Related papers: BQP is not in NP
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…
The relationship between BQP and PH has been an open problem since the earliest days of quantum computing. We present evidence that quantum computers can solve problems outside the entire polynomial hierarchy, by relating this question to…
One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed…
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
A clock is, from an information-theoretic perspective, a system that emits information about time. One may therefore ask whether the theory of information imposes any constraints on the maximum precision of clocks. Here we show a…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines…
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor's algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world…
Quantum computers can in principle solve certain problems exponentially more quickly than their classical counterparts. We have not yet reached the advent of useful quantum computation, but when we do, it will affect nearly all scientific…
Can the computational complexity theory of computer science and mathematics say something new about unresolved problems in quantum physics? Particularly, can the P versus NP question in the computational complexity theory be a factor in 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…
Simon as extended by Brassard and H{\o}yer shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine infinitely often. The present paper shows that there are tasks on which…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this…