Related papers: Quantum Advantage via Solving Multivariate Polynom…
We study the fundamental problem of guessing cryptographic keys, drawn from some non-uniform probability distribution $D$, as e.g. in LPN, LWE or for passwords. The optimal classical algorithm enumerates keys in decreasing order of…
In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing…
The most general examples of quantum learning advantages involve data labeled by cryptographic or intrinsically quantum functions, where classical learners are limited by the infeasibility of evaluating the labeling functions using…
As quantum computing approaches the threshold where certain tasks demonstrably outpace their classical machines, the need for a precise, clear, consensus-driven definition of quantum advantage becomes essential. Rapid progress in the field…
Quantum machine learning is considered one of the current research fields with immense potential. In recent years, Havl\'i\v{c}ek et al. [Nature 567, 209-212 (2019)] have proposed a quantum machine learning algorithm with quantum-enhanced…
One of the core challenges of research in quantum computing is concerned with the question whether quantum advantages can be found for near-term quantum circuits that have implications for practical applications. Motivated by this mindset,…
In this note we study the number of quantum queries required to identify an unknown multilinear polynomial of degree d in n variables over a finite field F_q. Any bounded-error classical algorithm for this task requires Omega(n^d) queries…
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…
We present new theoretical mechanisms for quantum speedup in the global optimization of nonconvex functions, expanding the scope of quantum advantage beyond traditional tunneling-based explanations. As our main building-block, we…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
It is known in the context of decentralised control that there exist control strategies consistent with the requirements of a given information structure, yet physically unimplementable through any amount of passive common randomness. This…
Fast quantum algorithms can solve important computational problems more efficiently than classical algorithms. However, little is known about whether quantum computing can speed up solving geometric problems. This article explores quantum…
Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
We show the following hold, unconditionally unless otherwise stated, relative to a random oracle: - There are NP search problems solvable by quantum polynomial-time machines but not classical probabilistic polynomial-time machines. - There…