相关论文: Quantum lower bounds by quantum arguments
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the…
In the quantum database search problem we are required to search for an item in a database. In this paper, we consider a generalization of this problem, where we are provided d identical copes of a database each with N items which we can…
In symmetric cryptanalysis, the model of superposition queries has led to surprising results, with many constructions being broken in polynomial time thanks to Simon's period-finding algorithm. But the practical implications of these…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
Quantum algorithm is constructed which verifies the formulas of predicate calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the time required for classical algorithms. This algorithm uses the polynomial number of…
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…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
Given a random permutation $f: [N] \to [N]$ as a black box and $y \in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
Adversarial learning is one of the most successful approaches to modelling high-dimensional probability distributions from data. The quantum computing community has recently begun to generalize this idea and to look for potential…
A reinforcement algorithm solves a classical optimization problem by introducing a feedback to the system which slowly changes the energy landscape and converges the algorithm to an optimal solution in the configuration space. Here, we use…
The compressed oracle technique, introduced in the context of quantum cryptanalysis, is the latest method for proving quantum query lower bounds, and has had an impressive number of applications since its introduction, due in part to the…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary…
In his seminal work on recording quantum queries [Crypto 2019], Zhandry studied interactions between quantum query algorithms and the quantum oracle corresponding to random functions. Zhandry presented a framework for interpreting various…