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Noise detrimentally affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, LOWESA (low weight efficient simulation…

Computing numerical solutions to fractional differential equations can be computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In general, numerical…

We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is…

Variational quantum metrology represents a powerful tool for optimizing generic estimation strategies, combining the principles of variational optimization with the techniques of quantum metrology. Such optimization procedures result…

Coherent optical memories will likely play an important role in future quantum communication networks. Among the different platforms, memories based on ladder-type orbital transitions in atomic gasses offer high bandwidth ($>100$ MHz),…

In this paper we describe, implement, and test the performance of distributed memory simulations of quantum circuits on the MSU Laconia Top500 supercomputer. Using OpenMP and MPI hybrid parallelization, we first use a distributed…

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…

Noise-tolerant PAC learning of linear models has been of central interests in machine learning community since the last century. In recent years, many computationally-efficient algorithms have been proposed for the problem of learning…

Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett. 100, 160501] proposed a quantum random access memory (QRAM) architecture to retrieve arbitrary superpositions of $N$ (quantum) memory cells via $O(\log(N))$ quantum switches and $O(\log(N))$…

Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…

Identification of a linear time-invariant dynamical system from partial observations is a fundamental problem in control theory. Particularly challenging are systems exhibiting long-term memory. A natural question is how learn such systems…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

We propose a novel algorithm for fast training of variational classifiers by processing multiple samples parallelly. The algorithm can be adapted for any ansatz used in the variational circuit. The presented algorithm utilizes qRAM and…

Quantum computers have long been expected to efficiently solve complex classical differential equations. Most digital, fault-tolerant approaches use Carleman linearization to map nonlinear systems to linear ones and then apply quantum…

We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear…

Simulating noisy quantum circuits is vital in designing and verifying quantum algorithms in the current NISQ (Noisy Intermediate-Scale Quantum) era, where quantum noise is unavoidable. However, it is much more inefficient than the classical…

In this paper, we strengthen the connection between qubit-based quantum circuits and photonic quantum computation. Within the framework of circuit-based quantum computation, the sum-over-paths interpretation of quantum probability…

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…