Related papers: Oracle problems as communication tasks and optimiz…
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
Frequently, the burgeoning field of black-box optimization encounters challenges due to a limited understanding of the mechanisms of the objective function. To address such problems, in this work we focus on the deterministic concept of…
The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
In the standard oracle model, an oracle efficiently evaluates an unknown classical function independent of the quantum algorithm itself. Quantum algorithms have a complex interrelationship to their oracles; for example the possibility of…
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum…
We study a model of communication complexity that encompasses many well-studied problems, including classical and quantum communication complexity, the complexity of simulating distributions arising from bipartite measurements of shared…
Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…
We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it.…
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation.…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
In the oracle identification problem we have oracle access to bits of an unknown string $x$ of length $n$, with the promise that it belongs to a known set $C\subseteq\{0,1\}^n$. The goal is to identify $x$ using as few queries to the oracle…
We present a quantum algorithm which identifies with certainty a hidden subgroup of an arbitrary finite group G in only a polynomial (in log |G|) number of calls to the oracle. This is exponentially better than the best classical algorithm.…
The challenges of black box optimization arise due to imprecise responses and limited output information. This article describes new results on optimizing multivariable functions using an Order Oracle, which provides access only to the…
Quantum computing has shown promise for solving complex optimization problems in databases, such as join ordering and index selection. Prior work often submits formulated problems directly to black-box quantum or quantum-inspired solvers…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an {\em oracle} for noisy information about the unknown…
As small quantum computers are becoming available on different physical platforms, a benchmarking task known as cross-platform verification has been proposed that aims to estimate the fidelity of states prepared on two quantum computers.…