{"user_id":"71541","publication":"Proceedings of 49th International Symposium on Mathematical Foundations of Computer Science (MFCS)","issue":"7","external_id":{"arxiv":["2401.01633"]},"year":"2024","page":"7-17","citation":{"ama":"Agarwal A, Gharibian S, Koppula V, Rudolph D. Quantum Polynomial Hierarchies: Karp-Lipton, error reduction, and lower  bounds. In: <i>Proceedings of 49th International Symposium on Mathematical Foundations of Computer Science (MFCS)</i>. Vol 306. ; 2024:7-17. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2024.7\">10.4230/LIPIcs.MFCS.2024.7</a>","short":"A. Agarwal, S. Gharibian, V. Koppula, D. Rudolph, in: Proceedings of 49th International Symposium on Mathematical Foundations of Computer Science (MFCS), 2024, pp. 7–17.","apa":"Agarwal, A., Gharibian, S., Koppula, V., &#38; Rudolph, D. (2024). Quantum Polynomial Hierarchies: Karp-Lipton, error reduction, and lower  bounds. <i>Proceedings of 49th International Symposium on Mathematical Foundations of Computer Science (MFCS)</i>, <i>306</i>(7), 7–17. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2024.7\">https://doi.org/10.4230/LIPIcs.MFCS.2024.7</a>","chicago":"Agarwal, Avantika, Sevag Gharibian, Venkata Koppula, and Dorian Rudolph. “Quantum Polynomial Hierarchies: Karp-Lipton, Error Reduction, and Lower  Bounds.” In <i>Proceedings of 49th International Symposium on Mathematical Foundations of Computer Science (MFCS)</i>, 306:7–17, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2024.7\">https://doi.org/10.4230/LIPIcs.MFCS.2024.7</a>.","mla":"Agarwal, Avantika, et al. “Quantum Polynomial Hierarchies: Karp-Lipton, Error Reduction, and Lower  Bounds.” <i>Proceedings of 49th International Symposium on Mathematical Foundations of Computer Science (MFCS)</i>, vol. 306, no. 7, 2024, pp. 7–17, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2024.7\">10.4230/LIPIcs.MFCS.2024.7</a>.","ieee":"A. Agarwal, S. Gharibian, V. Koppula, and D. Rudolph, “Quantum Polynomial Hierarchies: Karp-Lipton, error reduction, and lower  bounds,” in <i>Proceedings of 49th International Symposium on Mathematical Foundations of Computer Science (MFCS)</i>, 2024, vol. 306, no. 7, pp. 7–17, doi: <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2024.7\">10.4230/LIPIcs.MFCS.2024.7</a>.","bibtex":"@inproceedings{Agarwal_Gharibian_Koppula_Rudolph_2024, title={Quantum Polynomial Hierarchies: Karp-Lipton, error reduction, and lower  bounds}, volume={306}, DOI={<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2024.7\">10.4230/LIPIcs.MFCS.2024.7</a>}, number={7}, booktitle={Proceedings of 49th International Symposium on Mathematical Foundations of Computer Science (MFCS)}, author={Agarwal, Avantika and Gharibian, Sevag and Koppula, Venkata and Rudolph, Dorian}, year={2024}, pages={7–17} }"},"title":"Quantum Polynomial Hierarchies: Karp-Lipton, error reduction, and lower  bounds","_id":"50273","volume":306,"type":"conference","date_created":"2024-01-07T20:09:32Z","date_updated":"2024-08-23T06:18:02Z","intvolume":"       306","doi":"10.4230/LIPIcs.MFCS.2024.7","publication_status":"published","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"The Polynomial-Time Hierarchy ($\\mathsf{PH}$) is a staple of classical\r\ncomplexity theory, with applications spanning randomized computation to circuit\r\nlower bounds to ''quantum advantage'' analyses for near-term quantum computers.\r\nQuantumly, however, despite the fact that at least \\emph{four} definitions of\r\nquantum $\\mathsf{PH}$ exist, it has been challenging to prove analogues for\r\nthese of even basic facts from $\\mathsf{PH}$. This work studies three\r\nquantum-verifier based generalizations of $\\mathsf{PH}$, two of which are from\r\n[Gharibian, Santha, Sikora, Sundaram, Yirka, 2022] and use classical strings\r\n($\\mathsf{QCPH}$) and quantum mixed states ($\\mathsf{QPH}$) as proofs, and one\r\nof which is new to this work, utilizing quantum pure states\r\n($\\mathsf{pureQPH}$) as proofs. We first resolve several open problems from\r\n[GSSSY22], including a collapse theorem and a Karp-Lipton theorem for\r\n$\\mathsf{QCPH}$. Then, for our new class $\\mathsf{pureQPH}$, we show one-sided\r\nerror reduction for $\\mathsf{pureQPH}$, as well as the first bounds relating\r\nthese quantum variants of $\\mathsf{PH}$, namely $\\mathsf{QCPH}\\subseteq\r\n\\mathsf{pureQPH} \\subseteq \\mathsf{EXP}^{\\mathsf{PP}}$."}],"author":[{"last_name":"Agarwal","full_name":"Agarwal, Avantika","first_name":"Avantika"},{"full_name":"Gharibian, Sevag","orcid":"0000-0002-9992-3379","last_name":"Gharibian","id":"71541","first_name":"Sevag"},{"last_name":"Koppula","full_name":"Koppula, Venkata","first_name":"Venkata"},{"full_name":"Rudolph, Dorian","last_name":"Rudolph","first_name":"Dorian"}],"status":"public"}