Related papers: The Quantum Complexity of Set Membership

We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be…

We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of…

The advent of noisy-intermediate scale quantum computers has introduced the exciting possibility of achieving quantum speedups in machine learning tasks. These devices, however, are composed of a small number of qubits, and can faithfully…

An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

Quantum machine learning has received significant attention in recent years, and promising progress has been made in the development of quantum algorithms to speed up traditional machine learning tasks. In this work, however, we focus on…

The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…

In this paper we propose a general method to quantify how "quantum" a set of quantum states is. The idea is to gauge the quantumness of the set by the worst-case difficulty of transmitting the states through a purely classical communication…

We improve the test to show the impossibility of a quantum theory based on real numbers by a larger ratio of complex-to-real bound on a Bell-type parameter. In contrast to previous theoretical and experimental proposals the test requires…

We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…

In this work, we introduce an online model for communication complexity. Analogous to how online algorithms receive their input piece-by-piece, our model presents one of the players, Bob, his input piece-by-piece, and has the players Alice…

The communication complexity of a quantum channel is the minimal amount of classical communication required for classically simulating a process of state preparation, transmission through the channel and subsequent measurement. It…

We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result of our simulation, we show that if the quantum k-party communication complexity of a…

We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize quantum…

Learning on small data is a challenge frequently encountered in many real-world applications. In this work we study how effective quantum ensemble models are when trained on small data problems in healthcare and life sciences. We…

In this work, we consider the performance of using a quantum algorithm to predict a result for a binary classification problem if a machine learning model is an ensemble from any simple classifiers. Such an approach is faster than classical…

Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and…

We investigate the relationship between two distinct classical approaches to quantum systems: direct simulation from a classical description and sample-based learning from measurement data. While both tasks ultimately aim to reproduce…

Quantifying the complexity of quantum states is a longstanding key problem in various subfields of science, ranging from quantum computing to the black-hole theory. The lower bound on quantum pure state complexity has been shown to grow…

In this paper, we look into the adaptive bitprobe model that stores subsets of size at most four from a universe of size m, and answers membership queries using two bitprobes. We propose a scheme that stores arbitrary subsets of size four…