Related papers: Recovering the original simplicity: succinct and d…
Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks…
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential…
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…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
A quantum algorithm that solves the time-dependent Dirac equation on a digital quantum computer is developed and analyzed. The time evolution is performed by an operator splitting decomposition technique that allows for a mapping of the…
We initiate a systematic study of pseudo-deterministic quantum algorithms. These are quantum algorithms that, for any input, output a canonical solution with high probability. Focusing on the query complexity model, our main contributions…
We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
In the traditional random-conformational-search model, various hypotheses with a series of meta-stable intermediate states were often proposed to resolve the Levinthal paradox. Here we introduce a quantum strategy to formulate protein…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
We give a quantum algorithm for a novel type of black-box problem: identifying a hidden $d$-regular base graph $G$ on $n$ vertices from oracle access to an obfuscated version of it, rather than traversing it. From $G$ we build the spired…
Quantum random walks have been much studied recently, largely due to their highly nonclassical behavior. In this paper, we study one possible route to classical behavior for the discrete quantum random walk on the line: the use of multiple…
After the first detection of a gravitational wave in 2015, the number of successes achieved by this innovative way of looking through the universe has not stopped growing. However, the current techniques for analyzing this type of events…
Quantum computing is fast evolving as a technology due to recent advances in hardware, software, as well as the development of promising applications. To use this technology for solving specific problems, a suitable quantum algorithm has to…
We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear system $A\x = \b$, we show that there is a classical algorithm that…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
While the quantum query complexity of $k$-distinctness is known to be $O\left(n^{3/4-1/4(2^k-1)}\right)$ for any constant $k \geq 4$, the best previous upper bound on the time complexity was $\widetilde{O}\left(n^{1-1/k}\right)$. We give a…