Related papers: On the Existence of certain Quantum Algorithms

We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…

The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…

The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…

In this paper, we give a quantum algorithm which solves collision problem in an expected polynomial time. Especially, when the function is two-to-one, we present a quantum algorithm which can find a collision with certainty in a worst-case…

We motivate the use of quantum algorithms in particle physics and provide a brief overview of the most recent applications at high-energy colliders. In particular, we discuss in detail how a quantum approach reduces the complexity of jet…

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…

Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…

Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of…

The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…

We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…

We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…

We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…

A quantum computer consists of a set of quantum bits upon which operations called gates are applied to perform computations. In order to perform quantum algorithms, physicists would like to design arbitrary gates to apply to quantum bits.…

We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its…

We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible families corresponding to $\gcd(deg(P),deg(Q))\le 35$, and…

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…

Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…

Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…