相关论文: An Almost-Quadratic Lower Bound for Quantum Formul…

We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct…

Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…

We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…

We prove new lower bounds for bounded error quantum communication complexity. Our methods are based on the Fourier transform of the considered functions. First we generalize a method for proving classical communication complexity lower…

We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…

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…

We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves…

The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…

The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…

It is shown that the dimension of the multilinear quantum Lie operations space is either equal to zero or included between $(n-2)!$ and $(n-1)!.$ The lower bound is achieved if the intersection of all conforming subsets is nonempty, while…

While quantum computers hold the promise of significant computational speedups, the limited size of early quantum machines motivates the study of space-bounded quantum computation. We relate the quantum space complexity of computing a…

The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity…

The weight decision problem, which requires to determine the Hamming weight of a given binary string, is a natural and important problem, with applications in cryptanalysis, coding theory, fault-tolerant circuit design and so on. In…

Quantum backflow is the classically-forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to…

We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…

In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…

Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop…

We review, correct, and develop an algorithm which determines arbitrary Quantum Bounds, based on the seminal work of Tsirelson [Lett. Math. Phys. 4, 93 (1980)]. The potential of this algorithm is demonstrated by deriving both new…

A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…