Related papers: BQP and PPAD
We give proofs of the PBW and duality theorems for the quantum Kac-Moody algebras and quantum current algebras, relying on Lie bialgebra duality. We also show that the classical limit of the quantum current algebras associated with an…
We classify pro-$p$ Poincar\'e duality pairs in dimension two. We then use this classification to build a pro-$p$ analogue of the curve complex and establish its basic properties. We conclude with some statements concerning separability…
Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…
We study a subclass of the Instantaneous Quantum Polynomial-time (IQP) circuit with a varying density of two-qubit gates. In addition to a known anticoncentration regime, we identify novel parameter conditions where the model is classically…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. We give…
In 2004, Aaronson introduced the complexity class $\mathsf{PostBQP}$ ($\mathsf{BQP}$ with postselection) and showed that it is equal to $\mathsf{PP}$. Following their line of work, we introduce two new complexity classes. The first,…
In this research, as the new results of our previously proposed definition for the new class of $2D$ $q$-Appell polynomials, we derive some interesting relations including the recurrence relation and partial $q$-difference equation of the…
A new class UF of problems is introduced, strictly included in the class NP, which arises in the analysis of the time verifying the intermediate results of computations. The implications of the introduction of this class are considered.…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
We introduce the problem EndOfPotentialLine and the corresponding complexity class EOPL of all problems that can be reduced to it in polynomial time. This class captures problems that admit a single combinatorial proof of their joint…
This paper calls attention to the current state of the probability (P) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper notices how fundamental issues raised in quantum…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
Student-Teacher Games are a model of computation in which a computationally restricted Student attempts to produce a string satisfying a refutable property, while an all-powerful Teacher refutes incorrect candidates by providing…
Integrable probability has emerged as an active area of research at the interface of probability/mathematical physics/statistical mechanics on the one hand, and representation theory/integrable systems on the other. Informally, integrable…
Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
In a scenario where two parties share, act on and exchange some physical resource, the assumption that the parties' actions are ordered according to a definite causal structure yields constraints on the possible correlations that can be…