Related papers: Differentiable Quantum Computing for Large-scale L…
Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore,…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
For the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Extracting the full potential of computation and realizing quantum algorithms with a…
This paper offers a unified perspective on different approaches to the solution of optimal control problems through the lens of constrained sequential quadratic programming. In particular, it allows us to find the relationships between…
We apply our recent work on empirical estimates of quantum speedups to the practical task of community detection in complex networks. We design several quantum variants of a popular classical algorithm -- the Louvain algorithm for community…
A Linear-quadratic optimal control problem is considered for mean-field stochastic differential equations with deterministic coefficients. By a variational method, the optimality system is derived, which turns out to be a linear mean-field…
This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that…
Quantum computing promises to tackle technological and industrial problems insurmountable for classical computers. However, today's quantum computers still have limited demonstrable functionality, and it is expected that scaling up to…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
Robust and high-precision quantum control is extremely important but challenging for the functionization of scalable quantum computation. In this paper, we show that this hard problem can be translated to a supervised machine learning task…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
Mixed Integer Programs (MIPs) model many optimization problems of interest in Computer Science, Operations Research, and Financial Engineering. Solving MIPs is NP-Hard in general, but several solvers have found success in obtaining…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
Adiabatic quantum computers can solve difficult optimization problems (e.g., the quadratic unconstrained binary optimization problem), and they seem well suited to train machine learning models. In this paper, we describe an adiabatic…
Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…
Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum…