Showing papers on "Computation published in 2017"

Efficient Variational Quantum Simulator Incorporating Active Error Minimization

Abstract: Quantum computers will need to be tolerant to errors introduced by noise, but current proposals estimate that the number of qubits required for error correction will be many orders of magnitude larger than the number needed for useful computation. A new proposal uses a classical-quantum hybrid scheme to implement simple error-tolerant quantum processors with relatively few resources.

A roadmap for the computation of persistent homology

Abstract: Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. The computation of PH is an open area with numerous important and fascinating challenges. The field of PH computation is evolving rapidly, and new algorithms and software implementations are being updated and released at a rapid pace. The purposes of our article are to (1) introduce theory and computational methods for PH to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of PH. We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH. Based on our benchmarking, we indicate which algorithms and implementations are best suited to different types of data sets. In an accompanying tutorial, we provide guidelines for the computation of PH. We make publicly available all scripts that we wrote for the tutorial, and we make available the processed version of the data sets used in the benchmarking.

Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States

Abstract: Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. We demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.

High-dimensional coded matrix multiplication

Abstract: Coded computation is a framework for providing redundancy in distributed computing systems to make them robust to slower nodes, or stragglers. In [1], the authors propose a coded computation scheme based on maximum distance separable (MDS) codes for computing the product ATB, and this scheme is suitable for the case where one of the matrices is small enough to fit into a single compute node. In this work, we study coded computation involving large matrix multiplication where both matrices are large, and propose a new coded computation scheme, which we call product-coded matrix multiplication. Our analysis reveals interesting insights into which schemes perform best in which regimes. When the number of backup nodes scales sub-linearly in the size of the product, the product-coded scheme achieves the best run-time performance. On the other hand, when the number of backup nodes scales linearly in the size of the product, the MDS-coded scheme achieves the fundamental limit on the run-time performance. Further, we propose a novel application of low-density-parity-check (LDPC) codes to achieve linear-time decoding complexity, thus allowing our proposed solutions to scale gracefully.

In-Network Computation is a Dumb Idea Whose Time Has Come

Abstract: Programmable data plane hardware creates new opportunities for infusing intelligence into the network. This raises a fundamental question: what kinds of computation should be delegated to the network? In this paper, we discuss the opportunities and challenges for co-designing data center distributed systems with their network layer. We believe that the time has finally come for offloading part of their computation to execute in-network. However, in-network computation tasks must be judiciously crafted to match the limitations of the network machine architecture of programmable devices. With the help of our experiments on machine learning and graph analytics workloads, we identify that aggregation functions raise opportunities to exploit the limited computation power of networking hardware to lessen network congestion and improve the overall application performance. Moreover, as a proof-of-concept, we propose Daiet, a system that performs in-network data aggregation. Experimental results with an initial prototype show a large data reduction ratio (86.9%-89.3%) and a similar decrease in the workers' computation time.

Factorized Convolutional Neural Networks

Abstract: In this paper, we propose to factorize the convolutional layer to reduce its computation. The 3D convolution operation in a convolutional layer can be considered as performing spatial convolution in each channel and linear projection across channels simultaneously. By unravelling them and arranging the spatial convolutions sequentially, the proposed layer is composed of a low-cost single intra-channel convolution and a linear channel projection. When combined with residual connection, it can effectively preserve the spatial information and maintain the accuracy with significantly less computation. We also introduce a topological subdivisioning to reduce the connection between the input and output channels. Our experiments demonstrate that the proposed layers outperform the standard convolutional layers on performance/complexity ratio. Our models achieve similar performance to VGG-16, ResNet-34, ResNet-50, ResNet-101 while requiring 42x,7.32x,4.38x,5.85x less computation respectively.

Automated optimization of large quantum circuits with continuous parameters

Abstract: We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale quantum circuits. For the suite of benchmarks considered, we obtain substantial reductions in gate counts. In particular, we provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. Our results help bridge the gap between the computations that can be run on existing hardware and those that are expected to outperform classical computers.

Temporal correlation detection using computational phase-change memory

Abstract: Conventional computers based on the von Neumann architecture perform computation by repeatedly transferring data between their physically separated processing and memory units. As computation becomes increasingly data centric and the scalability limits in terms of performance and power are being reached, alternative computing paradigms with collocated computation and storage are actively being sought. A fascinating such approach is that of computational memory where the physics of nanoscale memory devices are used to perform certain computational tasks within the memory unit in a non-von Neumann manner. We present an experimental demonstration using one million phase change memory devices organized to perform a high-level computational primitive by exploiting the crystallization dynamics. Its result is imprinted in the conductance states of the memory devices. The results of using such a computational memory for processing real-world data sets show that this co-existence of computation and storage at the nanometer scale could enable ultra-dense, low-power, and massively-parallel computing systems. New computing paradigms, such as in-memory computing, are expected to overcome the limitations of conventional computing approaches. Sebastian et al. report a large-scale demonstration of computational phase change memory (PCM) by performing high-level computational primitives using one million PCM devices.

Coded convolution for parallel and distributed computing within a deadline

Abstract: We consider the problem of computing the convolution of two long vectors using parallel processors in the presence of “stragglers”. Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation in time-critical distributed systems. We first show that splitting the vectors into smaller pieces and using a linear code to encode these pieces provides improved resilience against stragglers than replication-based schemes under a simple, worst-case straggler analysis. We then demonstrate that under commonly used models of computation time, coding can dramatically improve the probability of finishing the computation within a target “deadline” time. As opposed to the more commonly used technique of expected computation time analysis, we quantify the exponents of the probability of failure in the limit of large deadlines. Our exponent metric captures the probability of failing to finish before a specified deadline time, i.e., the behavior of the “tail”. Moreover, our technique also allows for simple closed form expressions for more general models of computation time, e.g. shifted Weibull models instead of only shifted exponentials. Thus, through this problem of coded convolution, we establish the utility of a novel asymptotic failure exponent analysis for distributed systems.

The heat method for distance computation

Abstract: We introduce the heat method for solving the single- or multiple-source shortest path problem on both flat and curved domains. A key insight is that distance computation can be split into two stages: first find the direction along which distance is increasing, then compute the distance itself. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of standard sparse linear systems. These systems can be factored once and subsequently solved in near-linear time, substantially reducing amortized cost. Real-world performance is an order of magnitude faster than state-of-the-art methods, while maintaining a comparable level of accuracy. The method can be applied in any dimension, and on any domain that admits a gradient and inner product---including regular grids, triangle meshes, and point clouds. Numerical evidence indicates that the method converges to the exact distance in the limit of refinement; we also explore smoothed approximations of distance suitable for applications where greater regularity is desired.

Straggler Mitigation in Distributed Optimization Through Data Encoding

Abstract: Slow running or straggler tasks can significantly reduce computation speed in distributed computation. Recently, coding-theory-inspired approaches have been applied to mitigate the effect of straggling, through embedding redundancy in certain linear computational steps of the optimization algorithm, thus completing the computation without waiting for the stragglers. In this paper, we propose an alternate approach where we embed the redundancy directly in the data itself, and allow the computation to proceed completely oblivious to encoding. We propose several encoding schemes, and demonstrate that popular batch algorithms, such as gradient descent and L-BFGS, applied in a coding-oblivious manner, deterministically achieve sample path linear convergence to an approximate solution of the original problem, using an arbitrarily varying subset of the nodes at each iteration. Moreover, this approximation can be controlled by the amount of redundancy and the number of nodes used in each iteration. We provide experimental results demonstrating the advantage of the approach over uncoded and data replication strategies.

A simple tensor network algorithm for two-dimensional steady states.

Abstract: Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady states of 2D quantum lattice dissipative systems in the thermodynamic limit. Our method is based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle. We test its validity by simulating a dissipative quantum Ising model, relevant for dissipative systems of interacting Rydberg atoms, and benchmark our simulations with a variational algorithm based on product and correlated states. Our results support the existence of a first order transition in this model, with no bistable region. We also simulate a dissipative spin 1/2 XYZ model, showing that there is no re-entrance of the ferromagnetic phase. Our method enables the computation of steady states in 2D quantum lattice systems.

KickStarter: Fast and Accurate Computations on Streaming Graphs via Trimmed Approximations

Abstract: Continuous processing of a streaming graph maintains an approximate result of the iterative computation on a recent version of the graph. Upon a user query, the accurate result on the current graph can be quickly computed by feeding the approximate results to the iterative computation --- a form of incremental computation that corrects the (small amount of) error in the approximate result. Despite the effectiveness of this approach in processing growing graphs, it is generally not applicable when edge deletions are present --- existing approximations can lead to either incorrect results (e.g., monotonic computations terminate at an incorrect minima/maxima) or poor performance (e.g., with approximations, convergence takes longer than performing the computation from scratch).This paper presents KickStarter, a runtime technique that can trim the approximate values for a subset of vertices impacted by the deleted edges. The trimmed approximation is both safe and profitable, enabling the computation to produce correct results and converge quickly. KickStarter works for a class of monotonic graph algorithms and can be readily incorporated in any existing streaming graph system. Our experiments with four streaming algorithms on five large graphs demonstrate that trimming not only produces correct results but also accelerates these algorithms by 8.5--23.7x.

Optimizing quantum optimization algorithms via faster quantum gradient computation

Abstract: We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it at only a logarithmic number of points in superposition. Our algorithm is an improved version of Stephen Jordan's gradient computation algorithm, providing an approximation of the gradient $ abla f$ with quadratically better dependence on the evaluation accuracy of $f$, for an important class of smooth functions. Furthermore, we show that most objective functions arising from quantum optimization procedures satisfy the necessary smoothness conditions, hence our algorithm provides a quadratic improvement in the complexity of computing their gradient. We also show that in a continuous phase-query model, our gradient computation algorithm has optimal query complexity up to poly-logarithmic factors, for a particular class of smooth functions. Moreover, we show that for low-degree multivariate polynomials our algorithm can provide exponential speedups compared to Jordan's algorithm in terms of the dimension $d$. One of the technical challenges in applying our gradient computation procedure for quantum optimization problems is the need to convert between a probability oracle (which is common in quantum optimization procedures) and a phase oracle (which is common in quantum algorithms) of the objective function $f$. We provide efficient subroutines to perform this delicate interconversion between the two types of oracles incurring only a logarithmic overhead, which might be of independent interest. Finally, using these tools we improve the runtime of prior approaches for training quantum auto-encoders, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA).

Online dynamic mode decomposition for time-varying systems

Abstract: Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow analysis, and reduced-order modeling. In situations where a system is time varying, one would like to update the system's description online as time evolves. This work provides an efficient method for computing DMD in real time, updating the approximation of a system's dynamics as new data becomes available. The algorithm does not require storage of past data, and computes the exact DMD matrix using rank-1 updates. A weighting factor that places less weight on older data can be incorporated in a straightforward manner, making the method particularly well suited to time-varying systems. A variant of the method may also be applied to online computation of "windowed DMD", in which only the most recent data are used. The efficiency of the method is compared against several existing DMD algorithms: for problems in which the state dimension is less than about~200, the proposed algorithm is the most efficient for real-time computation, and it can be orders of magnitude more efficient than the standard DMD algorithm. The method is demonstrated on several examples, including a time-varying linear system and a more complex example using data from a wind tunnel experiment. In particular, we show that the method is effective at capturing the dynamics of surface pressure measurements in the flow over a flat plate with an unsteady separation bubble.

The engineering challenges in quantum computing

Abstract: Quantum computers may revolutionize the field of computation by solving some complex problems that are intractable even for the most powerful current supercomputers. This paper first introduces the basic concepts of quantum computing and describes what the required layers are for building a quantum system. Thereafter, it discusses the different engineering challenges when building a quantum computer ranging from the core qubit technology, the control electronics, to the microarchitecture for the execution of quantum circuits and efficient quantum error correction. We conclude by discussing some compiler and programming issues relative to quantum algorithms.

Acceleration of Frequency Sweeping in Eddy-Current Computation

Abstract: In this paper, a novel method for accelerating frequency sweeping in eddy-current calculation using finite-element method is presented. Exploiting the fact that between adjacent frequencies, the eddy-current distributions are similar, an algorithm is proposed to accelerate the frequency sweeping computation. The solution of the field quantities under each frequency, which involves solving a system of linear equations using the conjugate gradients squared (CGS) method, is accelerated by using an optimized initial guess—the final solution from the previous frequency. Numerical tests show that this treatment could speed up the convergence of the CGS solving process, i.e., reduced number of iterations reaching the same relative residuals or reaching smaller residuals with the same iteration number.

Exact Complexity Certification of Active-Set Methods for Quadratic Programming

Abstract: Active-set methods are recognized to often outperform other methods in terms of speed and solution accuracy when solving small-size quadratic programming (QP) problems, making them very attractive in embedded linear model predictive control (MPC) applications. A drawback of active-set methods is the lack of tight bounds on the worst-case number of iterations, a fundamental requirement for their implementation in a real-time system. Extensive simulation campaigns provide an indication of the expected worst-case computation load, but not a complete guarantee. This paper solves such a certification problem by proposing an algorithm to compute the exact bound on the maximum number of iterations and floating point operations required by a state-of-the-art dual active-set QP solver. The algorithm is applicable to a given QP problem whose linear term of the cost function and right-hand side of the constraints depend linearly on a vector of parameters, as in the case of linear MPC. In addition, a new solver is presented that combines explicit and implicit MPC ideas, guaranteeing improvements of the worst-case computation time. The ability of the approach to exactly quantify memory and worst-case computation requirements is tested on a few MPC examples, also highlighting when online optimization should be preferred to explicit MPC.

Computation Partitioning for Mobile Cloud Computing in a Big Data Environment

Abstract: The growth of mobile cloud computing (MCC) is challenged by the need to adapt to the resources and environment that are available to mobile clients while addressing the dynamic changes in network bandwidth. Big data can be handled via MCC. In this paper, we propose a model of computation partitioning for stateful data in the dynamic environment that will improve the performance. First, we constructed a model of stateful data streaming and investigated the method of computation partitioning in a dynamic environment. We developed a definition of direction and calculation of the segmentation scheme, including single-frame data flow, task scheduling, and executing efficiency. We also defined the problem for a multiframe data flow calculation segmentation decision that is optimized for dynamic conditions and provided an analysis. Second, we proposed a computation partitioning method for single-frame data flow. We determined the data parameters of the application model, the computation partitioning scheme, and the task and work order data stream model. We followed the scheduling method to provide the optimal calculation for data frame execution time after computation partitioning and the best computation partitioning method. Third, we explored a calculation segmentation method for single-frame data flow based on multiframe data using multiframe data optimization adjustment and prediction of future changes in network bandwidth. We were able to demonstrate that the calculation method for multiframe data in a changing network bandwidth environment is more efficient than the calculation method with the limitation of calculations for single-frame data. Finally, our research verified the effectiveness of single-frame data in the application of the data stream and analyzed the performance of the method to optimize the adjustment of multiframe data. We used a MCC platform prototype system for face recognition to verify the effectiveness of the method.

Two-Message Witness Indistinguishability and Secure Computation in the Plain Model from New Assumptions

Abstract: We study the feasibility of two-message protocols for secure two-party computation in the plain model, for functionalities that deliver output to one party, with security against malicious parties. Since known impossibility results rule out polynomial-time simulation in this setting, we consider the common relaxation of allowing super-polynomial simulation.

Computing Linear Transformations With Unreliable Components

Abstract: We consider the problem of computing a binary linear transformation when all circuit components are unreliable. Two models of unreliable components are considered: probabilistic errors and permanent errors. We introduce the “ENCODED” technique that ensures that the error probability of the computation of the linear transformation is kept bounded below a small constant independent of the size of the linear transformation even when all logic gates in the computation are noisy. By deriving a lower bound, we show that in some cases, the computational complexity of the ENCODED technique achieves the optimal scaling in error probability. Further, we examine the gain in energy-efficiency from the use of a “voltage-scaling” scheme, where gate-energy is reduced by lowering the supply voltage. We use a gate energy-reliability model to show that tuning gate-energy appropriately at different stages of the computation (“dynamic” voltage scaling), in conjunction with ENCODED, can lead to orders of magnitude energy-savings over the classical “uncoded” approach. Finally, we also examine the problem of computing a linear transformation when noiseless decoders can be used, providing upper and lower bounds to the problem.

A Tucker Deep Computation Model for Mobile Multimedia Feature Learning

Abstract: Recently, the deep computation model, as a tensor deep learning model, has achieved super performance for multimedia feature learning. However, the conventional deep computation model involves a large number of parameters. Typically, training a deep computation model with millions of parameters needs high-performance servers with large-scale memory and powerful computing units, limiting the growth of the model size for multimedia feature learning on common devices such as portable CPUs and conventional desktops. To tackle this problem, this article proposes a Tucker deep computation model by using the Tucker decomposition to compress the weight tensors in the full-connected layers for multimedia feature learning. Furthermore, a learning algorithm based on the back-propagation strategy is devised to train the parameters of the Tucker deep computation model. Finally, the performance of the Tucker deep computation model is evaluated by comparing with the conventional deep computation model on two representative multimedia datasets, that is, CUAVE and SNAE2, in terms of accuracy drop, parameter reduction, and speedup in the experiments. Results imply that the Tucker deep computation model can achieve a large-parameter reduction and speedup with a small accuracy drop for multimedia feature learning.

Attributed Scattering Center Extraction Algorithm Based on Sparse Representation With Dictionary Refinement

Abstract: Compared with the point-scattering model, the attributed scattering center model (ASCM) is able to describe the frequency and aspect dependence of canonical scattering objects using solutions from both physical optics and the geometric theory of diffraction. As the ASCM is complicated, it may increase the dimension of the parameterized dictionary, which will increase the cost of computation and storage significantly. Aiming at this problem, a novel sparse representation-based algorithm, combined with an alternative optimization and dictionary refinement, is proposed. Utilizing the orthogonal matching pursuit algorithm combined with relaxation algorithm, the solution to the sparse signal recovery problem can be obtained. Numerical results on both electromagnetic computation data and measured SAR data verify the validity of the proposed algorithm.

Computation of ground-state properties in molecular systems: back-propagation with auxiliary-field quantum Monte Carlo

Abstract: We address the computation of ground-state properties of chemical systems and realistic materials within the auxiliary-field quantum Monte Carlo method. The phase constraint to control the Fermion phase problem requires the random walks in Slater determinant space to be open-ended with branching. This in turn makes it necessary to use back-propagation (BP) to compute averages and correlation functions of operators that do not commute with the Hamiltonian. Several BP schemes are investigated, and their optimization with respect to the phaseless constraint is considered. We propose a modified BP method for the computation of observables in electronic systems, discuss its numerical stability and computational complexity, and assess its performance by computing ground-state properties in several molecular systems, including small organic molecules.

Computation Diversity in Emerging Networking Paradigms

Abstract: Nowadays, computation is playing an increasingly more important role in the future generation of computer and communication networks, as exemplified by the recent progress in software defined networking (SDN) for wired networks as well as cloud radio access networks (C-RAN) and mobile cloud computing (MCC) for wireless networks. This paper proposes a unified concept, i.e., computation diversity, to describe the impact and diverse forms of the computation resources on both wired and wireless communications. By linking the computation resources to the communication networks based on quality of service (QoS) requirements, we can show how computation resources influence the networks. Moreover, by analyzing the different functionalities of computation resources in SDN, C-RAN, and MCC, we can show diverse and flexible form that the computation resources present in different networks. The study of computation diversity can provide guidance to the future networks design, i.e., how to allocate the resources jointly between computation (e.g., CPU capacity) and communication (e.g., bandwidth), and thereby saving system energy and increase users' experiences.

Mutual potential between two rigid bodies with arbitrary shapes and mass distributions

Abstract: Formulae to compute the mutual potential, force, and torque between two rigid bodies are given. These formulae are expressed in Cartesian coordinates using inertia integrals. They are valid for rigid bodies with arbitrary shapes and mass distributions. By using recursive relations, these formulae can be easily implemented on computers. Comparisons with previous studies show their superiority in computation speed. Using the algorithm as a tool, the planar problem of two ellipsoids is studied. Generally, potential truncated at the second order is good enough for a qualitative description of the mutual dynamics. However, for ellipsoids with very large non-spherical terms, higher order terms of the potential should be considered, at the cost of a higher computational cost. Explicit formulae of the potential truncated to the fourth order are given.