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Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
Predicting the execution time of queries is an important problem with applications in scheduling, service level agreements and error detection. During query planning, a cost is associated with the chosen execution plan and used to rank…
A worst-case complexity bound is proved for a sequential quadratic optimization (commonly known as SQP) algorithm that has been designed for solving optimization problems involving a stochastic objective function and deterministic nonlinear…
The element distinctness problem is to determine whether a string $x=(x_1,\ldots,x_N)$ of $N$ elements contains two elements of the same value (a.k.a colliding pair), for which Ambainis proposed an optimal quantum algorithm. The idea behind…
The continuous improvements on image compression with variational autoencoders have lead to learned codecs competitive with conventional approaches in terms of rate-distortion efficiency. Nonetheless, taking the quantization into account…
Efficiency of self-optimizing systems is heavily dependent on their optimization strategies, e.g., choosing exact or approximate solver. A choice of such a strategy, in turn, is influenced by numerous factors, such as re-optimization time,…
Different from the view that information is objective reality, this paper adopts the idea that all information needs to be compiled by the interpreter before it can be observed. From the traditional complexity definition, this paper defines…
This paper studies theoretically and empirically a method of turning machine-learning algorithms into probabilistic predictors that automatically enjoys a property of validity (perfect calibration) and is computationally efficient. The…
Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
This paper is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies in the fact that consistency of overdetermined systems is…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
A general condition determining the optimal performance of a complex system has not yet been found and the possibility of its existence is unknown. To contribute in this direction, an optimization algorithm as a complex system is presented.…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
Machine teaching can be viewed as optimal control for learning. Given a learner's model, machine teaching aims to determine the optimal training data to steer the learner towards a target hypothesis. In this paper, we are interested in…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
We address the problem of unambiguous comparison of a pair of unknown qudit unitary channels. Using the framework of process positive operator valued measures (PPOVM) we characterize all solutions and identify the optimal ones. We prove…
Conformal predictors are an important class of algorithms that allow predictions to be made with a user-defined confidence level. They are able to do this by outputting prediction sets, rather than simple point predictions. The conformal…
One of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware…