Related papers: Practical Groebner Basis Computation
This report presents a practical approach to teaching quantum computing to Electrical Engineering & Computer Science (EECS) students through dedicated hands-on programming labs. The labs cover a diverse range of topics, encompassing…
The rapid progress of computer science has been accompanied by a corresponding evolution of computation, from classical computation to quantum computation. As quantum computing is on its way to becoming an established discipline of…
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional…
Open-source libraries are have a catalytic role in research pipelines, where new methods must be compared against up-to-date baselines. We present the GLobal Optimization Benchmark (GLOBe) modular Python library that unifies classical and…
Quantum algorithms and circuits can, in principle, outperform the best non-quantum (classical) techniques for some hard computational problems. However, this does not necessarily lead to useful applications. To gauge the practical…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…
Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr\"obner basis or…
Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-user wants to exclude from the solution set. The…
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, GRworkbench has been significantly extended to facilitate numerical experimentation in…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
Binary field extensions are fundamental to many applications, such as multivariate public key cryptography, code-based cryptography, and error-correcting codes. Their implementation requires a foundation in number theory and algebraic…
We present a quantum algorithmic routine that extends the realm of Grover-based heuristics for tackling combinatorial optimization problems with arbitrary efficiently computable objective and constraint functions. Building on previously…
This paper considers parallel Gr\"obner bases algorithms on distributed memory parallel computers with multi-core compute nodes. We summarize three different Gr\"obner bases implementations: shared memory parallel, pure distributed memory…
Quorum systems are a key mathematical abstraction in distributed fault-tolerant computing for capturing trust assumptions. A quorum system is a collection of subsets of all processes, called quorums, with the property that each pair of…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
We present a new algorithm for reducing an arbitrary unitary matrix into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of…
In the effort to develop useful quantum computers simulating quantum machines with conventional computing resources is a key capability. Such simulations will always face limits preventing the emulation of quantum computers of substantial…