scholarly journals Improving quantum algorithms for quantum chemistry

2015 ◽  
Vol 15 (1&2) ◽  
pp. 1-21 ◽  
Author(s):  
Matthew B. Hastings ◽  
Dave Wecker ◽  
Bela Bauer ◽  
Matthias Troyer
Keyword(s):  
Numerical Simulation ◽  
Quantum Chemistry ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Constant Factor ◽  
Linear Decrease ◽  
Small Constant ◽  
Term Order ◽  
The Cost

We present several improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer. First, we modify how Jordan-Wigner transformations are implemented to reduce their cost from linear or logarithmic in the number of orbitals to a constant. Our modification does not require additional ancilla qubits. Then, we demonstrate how many operations can be parallelized, leading to a further linear decrease in the parallel depth of the circuit, at the cost of a small constant factor increase in number of qubits required. Thirdly, we modify the term order in the Trotter-Suzuki decomposition, significantly reducing the error at given Trotter-Suzuki timestep. A final improvement modifies the Hamiltonian to reduce errors introduced by the non-zero Trotter-Suzuki timestep. All of these techniques are validated using numerical simulation and detailed gate counts are given for realistic molecules.

scholarly journals Entanglement and its role in Shor's algorithm

2006 ◽  
Vol 6 (7) ◽  
pp. 630-640
Author(s):  
V.M. Kendon ◽  
W.J. Munro
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Fourier Transform ◽  
Shor's Algorithm ◽  
Critical Resource ◽  
Factoring Algorithm

Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The shifting patterns in the entanglement are found to relate to the choice of basis for the quantum Fourier transform.

Evaluation Of The Functional Of Space-Planning Arrangement Of A Building

2019 ◽  
pp. 4-9
Keyword(s):  
Numerical Simulation ◽  
Life Cycle ◽  
Initial Data ◽  
Objective Assessment ◽  
Objective Evaluation ◽  
Point Of View ◽  
Shopping Centers ◽  
Space Planning ◽  
Planning Decisions ◽  
The Cost

The article focuses on the problem of the lack of objective evaluation of space-planning arrangement of buildings as a creative approach of the architect to the performing of functional tasks by the object. It is proposed to create a methodology for assessing the functional of space-planning solutions of buildings on the basis of numerical simulation of functional processes using the theory of human flows. There is a description of the prospects of using this method, which makes it possible to increase the coefficient of compactness, materials and works saving, more efficient use of space, reduce the cost of the life cycle of the building, save human forces and time to implement the functional of the building. The necessary initial data for modeling on the example of shopping and shopping-entertainment centers are considered. There are three main tasks for algorithmization of the functional of shopping centers. The conclusion is made about necessity of development of a method for objective assessment of buildings from the point of view of ergonomics of space-planning decisions based on the study of human behavior in buildings of different purposes.

scholarly journals Smooth input preparation for quantum and quantum-inspired machine learning

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Zhikuan Zhao ◽  
Jack K. Fitzsimons ◽  
Patrick Rebentrost ◽  
Vedran Dunjko ◽  
Joseph F. Fitzsimons
Keyword(s):  
Machine Learning ◽  
Quantum Algorithms ◽  
Machine Learning Algorithms ◽  
Low Rank ◽  
Smoothed Analysis ◽  
Machine Learning Applications ◽  
Data Points ◽  
Input Model ◽  
The Cost ◽  
Input Perturbation

AbstractMachine learning has recently emerged as a fruitful area for finding potential quantum computational advantage. Many of the quantum-enhanced machine learning algorithms critically hinge upon the ability to efficiently produce states proportional to high-dimensional data points stored in a quantum accessible memory. Even given query access to exponentially many entries stored in a database, the construction of which is considered a one-off overhead, it has been argued that the cost of preparing such amplitude-encoded states may offset any exponential quantum advantage. Here we prove using smoothed analysis that if the data analysis algorithm is robust against small entry-wise input perturbation, state preparation can always be achieved with constant queries. This criterion is typically satisfied in realistic machine learning applications, where input data is subjective to moderate noise. Our results are equally applicable to the recent seminal progress in quantum-inspired algorithms, where specially constructed databases suffice for polylogarithmic classical algorithm in low-rank cases. The consequence of our finding is that for the purpose of practical machine learning, polylogarithmic processing time is possible under a general and flexible input model with quantum algorithms or quantum-inspired classical algorithms in the low-rank cases.

scholarly journals Practical Quantum Computing

2021 ◽  
Vol 2 (1) ◽  
pp. 1-35
Author(s):  
Adrien Suau ◽  
Gabriel Staffelbach ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Equation Solving ◽  
Small Quantum ◽  
Quantum Wave ◽  
Variational Algorithms ◽  
The One

In the last few years, several quantum algorithms that try to address the problem of partial differential equation solving have been devised: on the one hand, “direct” quantum algorithms that aim at encoding the solution of the PDE by executing one large quantum circuit; on the other hand, variational algorithms that approximate the solution of the PDE by executing several small quantum circuits and making profit of classical optimisers. In this work, we propose an experimental study of the costs (in terms of gate number and execution time on a idealised hardware created from realistic gate data) associated with one of the “direct” quantum algorithm: the wave equation solver devised in [32]. We show that our implementation of the quantum wave equation solver agrees with the theoretical big-O complexity of the algorithm. We also explain in great detail the implementation steps and discuss some possibilities of improvements. Finally, our implementation proves experimentally that some PDE can be solved on a quantum computer, even if the direct quantum algorithm chosen will require error-corrected quantum chips, which are not believed to be available in the short-term.

Quantum Algorithms of the Vertex Cover Problem on a Quantum Computer

2009 ◽  
Author(s):  
Weng-Long Chang ◽  
Ting-Ting Ren ◽  
Mang Feng ◽  
Shu-Chien Huang ◽  
Lai Chin Lu ◽  
...  
Keyword(s):  
Quantum Computer ◽  
Quantum Algorithms ◽  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Cover Problem

Based on Numerical Simulation of High-Performance Parallel Machine Muffler Experimental Calibration

2013 ◽  
Vol 718-720 ◽  
pp. 1645-1650
Author(s):  
Gen Yin Cheng ◽  
Sheng Chen Yu ◽  
Zhi Yong Wei ◽  
Shao Jie Chen ◽  
You Cheng
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Boundary Element ◽  
Message Passing ◽  
High Performance ◽  
Message Passing Interface ◽  
Parallel Machine ◽  
Simulation Software ◽  
Experimental Calibration ◽  
The Cost

Commonly used commercial simulation software SYSNOISE and ANSYS is run on a single machine (can not directly run on parallel machine) when use the finite element and boundary element to simulate muffler effect, and it will take more than ten days, sometimes even twenty days to work out an exact solution as the large amount of numerical simulation. Use a high performance parallel machine which was built by 32 commercial computers and transform the finite element and boundary element simulation software into a program that can running under the MPI (message passing interface) parallel environment in order to reduce the cost of numerical simulation. The relevant data worked out from the simulation experiment demonstrate that the result effect of the numerical simulation is well. And the computing speed of the high performance parallel machine is 25 ~ 30 times a microcomputer.

Application and Research of Digital Technology in Optimal Design of CNC Floor Boring and Milling Machine

2012 ◽  
Vol 429 ◽  
pp. 111-115
Author(s):  
Zhen Long Leng ◽  
Jin Feng Yang ◽  
Qun Ping Liu ◽  
Xun Deng
Keyword(s):  
Numerical Simulation ◽  
Optimal Design ◽  
Digital Technology ◽  
Three Dimensional ◽  
Milling Machine ◽  
Machine Model ◽  
Digital Modeling ◽  
Key Technologies ◽  
The Cost ◽  
Interference Checking

This paper focuses on application of the three-dimensional digital modeling, numerical analysis and optimization, digital control and other key technologies which provide technical support for the design and development in CNC floor boring and milling machine manufactruing. The three-dimensional digital modeling, digital assembly, interference checking help to eliminate some hidden trouble before processing and assembly. Numerical simulation reduces the cost and shortens the cycle of designand manufactruing in the optimal design of the machine. This technique has been successfully applied to a CNC Floor Boring and Milling Machine Model, which has been running for three years and achieved satisfactary economic result.

Numerical Simulation of Dynamics of a Spar Type Floating Wind Turbine and Comparison With Laboratory Measurements

2016 ◽  
Author(s):  
Hyunseong Min ◽  
Cheng Peng ◽  
Fei Duan ◽  
Zhiqiang Hu ◽  
Jun Zhang
Keyword(s):  
Numerical Simulation ◽  
Wind Speed ◽  
Numerical Simulations ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Deep Water ◽  
Offshore Wind ◽  
Wind Loads ◽  
Floating Offshore Wind Turbines ◽  
The Cost

Wind turbines are popular for harnessing wind energy. Floating offshore wind turbines (FOWT) installed in relatively deep water may have advantages over their on-land or shallow-water cousins because winds over deep water are usually steadier and stronger. As the size of wind turbines becomes larger and larger for reducing the cost per kilowatt, it could bring installation and operation risks in the deep water due to the lack of track records. Thus, together with laboratory tests, numerical simulations of dynamics of FOWT are desirable to reduce the probability of failure. In this study, COUPLE-FAST was initially employed for the numerical simulations of the OC3-HYWIND, a spar type platform equipped with the 5-MW baseline wind turbine proposed by National Renewable Energy Laboratory (NREL). The model tests were conducted at the Deepwater Offshore Basin in Shanghai Jiao Tong University (SJTU) with a 1:50 Froude scaling [1]. In comparison of the simulation using COUPLE-FAST with the corresponding measurements, it was found that the predicted motions were in general significantly smaller than the related measurements. The main reason is that the wind loads predicted by FAST were well below the related measurements. Large discrepancies are expected because the prototype and laboratory wind loads do not follow Froude number similarity although the wind speed was increased (or decreased) in the tests such that the mean surge wind force matched that predicted by FAST at the nominal wind speed (Froude similarity) in the cases of a land wind turbine [1]. Therefore, an alternative numerical simulation was made by directly inputting the measured wind loads to COUPLE instead of the ones predicted by FAST. The related simulated results are much improved and in satisfactory agreement with the measurements.

Quantum Algorithms

2021 ◽  
pp. 82-101
Author(s):  
Renata Wong ◽  
Amandeep Singh Bhatia
Keyword(s):  
Quantum Computing ◽  
Fault Tolerance ◽  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Computer Hardware ◽  
Quantum Mechanical ◽  
Computational Power ◽  
Quantum Devices ◽  
The Core

In the last two decades, the interest in quantum computation has increased significantly among research communities. Quantum computing is the field that investigates the computational power and other properties of computers on the basis of the underlying quantum-mechanical principles. The main purpose is to find quantum algorithms that are significantly faster than any existing classical algorithms solving the same problem. While the quantum computers currently freely available to wider public count no more than two dozens of qubits, and most recently developed quantum devices offer some 50-60 qubits, quantum computer hardware is expected to grow in terms of qubit counts, fault tolerance, and resistance to decoherence. The main objective of this chapter is to present an introduction to the core quantum computing algorithms developed thus far for the field of cryptography.

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