Related papers: Quantum Advantage via Solving Multivariate Quadrat…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
Molecular simulations are widely regarded as leading candidates to demonstrate quantum advantage--defined as the point at which quantum methods surpass classical approaches in either accuracy or scale. Yet the qubit counts and error rates…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
We initiate the study of quantum algorithms for escaping from saddle points with provable guarantee. Given a function $f\colon\mathbb{R}^{n}\to\mathbb{R}$, our quantum algorithm outputs an $\epsilon$-approximate second-order stationary…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial. We show that for average-case complexity under the…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
In this study, we give an extension of Montanaro's arXiv/archive:1504.06987 quantum Monte Carlo method, tailored for computing expected values of random variables that exhibit infinite variance. This addresses a challenge in analyzing…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
We observe that fault-tolerant quantum computers have an optimal advantage over classical computers in approximating solutions to many NP optimization problems. This observation however gives nothing in practice.
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…
We give a natural problem over input quantum oracles $U$ which cannot be solved with exponentially many black-box queries to $U$ and $U^\dagger$, but which can be solved with constant many queries to $U$ and $U^*$, or $U$ and…
Assuming the polynomial hierarchy is infinite, we prove a sufficient condition for determining if uniform and polynomial size quantum circuits over a non-universal gate set are not efficiently classically simulable in the weak…
Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
Relational quantum queries are sometimes capable to effectively decide between collections of mutually exclusive elementary cases without completely resolving and determining those individual instances. Thereby the set of mutually exclusive…
Sampling problems demonstrating beyond classical computing power with noisy intermediate scale quantum devices have been experimentally realized. In those realizations, however, our trust that the quantum devices faithfully solve the…
An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors…