scholarly journals Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 426
Author(s):  
Amir Kalev ◽  
Itay Hen
Keyword(s):  
Series Expansion ◽  
Evolution Operator ◽  
State Of The Art ◽  
Hamiltonian Dynamics ◽  
Power Series Expansion ◽  
Quantum Algorithm ◽  
Time Evolution Operator ◽  
Diagonal Component ◽  
Current State ◽  
Diagonal Part

We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its off-diagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current state-of-the-art. We provide an analysis of resource costs for several sample models.

scholarly journals Preparation of Approximate Eigenvector by Unitary Operations on Eigenstate in Abrams-Lloyd Quantum Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Latha S. Warrier
Keyword(s):  
Time Evolution ◽  
Programming Language ◽  
Spin Chain ◽  
Evolution Operator ◽  
Unitary Operator ◽  
Language Model ◽  
Quantum Algorithm ◽  
Basis Vector ◽  
Unitary Matrix ◽  
Time Evolution Operator

The Abrams-Lloyd quantum algorithm computes an eigenvalue and the corresponding eigenstate of a unitary matrix from an approximate eigenvector Va. The eigenstate is a basis vector in the orthonormal eigenspace. Finding another eigenvalue, using a random approximate eigenvector, may require many trials as the trial may repeatedly result in the eigenvalue measured earlier. We present a method involving orthogonalization of the eigenstate obtained in a trial. It is used as the Va for the next trial. Because of the orthogonal construction, Abrams-Lloyd algorithm will not repeat the eigenvalue measured earlier. Thus, all the eigenvalues are obtained in sequence without repetitions. An operator that anticommutes with a unitary operator orthogonalizes the eigenvectors of the unitary. We implemented the method on the programming language model of quantum computation and tested it on a unitary matrix representing the time evolution operator of a small spin chain. All the eigenvalues of the operator were obtained sequentially. Another use of the first eigenvector from Abrams-Lloyd algorithm is preparing a state that is the uniform superposition of all the eigenvectors. This is possible by nonorthogonalizing the first eigenvector in all dimensions and then applying the Abrams-Lloyd algorithm steps stopping short of the last measurement.

Behavioral Genetics: Concepts for Research and Practice in Language Development and Disorders

1995 ◽  
Vol 38 (5) ◽  
pp. 1126-1142 ◽  
Author(s):  
Jeffrey W. Gilger
Keyword(s):  
Language Development ◽  
Behavioral Genetics ◽  
State Of The Art ◽  
Genetic Research ◽  
Great Promise ◽  
Behavioral Genetic ◽  
Fine Grained ◽  
Future Goals ◽  
Current State ◽  
Research Designs

This paper is an introduction to behavioral genetics for researchers and practioners in language development and disorders. The specific aims are to illustrate some essential concepts and to show how behavioral genetic research can be applied to the language sciences. Past genetic research on language-related traits has tended to focus on simple etiology (i.e., the heritability or familiality of language skills). The current state of the art, however, suggests that great promise lies in addressing more complex questions through behavioral genetic paradigms. In terms of future goals it is suggested that: (a) more behavioral genetic work of all types should be done—including replications and expansions of preliminary studies already in print; (b) work should focus on fine-grained, theory-based phenotypes with research designs that can address complex questions in language development; and (c) work in this area should utilize a variety of samples and methods (e.g., twin and family samples, heritability and segregation analyses, linkage and association tests, etc.).

Schizophrenia Research: Current State of the Art

1976 ◽  
Vol 21 (7) ◽  
pp. 497-498
Author(s):  
STANLEY GRAND
Keyword(s):  
State Of The Art ◽  
Current State

Umbral Calculus

10.37236/24 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
A. Di Bucchianico ◽  
D. Loeb
Keyword(s):  
19Th Century ◽  
Finite Differences ◽  
State Of The Art ◽  
Umbral Calculus ◽  
Current State ◽  
Logical Foundation ◽  
Complete Bibliography ◽  
The 19Th Century ◽  
Mathematical Literature

We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of “magic rules” for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 500 references) which we expect to update regularly.

The Receptor-Dependent QSAR Paradigm: An Overview of the Current State of the Art

2009 ◽  
Vol 5 (4) ◽  
pp. 359-366 ◽  
Author(s):  
Osvaldo Santos-Filho ◽  
Anton Hopfinger ◽  
Artem Cherkasov ◽  
Ricardo de Alencastro
Keyword(s):  
State Of The Art ◽  
Current State
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