsf{QMA}_1$-complete: Direct embeddings and black-box simulation}, journal={arXiv:2401.02368}, author={Rudolph, Dorian and Gharibian, Sevag and Nagaj, Daniel}, year={2024} }","mla":"Rudolph, Dorian, et al. “Quantum 2-SAT on Low Dimensional Systems Is $\\mathsf{QMA}_1$-Complete: Direct Embeddings and Black-Box Simulation.” ArXiv:2401.02368, 2024.","ama":"Rudolph D, Gharibian S, Nagaj D. Quantum 2-SAT on low dimensional systems is $\\mathsf{QMA}_1$-complete: Direct embeddings and black-box simulation. arXiv:240102368. Published online 2024.","ieee":"D. Rudolph, S. Gharibian, and D. Nagaj, “Quantum 2-SAT on low dimensional systems is $\\mathsf{QMA}_1$-complete: Direct embeddings and black-box simulation,” arXiv:2401.02368. 2024.","chicago":"Rudolph, Dorian, Sevag Gharibian, and Daniel Nagaj. “Quantum 2-SAT on Low Dimensional Systems Is $\\mathsf{QMA}_1$-Complete: Direct Embeddings and Black-Box Simulation.” ArXiv:2401.02368, 2024.","short":"D. Rudolph, S. Gharibian, D. Nagaj, ArXiv:2401.02368 (2024).","apa":"Rudolph, D., Gharibian, S., & Nagaj, D. (2024). Quantum 2-SAT on low dimensional systems is $\\mathsf{QMA}_1$-complete: Direct embeddings and black-box simulation. In arXiv:2401.02368."},"abstract":[{"text":"Despite the fundamental role the Quantum Satisfiability (QSAT) problem has\r\nplayed in quantum complexity theory, a central question remains open: At which\r\nlocal dimension does the complexity of QSAT transition from \"easy\" to \"hard\"?\r\nHere, we study QSAT with each constraint acting on a $k$-dimensional and\r\n$l$-dimensional qudit pair, denoted $(k,l)$-QSAT. Our first main result shows\r\nthat, surprisingly, QSAT on qubits can remain $\\mathsf{QMA}_1$-hard, in that\r\n$(2,5)$-QSAT is $\\mathsf{QMA}_1$-complete. In contrast, $2$-SAT on qubits is\r\nwell-known to be poly-time solvable [Bravyi, 2006]. Our second main result\r\nproves that $(3,d)$-QSAT on the 1D line with $d\\in O(1)$ is also\r\n$\\mathsf{QMA}_1$-hard. Finally, we initiate the study of 1D $(2,d)$-QSAT by\r\ngiving a frustration-free 1D Hamiltonian with a unique, entangled ground state.\r\n Our first result uses a direct embedding, combining a novel clock\r\nconstruction with the 2D circuit-to-Hamiltonian construction of [Gosset, Nagaj,\r\n2013]. Of note is a new simplified and analytic proof for the latter (as\r\nopposed to a partially numeric proof in [GN13]). This exploits Unitary Labelled\r\nGraphs [Bausch, Cubitt, Ozols, 2017] together with a new \"Nullspace Connection\r\nLemma\", allowing us to break low energy analyses into small patches of\r\nprojectors, and to improve the soundness analysis of [GN13] from\r\n$\\Omega(1/T^6)$ to $\\Omega(1/T^2)$, for $T$ the number of gates. Our second\r\nresult goes via black-box reduction: Given an arbitrary 1D Hamiltonian $H$ on\r\n$d'$-dimensional qudits, we show how to embed it into an effective null-space\r\nof a 1D $(3,d)$-QSAT instance, for $d\\in O(1)$. Our approach may be viewed as a\r\nweaker notion of \"simulation\" (\\`a la [Bravyi, Hastings 2017], [Cubitt,\r\nMontanaro, Piddock 2018]). As far as we are aware, this gives the first\r\n\"black-box simulation\"-based $\\mathsf{QMA}_1$-hardness result, i.e. for\r\nfrustration-free Hamiltonians.","lang":"eng"}],"language":[{"iso":"eng"}],"status":"public","title":"Quantum 2-SAT on low dimensional systems is $\\mathsf{QMA}_1$-complete: Direct embeddings and black-box simulation","_id":"50272","author":[{"first_name":"Dorian","last_name":"Rudolph","full_name":"Rudolph, Dorian"},{"orcid":"0000-0002-9992-3379","first_name":"Sevag","last_name":"Gharibian","id":"71541","full_name":"Gharibian, Sevag"},{"last_name":"Nagaj","first_name":"Daniel","full_name":"Nagaj, Daniel"}]}]