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Recent experimental progress in quantum information processing with trapped ions have demonstrated most of the fundamental elements required to realize a scalable quantum computer. The next set of challenges lie in realization of a large…
NP-complete problems are widely and deeply involved in various real-life scenarios while still intractable to solve efficiently on conventional computers. It is of great practical significance to construct versatile computing architectures…
We study PCA as a stochastic optimization problem and propose a novel stochastic approximation algorithm which we refer to as "Matrix Stochastic Gradient" (MSG), as well as a practical variant, Capped MSG. We study the method both…
We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the…
This paper introduces algorithms for problems where a decision maker has to control a system composed of several components and has access to only partial information on the state of each component. Such problems are difficult because of…
Stochastic computing (SC) is a promising candidate for fault tolerant computing in digital circuits. We present a novel stochastic computing estimation architecture allowing to solve a large group of estimation problems including least…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
The increasing difficulty in continued development of digital electronic logic has led to a renewed interest in alternative approaches. Oscillatory computing is one such approach that leverages alternative physical systems and computation…
Combinatorial optimization problems represent a wide range of real-world scenarios where complicated interactions make it difficult to find the best solution. One example is the quadratic assignment problem (QAP), which involves determining…
To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic…
Ising machines offer a compelling approach to addressing NP-hard problems, but physical realizations that are simultaneously scalable, reconfigurable, fast, and stable remain elusive. Quantum annealers, like D-Wave's cryogenic hardware,…
In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Integrated photonic circuits play a crucial role in implementing quantum information processing in the noisy intermediate-scale quantum (NISQ) era. Variational learning is a promising avenue that leverages classical optimization techniques…
Ising machines are dedicated hardware solvers of NP-hard optimization problems. However, they do not always find the most optimal solution. The probability of finding this optimal solution depends on the problem at hand. Using continuation…
We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…
We discuss guidelines for evaluating the performance of parameterized stochastic solvers for optimization problems, with particular attention to systems that employ novel hardware, such as digital quantum processors running variational…
A new technique is demonstrated for carrying out exact positive-P phase-space simulations of the coherent Ising machine quantum computer. By suitable design of the coupling matrix, general hard optimization problems can be solved. Here,…
Stochastic computing has a long history as an alternative method of performing arithmetic on a computer. While it can be considered an unbiased estimator of real numbers, it has a variance and MSE on the order of $\Omega(\frac{1}{N})$. On…
It is well known in quantum optics that any process involving the preparation of a multimode gaussian state, followed by a gaussian operation and gaussian measurements, can be efficiently simulated by classical computers. Here, we provide…