相关论文: Solving the Decision Principal Ideal Problem with …
We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial-time. We provide two applications of the algorithm: judging whether a given ideal is prime…
Current quantum systems have significant limitations affecting the processing of large datasets with high dimensionality, typical of high energy physics. In the present paper, feature and data prototype selection techniques were studied to…
The problem of computing the dimension of a left/right ideal in a group algebra F[G] of a finite group G over a field F is considered. The ideal dimension is related to the rank of a matrix originating from a regular left/right…
The existence of ideal objects, such as maximal ideals in nonzero rings, plays a crucial role in commutative algebra. These are typically justified using Zorn's lemma, and thus pose a challenge from a computational point of view. Giving a…
State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…
Quantum state discrimination is a fundamental primitive in quantum information processing, underpinning tasks in quantum communication, sensing, and learning. We consider the general Bayes framework, as introduced by Helstrom, for state…
We present improvements to the index-calculus algorithm for the computation of the ideal class group and regulator of a real quadratic field. Our improvements consist of applying the double large prime strategy, an improved structured…
In this paper, we calculate the upper bound on quantum space complexity of the quantum algorithms proposed by Biasse and Song (SODA'16) for solving class group computation and the principal ideal problem using the reductions to $S$-unit…
It is usually assumed that a quantum computation is performed by applying gates in a specific order. One can relax this assumption by allowing a control quantum system to switch the order in which the gates are applied. This provides a more…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
We study the decidability of the Skolem Problem, the Positivity Problem, and the Ultimate Positivity Problem for linear recurrences with real number initial values and real number coefficients in the bit-model of real computation. We show…
The application of quantum computation to accelerate machine learning algorithms is one of the most promising areas of research in quantum algorithms. In this paper, we explore the power of quantum learning algorithms in solving an…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
We define a scheme for labelling and ordering integral ideals of number fields, including prime ideals as a special case. The order we define depends only on the choice of a monic irreducible integral defining polynomial for each field $K$,…
The task of learning to pick a single preferred example out a finite set of examples, an "optimal choice problem", is a supervised machine learning problem with complex, structured input. Problems of optimal choice emerge often in various…
Near-term quantum processors are limited in terms of the number of qubits and gates they can afford. They nevertheless give unprecedented access to programmable quantum systems that can efficiently, although imperfectly, simulate quantum…
Analyzing decision problems under uncertainty commonly relies on idealizing assumptions about the describability of the world, with the most prominent examples being the closed world and the small world assumption. Most assumptions are…
A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal…
Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum…