Related papers: Oracles and query lower bounds in generalised prob…
We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower bounded by a…
The oracle identification problem (OIP) is, given a set $S$ of $M$ Boolean oracles out of $2^{N}$ ones, to determine which oracle in $S$ is the current black-box oracle. We can exploit the information that candidates of the current oracle…
The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain…
We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we…
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…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
Classical mechanics and standard Copenhagen quantum mechanics respect subspace implications. For example, if a particle is confined in a particular region $R$ of space, then in these theories we can deduce that it is confined in regions…
The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…
In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically…
I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be…
We consider quantum search algorithms that have access to a noisy oracle that, for every oracle call, with probability $p>0$ completely depolarizes the query registers, while otherwise working properly. Previous results had not ruled out…
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…
Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several…
How can we take inspiration from a typical quantum algorithm to design heuristics for machine learning? A common blueprint, used from Deutsch-Josza to Shor's algorithm, is to place labeled information in superposition via an oracle,…
We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…
Given a prior probability distribution over a set of possible oracle functions, we define a number of queries to be useless for determining some property of the function if the probability that the function has the property is unchanged…
Characterizing quantum nonlocality in networks is a challenging, but important problem. Using quantum sources one can achieve distributions which are unattainable classically. A key point in investigations is to decide whether an observed…
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson's bound for the nonlocal correlations. Considering multiple-slit experiments -…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. In effect, they follow the same logical paradigm as (multi-particle)…