{"date_updated":"2024-04-14T19:33:42Z","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"What is the power of polynomial-time quantum computation with access to an NP\r\noracle? In this work, we focus on two fundamental tasks from the study of\r\nBoolean satisfiability (SAT) problems: search-to-decision reductions, and\r\napproximate counting. We first show that, in strong contrast to the classical\r\nsetting where a poly-time Turing machine requires $\\Theta(n)$ queries to an NP\r\noracle to compute a witness to a given SAT formula, quantumly $\\Theta(\\log n)$\r\nqueries suffice. We then show this is tight in the black-box model - any\r\nquantum algorithm with \"NP-like\" query access to a formula requires\r\n$\\Omega(\\log n)$ queries to extract a solution with constant probability.\r\nMoving to approximate counting of SAT solutions, by exploiting a quantum link\r\nbetween search-to-decision reductions and approximate counting, we show that\r\nexisting classical approximate counting algorithms are likely optimal. First,\r\nwe give a lower bound in the \"NP-like\" black-box query setting: Approximate\r\ncounting requires $\\Omega(\\log n)$ queries, even on a quantum computer. We then\r\ngive a \"white-box\" lower bound (i.e. where the input formula is not hidden in\r\nthe oracle) - if there exists a randomized poly-time classical or quantum\r\nalgorithm for approximate counting making $o(log n)$ NP queries, then\r\n$\\text{BPP}^{\\text{NP}[o(n)]}$ contains a $\\text{P}^{\\text{NP}}$-complete\r\nproblem if the algorithm is classical and $\\text{FBQP}^{\\text{NP}[o(n)]}$\r\ncontains an $\\text{FP}^{\\text{NP}}$-complete problem if the algorithm is\r\nquantum."}],"publication":"Proceedings of 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP)","title":"BQP, meet NP: Search-to-decision reductions and approximate counting","user_id":"71541","author":[{"last_name":"Gharibian","full_name":"Gharibian, Sevag","first_name":"Sevag","id":"71541","orcid":"0000-0002-9992-3379"},{"last_name":"Kamminga","full_name":"Kamminga, Jonas","first_name":"Jonas"}],"year":"2024","external_id":{"arxiv":["2401.03943"]},"publication_status":"accepted","date_created":"2024-01-09T13:59:44Z","status":"public","_id":"50406","type":"conference","citation":{"apa":"Gharibian, S., &#38; Kamminga, J. (n.d.). BQP, meet NP: Search-to-decision reductions and approximate counting. <i>Proceedings of 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>.","ieee":"S. Gharibian and J. Kamminga, “BQP, meet NP: Search-to-decision reductions and approximate counting.”","bibtex":"@inproceedings{Gharibian_Kamminga, title={BQP, meet NP: Search-to-decision reductions and approximate counting}, booktitle={Proceedings of 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP)}, author={Gharibian, Sevag and Kamminga, Jonas} }","ama":"Gharibian S, Kamminga J. BQP, meet NP: Search-to-decision reductions and approximate counting. In: <i>Proceedings of 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>.","chicago":"Gharibian, Sevag, and Jonas Kamminga. “BQP, Meet NP: Search-to-Decision Reductions and Approximate Counting.” In <i>Proceedings of 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>, n.d.","short":"S. Gharibian, J. Kamminga, in: Proceedings of 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP), n.d.","mla":"Gharibian, Sevag, and Jonas Kamminga. “BQP, Meet NP: Search-to-Decision Reductions and Approximate Counting.” <i>Proceedings of 51st EATCS International Colloquium on Automata, Languages and Programming (ICALP)</i>."}}