Related papers: Accuracy of Trace Formulas
A quantum algorithm is exact if, on any input data, it outputs the correct answer with certainty (probability 1). A key question is: how big is the advantage of exact quantum algorithms over their classical counterparts: deterministic…
Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure…
The accuracy of the time information generated by clocks can be enhanced by allowing them to communicate with each other. Here we consider a basic scenario where a quantum clock receives a low-accuracy time signal as input and ask whether…
Topological invariants of a dataset, such as the number of holes that survive from one length scale to another (persistent Betti numbers) can be used to analyze and classify data in machine learning applications. We present an improved…
Weak quantum measurements enable real-time tracking and control of dynamical quantum systems, producing quantum trajectories -- evolutions of the quantum state of the system conditioned on measurement outcomes. For classical systems, the…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
This paper studies the structure of several real-world traces (including Facebook, High-Performance Computing, Machine Learning, and simulation generated traces) and presents a systematic approach to quantify and compare the structure of…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
Correspondence in quantum chaotic systems is lost in short time scales. Introducing some noise we study the spectrum of the resulting coarse grained propagaor of density matrices. Some differen methods to compute the spectrum are reviewed.…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
Semiclassical techniques have proven to be a very powerful method to extract physical effects from different quantum theories. Therefore, it is expected that in the near future they will play a very prominent role in the context of quantum…
Diffractive systems are quantum-mechanical models with point-like singularities where usual semiclassical approximation breaks down. An overview of recent investigations of such systems is presented. The following examples are considered in…
The ability of fully reconstructing quantum maps is a fundamental task of quantum information, in particular when coupling with the environment and experimental imperfections of devices are taken into account. In this context we carry out a…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Gutzwiller's trace formula allows interpreting the density of states of a classically chaotic quantum system in terms of classical periodic orbits. It diverges when periodic orbits undergo bifurcations, and must be replaced with a uniform…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the…
The statistical properties of quantum transport through a chaotic cavity are encoded in the traces $\T={\rm Tr}(tt^\dag)^n$, where $t$ is the transmission matrix. Within the Random Matrix Theory approach, these traces are random variables…
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…
The statistical state of any (classical or quantum) system with non-trivial time evolution can be interpreted as the pointer of a clock. The quality of such a clock is given by the statistical distinguishability of its states at different…