Related papers: Quantum Register Algebra: the mathematical languag…
The concept of a quantum algebra is made easy through the investigation of the prototype algebras $u_{qp}(2)$, $su_q(2)$ and $u_{qp}(1,1)$. The latter quantum algebras are introduced as deformations of the corresponding Lie algebras~; this…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
Quantum computing (QC) is anticipated to provide a speedup over classical HPC approaches for specific problems in optimization, simulation, and machine learning. With the advances in quantum computing toward practical applications, the need…
We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations,…
We present the quantum programming language cQPL which is an extended version of QPL [P. Selinger, Math. Struct. in Comp. Sci. 14(4):527-586, 2004]. It is capable of quantum communication and it can be used to formulate all possible quantum…
Quantum reservoir computing (QRC) is a hardware-implementation-friendly quantum neural network scheme with minimal physical system requirements and a proven advantage over classical counterparts. We use an extension of the positive-P phase…
Recent studies on quantum computing algorithms focus on excavating features of quantum computers which have potential for contributing to computational model enhancements. Among various approaches, quantum annealing methods effectively…
This paper investigates the application of quantum computing technology to airline gate-scheduling quadratic assignment problems (QAP). We explore the quantum computing hardware architecture and software environment required for porting…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
Currency arbitrage capitalizes on price discrepancies in currency exchange rates between markets to produce profits with minimal risk. By employing a combinatorial optimization problem, one can ascertain optimal paths within directed…
Quantum Annealing (QA) can efficiently solve combinatorial optimization problems whose objective functions are represented by Quadratic Unconstrained Binary Optimization (QUBO) formulations. For broader applicability of QA, quadratization…
We introduce QuAlg, an open-source symbolic algebra package for quantum information. QuAlg supports working with qubit-states, qudit-states, fock-states and even wave-functions in infinite dimenional Hilbert spaces. States can have…
We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RA-Q). It reads a sequence of rational numbers and outputs another rational number. RA-Q is an extension of the…
Benchmarking of quantum machine learning (QML) algorithms is challenging due to the complexity and variability of QML systems, e.g., regarding model ansatzes, data sets, training techniques, and hyper-parameters selection. The QUantum…
In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics. A simulator for quantum algorithms must be capable of performing heavy mathematical matrix transforms. The design of the simulator…
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to…
A key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating…
Quantum fingerprinting is a technique that maps classical input word to a quantum state. The obtained quantum state is much shorter than the original word, and its processing uses less resources, making it useful in quantum algorithms,…