Related papers: Forrelation is Extremally Hard
PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to…
Understanding quantum speed-up over classical computing is fundamental for the development of efficient quantum algorithms. In this paper, we study such problem within the framework of the Quantum Query Model, which represents the…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…
We show two results about the relationship between quantum and classical messages. Our first contribution is to show how to replace a quantum message in a one-way communication protocol by a deterministic message, establishing that for all…
In the claw detection problem we are given two functions $f:D\rightarrow R$ and $g:D\rightarrow R$ ($|D|=n$, $|R|=k$), and we have to determine if there is exist $x,y\in D$ such that $f(x)=g(y)$. We show that the quantum query complexity of…
Consider a function f which is defined on the integers from 1 to N and takes the values -1 and +1. The parity of f is the product over all x from 1 to N of f(x). With no further information about f, to classically determine the parity of f…
Simon's problem is an essential example demonstrating the faster speed of quantum computers than classical computers for solving some problems. The optimal separation between exact quantum and classical query complexities for Simon's…
Given a classical query algorithm as a decision tree, when does there exist a quantum query algorithm with a speed-up over the classical one? We provide a general construction based on the structure of the underlying decision tree, and…
Leveraging the extraordinary phenomena of quantum superposition and quantum correlation, quantum computing offers unprecedented potential for addressing challenges beyond the reach of classical computers. This paper tackles two pivotal…
The question of what is genuinely quantum about weak values is only ever going to elicit strongly subjective opinions---it is not a scientific question. Good questions, when comparing theories, are operational---they deal with the…
The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $\ell$-collisions, where an $\ell$-collision for a function is a set of $\ell$ distinct inputs that are mapped by the function to the same…
Ongoing work in quantum information emphasises the need for a structural understanding of quantum speedups: in this work, we focus on the quantum Fourier transform and the structures in quantum theory that enable it. We elucidate a general…
We establish two results regarding the query complexity of bounded-error randomized algorithms. * Bounded-error separation theorem. There exists a total function $f : \{0,1\}^n \to \{0,1\}$ whose $\epsilon$-error randomized query complexity…
We analyze interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that "quantum nonlocality" is the…
We use an alternative approach to show that quantum entanglement-like correlations cannot be reproduced for any classical protocol. In our proposal, quantum geometric restrictions are impose over the physical system related to the existence…
Despite years of effort, the quantum machine learning community has only been able to show quantum learning advantages for certain contrived cryptography-inspired datasets in the case of classical data. In this note, we discuss the…
Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content…
We study a natural complexity measure of Boolean functions known as the rational degree. Denoted $\textrm{rdeg}(f)$, it is the minimal degree of a rational function that is equal to $f$ on the Boolean hypercube. For total functions $f$, it…
In this paper, we propose efficient probabilistic algorithms for several problems regarding the autocorrelation spectrum. First, we present a quantum algorithm that samples from the Walsh spectrum of any derivative of $f()$. Informally, the…
For almost a century, since Bernal\'s attempts at a molecular theory of liquid structure(Bernal [1]), correlation functions have been the bridge to compare theoretical calculations with experimental measurements in the study of disordered…