Bqp and the polynomial hierarchy
Webpolynomial of a knot, evaluated at the 5th root of unity, is BQP-complete. This constitutes one of the rare natural BQP-complete problems, and allows us to exploit the topology of knots as further structure to quantum computing. This thesis is about refining and generalizing our understanding of the aquantum complexity of WebSep 10, 2024 · Oracle Separation of BQP and The Polynomial Hierarchy Abstract We give an explicit black-box problem that can be solved by a bounded-error quantum …
Bqp and the polynomial hierarchy
Did you know?
BQP is defined for quantum computers; the corresponding complexity class for classical computers (or more formally for probabilistic Turing machines) is BPP. Just like P and BPP, BQP is low for itself, which means BQP = BQP. Informally, this is true because polynomial time algorithms are closed under composition. If a polynomial time algorithm calls polynomial time algorithms as subroutines, t… WebThis problem is known to provide the largest possible quantum speedup in terms of its query complexity and achieves the landmark oracle separation between the complexity class BQP and the Polynomial Hierarchy.
WebWe present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to topics in circuit complexity, … WebOct 31, 2024 · $\begingroup$ thanks. I understand. And in the case mentioned above (as of the knowledge we have now) we won't know anything more about the relationship b/w two sub branches below, even in the event of this collapse: namely NP, MA, AM and PSPACE and the other being the quantum ones BQP and QMA?
WebMar 6, 2024 · If a polynomial time algorithm calls polynomial time algorithms as subroutines, the resulting algorithm is still polynomial time. BQP contains P and BPP … WebOct 25, 2009 · The class AM is contained in the so-called polynomial hierarchy, while on the other hand, BQP, let alone QMA, is not believed to be contained in the polynomial …
WebBQP: Bounded-error quantum polynomial time, or BQP, is the set of problems solvable by a quantum computer in polynomial time. Formally, a language Lis in BQP i there exists …
WebBQP and the Polynomial Hierarchy Scott Aaronson∗ Abstract The relationship between BQP and PH has been an open problem since the earliest days of sign in sign up … raymond graham obituaryWebOct 25, 2009 · The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can … raymond granite quarry raymond caWebquestionshere: whether BQP ⊆ PH andwhether PromiseBQP ⊆ PromisePH. In the unrelativized world, it is entirely pos-sible that quantum computers can solve promise … raymond gransbery butte mtWebJan 20, 2024 · We demonstrated anomaly in the quasiparticle-band dispersions in the superconducting state, which is not expected from the Bogoliubov-quasiparticle (BQP) dispersion induced by a simple s -wave-gap opening. We discuss implications of our observation in relation to intra-FeSe-layer interactions. 2. Materials and Methods raymond graham footballWebJun 5, 2010 · BQP and the Polynomial Hierarchy Scott Aaronson MIT Â ABSTRACT The relationship between BQP and PH has been an open problem since the earliest days of … raymond grant limerick lakeWebUP (and its complement co-UP) contain both the integer factorization problem and parity game problem; because determined effort has yet to find a polynomial-time solution to any of these problems, it is suspected to be difficult to show P = UP, or even P = ( UP ∩ co-UP ). raymond grantWebJun 15, 1998 · There exists a relativized world where P=BQP and the polynomial-time hierarchy is infinite. There exists a relativized world where BQP does not have complete … raymond graham swing