scholarly journals Improved Hamiltonian simulation via a truncated Taylor series and corrections

2017 ◽  
Vol 17 (7&8) ◽  
pp. 623-635
Author(s):  
Leonardo Novo ◽  
Dominic Berry
Keyword(s):  
Quantum Chemistry ◽  
Taylor Series ◽  
Evolution Operator ◽  
Quantum Algorithm ◽  
Simulation Method ◽  
Quantum Simulation ◽  
Wide Range ◽  
Simulation Based ◽  
Extra Step ◽  
Hamiltonian Simulation

We describe an improved version of the quantum algorithm for Hamiltonian simulation based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an operator that corrects the weightings of the Taylor series. This way, the desired accuracy is achieved with an improvement in the overall complexity of the algorithm. This quantum simulation method is applicable to a wide range of Hamiltonians of interest, including to quantum chemistry problems.

scholarly journals Corrected quantum walk for optimal Hamiltonian simulation

2016 ◽  
Vol 16 (15&16) ◽  
pp. 1295-1317
Author(s):  
Dominic Berry ◽  
Leonardo Novo
Keyword(s):  
Lower Bound ◽  
Quantum Chemistry ◽  
Taylor Series ◽  
Quantum Computer ◽  
Quantum Walk ◽  
Query Complexity ◽  
Hamiltonian Simulation ◽  
Hamiltonian Evolution

We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This correction enables us to obtain complexity which is the same as the lower bound up to doublelogarithmic factors for all parameter regimes. The scaling of the query complexity is given. This technique should also be useful for improving the scaling of the Taylor series approach to simulation, which is relevant to applications such as quantum chemistry.

scholarly journals Study on Friction in Automotive Shock Absorbers Part 1: Friction Simulation Using a Dynamic Friction Model in the Contact Zone of an FEM Model

Vehicles ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 212-232
Author(s):  
Ludwig Herzog ◽  
Klaus Augsburg
Keyword(s):  
Ride Comfort ◽  
Viscous Friction ◽  
Simulation Method ◽  
Friction Model ◽  
Model Parameters ◽  
Dynamic Friction ◽  
Friction Modeling ◽  
Shock Absorbers ◽  
Operation Conditions ◽  
Wide Range

The important change in the transition from partial to high automation is that a vehicle can drive autonomously, without active human involvement. This fact increases the current requirements regarding ride comfort and dictates new challenges for automotive shock absorbers. There exist two common types of automotive shock absorber with two friction types: The intended viscous friction dissipates the chassis vibrations, while the unwanted solid body friction is generated by the rubbing of the damper’s seals and guides during actuation. The latter so-called static friction impairs ride comfort and demands appropriate friction modeling for the control of adaptive or active suspension systems. In this article, a simulation approach is introduced to model damper friction based on the most friction-relevant parameters. Since damper friction is highly dependent on geometry, which can vary widely, three-dimensional (3D) structural FEM is used to determine the deformations of the damper parts resulting from mounting and varying operation conditions. In the respective contact zones, a dynamic friction model is applied and parameterized based on the single friction point measurements. Subsequent to the parameterization of the overall friction model with geometry data, operation conditions, material properties and friction model parameters, single friction point simulations are performed, analyzed and validated against single friction point measurements. It is shown that this simulation method allows for friction prediction with high accuracy. Consequently, its application enables a wide range of parameters relevant to damper friction to be investigated with significantly increased development efficiency.

Uncertainty in Collapse Strength Prediction of Sandwich Pipelines

2021 ◽  
Author(s):  
U. Bhardwaj ◽  
A. P. Teixeira ◽  
C. Guedes Soares
Keyword(s):  
Probabilistic Models ◽  
Uncertainty Propagation ◽  
Simulation Method ◽  
External Pressure ◽  
Design Parameters ◽  
Collapse Strength ◽  
Parameters Uncertainty ◽  
Wide Range ◽  
Model Predictions ◽  
Strength Models

Abstract This paper assesses the uncertainty in the collapse strength of sandwich pipelines under external pressure predicted by various strength models in three categories based on interlayer adhesion conditions. First, the validity of the strength models is verified by comparing their predictions with sandwich pipeline collapse test data and the corresponding model uncertainty factors are derived. Then, a parametric analysis of deterministic collapse strength predictions by models is conducted, illustrating insights of models’ behaviour for a wide range of design configurations. Furthermore, the uncertainty among different model predictions is perceived at different configurations of outer and inner pipes and core thicknesses. A case study of a realistic sandwich pipeline is developed, and probabilistic models are defined to basic design parameters. Uncertainty propagation of models’ predictions is assessed by the Monte Carlo simulation method. Finally, the strength model predictions of sandwich pipelines are compared to that of an equivalent single walled pipe.

scholarly journals From behavioural simulation to computer models: how simulation can be used to improve healthcare management and policy

2018 ◽  
Vol 6 (2) ◽  
pp. 95-102 ◽  
Author(s):  
Guillaume Lamé ◽  
Rebecca K Simmons
Keyword(s):  
Computer Simulations ◽  
Policy Making ◽  
Simulation Method ◽  
Healthcare Management ◽  
Policies And Procedures ◽  
Simulation Based ◽  
Behavioural Simulation ◽  
Human Participants ◽  
New Policies

Simulation is a technique that evokes or replicates substantial aspects of the real world, in order to experiment with a simplified imitation of an operations system, for the purpose of better understanding and/or improving that system. Simulation provides a safe environment for investigating individual and organisational behaviour and a risk-free testbed for new policies and procedures. Therefore, it can complement or replace direct field observations and trial-and-error approaches, which can be time consuming, costly and difficult to carry out. However, simulation has low adoption as a research and improvement tool in healthcare management and policy-making. The literature on simulation in these fields is dispersed across different disciplinary traditions and typically focuses on a single simulation method. In this article, we examine how simulation can be used to investigate, understand and improve management and policy-making in healthcare organisations. We develop the rationale for using simulation and provide an integrative overview of existing approaches, using examples of in vivo behavioural simulations involving live participants, pure in silico computer simulations and intermediate approaches (virtual simulation) where human participants interact with computer simulations of health organisations. We also discuss the combination of these approaches to organisational simulation and the evaluation of simulation-based interventions.

scholarly journals Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation

2022 ◽  
Vol 3 (1) ◽  
pp. 1-37
Author(s):  
Almudena Carrera Vazquez ◽  
Ralf Hiptmair ◽  
Stefan Woerner
Keyword(s):  
Necessary Conditions ◽  
Linear Equations ◽  
Circuit Complexity ◽  
Quantum Algorithm ◽  
Richardson Extrapolation ◽  
Classical Simulation ◽  
Hamiltonian Simulation ◽  
Systems Of Linear Equations ◽  
Amplitude Amplification ◽  
Theoretical Results

We present a quantum algorithm to solve systems of linear equations of the form Ax = b , where A is a tridiagonal Toeplitz matrix and b results from discretizing an analytic function, with a circuit complexity of O (1/√ε, poly (log κ, log N )), where N denotes the number of equations, ε is the accuracy, and κ the condition number. The repeat-until-success algorithm has to be run O (κ/(1-ε)) times to succeed, leveraging amplitude amplification, and needs to be sampled O (1/ε 2 ) times. Thus, the algorithm achieves an exponential improvement with respect to N over classical methods. In particular, we present efficient oracles for state preparation, Hamiltonian simulation, and a set of observables together with the corresponding error and complexity analyses. As the main result of this work, we show how to use Richardson extrapolation to enhance Hamiltonian simulation, resulting in an implementation of Quantum Phase Estimation (QPE) within the algorithm with 1/√ε circuits that can be run in parallel each with circuit complexity 1/√ ε instead of 1/ε. Furthermore, we analyze necessary conditions for the overall algorithm to achieve an exponential speedup compared to classical methods. Our approach is not limited to the considered setting and can be applied to more general problems where Hamiltonian simulation is approximated via product formulae, although our theoretical results would need to be extended accordingly. All the procedures presented are implemented with Qiskit and tested for small systems using classical simulation as well as using real quantum devices available through the IBM Quantum Experience.

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.

A qualitative evaluation of the role of simulation in policy development for service improvement

2017 ◽  
Vol 4 (1) ◽  
pp. 19-22 ◽  
Author(s):  
Thomas Blanks ◽  
Nicholas Woodier ◽  
Bryn Baxendale ◽  
Mark Fores ◽  
Lynn Fullerton
Keyword(s):  
Drug Administration ◽  
Policy Development ◽  
Direct Injection ◽  
Qualitative Evaluation ◽  
Service Improvement ◽  
Semistructured Interview ◽  
Training Requirements ◽  
Wide Range ◽  
Simulation Based ◽  
New Policies

ObjectiveTo evaluate the efficacy of simulation-based techniques to prospectively assess developing polices prior to implementation.MethodsA self-selected sample of nursing staff from a local, acute hospital reviewed a draft intravenous drug administration policy before simulating drug administration of either an infusion or direct injection. The participants completed a postsimulation questionnaire regarding the new policy and simulation, took part in a semistructured interview and were observed during the simulation with their consent.Results10 staff attended the simulation. The emergent themes identified a wide range of factors relating to the everyday usability and practicalities of the policy. There were issues surrounding inconsistent language between different clinical teams and training requirements for the new policy.ConclusionSimulation, using simple scenarios, allows the safe evaluation of new policies before publication to ensure they are appropriate for front-line use. It engages staff in user-centred design in their own healthcare system.

scholarly journals A Comparison of the Bravyi–Kitaev and Jordan–Wigner Transformations for the Quantum Simulation of Quantum Chemistry

2018 ◽  
Vol 14 (11) ◽  
pp. 5617-5630 ◽  
Author(s):  
Andrew Tranter ◽  
Peter J. Love ◽  
Florian Mintert ◽  
Peter V. Coveney
Keyword(s):  
Quantum Chemistry ◽  
Quantum Simulation

scholarly journals Holographic Interferometer for the Study of Phase Media, Which Has Four Output Channels of Different Sensitivity

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Yusupzhan Kh. Ismanov ◽  
Nasipbek K. Dzhamankyzov
Keyword(s):  
Computer Simulation ◽  
Simulation Method ◽  
Talbot Effect ◽  
Complex Phase ◽  
Computer Simulation Method ◽  
Holographic Interferometer ◽  
Wide Range ◽  
Talbot Interferometer ◽  
Spatial Filtration

Computer simulation of the interferometer combining properties of low-sensitive Talbot interferometer and high-sensitive holographic interferometer is considered. The interferometer has four output channels having different sensitivity. Channel sensibility can be varied by means of spatial filtration. The base of the interferometer is the holographic Talbot effect. The efficiency of this interferometer was verified by computer simulation method. Some results of the computer simulation are presented in the article. These results were compared with results obtained in optical experiments under the same conditions. A wide range of sensitivity of the interferometer makes it possible to use the interferometer to study complex phase objects, primarily dynamic media.

scholarly journals simuG: a general-purpose genome simulator

2019 ◽  
Vol 35 (21) ◽  
pp. 4442-4444 ◽  
Author(s):  
Jia-Xing Yue ◽  
Gianni Liti
Keyword(s):  
Copy Number Variants ◽  
General Purpose ◽  
Supplementary Information ◽  
Nucleotide Polymorphisms ◽  
Bioinformatics Analyses ◽  
Full Spectrum ◽  
Single Nucleotide ◽  
Genomic Variants ◽  
Wide Range ◽  
Simulation Based

Abstract Summary Simulated genomes with pre-defined and random genomic variants can be very useful for benchmarking genomic and bioinformatics analyses. Here we introduce simuG, a lightweight tool for simulating the full-spectrum of genomic variants (single nucleotide polymorphisms, Insertions/Deletions, copy number variants, inversions and translocations) for any organisms (including human). The simplicity and versatility of simuG make it a unique general-purpose genome simulator for a wide-range of simulation-based applications. Availability and implementation Code in Perl along with user manual and testing data is available at https://github.com/yjx1217/simuG. This software is free for use under the MIT license. Supplementary information Supplementary data are available at Bioinformatics online.

Sign in / Sign up

Export Citation Format

Share Document