相关论文: Optimal quantum adversary lower bounds for ordered…

We prove tight lower bounds for the following variant of the counting problem considered by Aaronson, Kothari, Kretschmer, and Thaler (2020). The task is to distinguish whether an input set $x\subseteq [n]$ has size either $k$ or…

Aaronson, Bouland, Fitzsimons and Lee introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without…

In the quantum database search problem we are required to search for an item in a database. In this paper, we consider a generalization of this problem, where we are provided d identical copes of a database each with N items which we can…

We improve the lower bound on the asymptotic competitive ratio of any online algorithm for bin packing to above 1.54278. We demonstrate for the first time the advantage of branching and the applicability of full adaptivity in the design of…

In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function $f$ on $n$ variables that only depends on $k$ variables, and, when restricted to them, equals some predefined…

In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…

The search task is one of the most difficult when it comes to execution speed, and reducing the latter is important both when working with large data and with small samples, if they need to be processed frequently and in a limited time.…

We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…

We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…

We propose a $O(\log k \log n)$-competitive randomized algorithm for online node-weighted Steiner forest. This is essentially optimal and significantly improves over the previous bound of $O(\log^2 k \log n)$ by Hajiaghayi et al. [2017]. In…

In the online sorting problem, we have an array $A$ of $n$ cells, and receive a stream of $n$ items $x_1,\dots,x_n\in [0,1]$. When an item arrives, we need to immediately and irrevocably place it into an empty cell. The goal is to minimize…

We study the most practical problem setup for evaluating adversarial robustness of a machine learning system with limited access: the hard-label black-box attack setting for generating adversarial examples, where limited model queries are…

Searching for a line on the plane with $n$ unit speed robots is a classic online problem that dates back to the 50's, and for which competitive ratio upper bounds are known for every $n\geq 1$. In this work we improve the best lower bound…

In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…

We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…

We give an improved lower bound of 10/3 on the competitive ratio for the exploration of an undirected, edge-weighted graph with a single agent that needs to return to the starting location after visiting all vertices. We assume that the…

Given two sets A and B and two oracles O(A) and O(B) that can identify the elements of these sets respectively, the goal is to find an element common to both sets using minimum number of oracle queries. Each application of either O(A) or…

Consider the finite regular language L_n = {w0 : w \in {0,1}^*, |w| \le n}. It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum…

In online minimum cost matching on the line, $n$ requests appear one by one and have to be matched immediately and irrevocably to a given set of servers, all on the real line. The goal is to minimize the sum of distances from the requests…

For online matching with the line metric, we present a lower bound of $\Omega(\log n)$ on the approximation ratio of any online (possibly randomized) algorithm. This beats the previous best lower bound of $\Omega(\sqrt{\log n})$ and matches…