Related papers: Improved separation between quantum and classical …
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,…
While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special…
A quantum algorithm succeeds not because the superposition principle allows 'the computation of all values of a function at once' via 'quantum parallelism,' but rather because the structure of a quantum state space allows new sorts of…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is…
Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Error correction will add so much overhead to large quantum computations that we suspect the most efficient algorithms will use a classical co-processor to do as much work as possible. We present a method to offload portions of a quantum…
Quantum computing provides a new way for approaching problem solving, enabling efficient solutions for problems that are hard on classical computers. It is based on leveraging how quantum particles behave. With researchers around the world…
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors,…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
The search for new, application-specific quantum computers designed to outperform any classical computer is driven by the ending of Moore's law and the quantum advantages potentially obtainable. Photonic networks are promising examples,…
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…
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…
Despite significant effort, the quantum machine learning community has only demonstrated quantum learning advantages for artificial cryptography-inspired datasets when dealing with classical data. In this paper we address the challenge of…
We study the classical complexity of the exact Boson Sampling problem where the objective is to produce provably correct random samples from a particular quantum mechanical distribution. The computational framework was proposed by Aaronson…