Since the discovery of adiabatic quantum computing, a need has arisen for rigorously proven bounds for the error in the adiabatic approximation. We present in this paper, a rigorous and elementary derivation of upper and lower bounds on the error incurred from using the adiabatic approximation for quantum systems. Our bounds are often asymptotically tight in the limit of slow evolution for fixed Hamiltonians, and are used to provide sufficient conditions for the application of the adiabatic approximation. We show that our sufficiency criteria exclude the Marzlin-Sanders counterexample from the class of Hamiltonians that obey the adiabatic approximation. Finally, we demonstrate the existence of classes of Hamiltonians that resemble the Marzlin-Sanders counterexample Hamiltonian, but also obey the adiabatic approximation.
In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. It is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: universality, strong connections to the circuit model, simple implementation on quantum hardware, and a wealth of applications.
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NPhard. There is a highly inefficient 'basic algorithm' for solving the quantum separability problem which follows from the definition of a separable state. By exploiting specific properties of the set of separable states, we introduce a new classical algorithm that solves the problem significantly faster than the 'basic algorithm', allowing a feasible separability test where none previously existed e.g. in 3-by-3-dimensional systems. Our algorithm also provides a novel tool in the experimental detection of entanglement.Entangled quantum states are interesting both from theoretical and practical points of view. Theoretically, entanglement is connected to the confounding issue of nonlocality. Practically, entangled states are useful in quantum cryptography and other quantum information processing tasks (see [1] and references therein). A mixed quantum state is defined as separable if and only if it can be written as a convex combination of pure separable states (and defined as entangled, otherwise). Solving the quantum separability problem simply means determining whether a given quantum state is entangled or separable. The problem comes in two flavors -one theoretical, and the other experimental. In this paper, we describe an algorithm for solving the quantum separability problem in the theoretical setting. We also describe the algorithm's utility in the experimental setting.
Abstract. We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over GF (2 m ). We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of binary finite fields and by representing elliptic curve points using a technique based on projective coordinates. The depth of our proposed implementation is O(m 2 ), which is an improvement over the previous bound of O(m 3 ).
This paper introduces the COVID-19 Open Dataset (COD), available at goo.gle/covid-19-open-data. A static copy is of the dataset is also available at 10.6084/m9.figshare.c.5399355. This is a very large “meta-dataset” of COVID-related data, containing epidemiological information, from 22,579 unique locations within 232 different countries and independent territories. For 62 of these countries we have state-level data, and for 23 of these countries we have county-level data. For 15 countries, COD includes cases and deaths stratified by age or sex. COD also contains information on hospitalizations, vaccinations, and other relevant factors such as mobility, non-pharmaceutical interventions and static demographic attributes. Each location is tagged with a unique identifier so that these different types of information can be easily combined. The data is automatically extracted from 121 different authoritative sources, using scalable open source software. This paper describes the format and construction of the dataset, and includes a preliminary statistical analysis of its content, revealing some interesting patterns.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.