Related papers: Quantum Algorithms and Oracles with the Scalable Z…
Machine Learning algorithms are extensively used in an increasing number of systems, applications, technologies, and products, both in industry and in society as a whole. They enable computing devices to learn from previous experience and…
Quantum algorithms for computational linear algebra promise up to exponential speedups for applications such as simulation and regression, making them prime candidates for hardware realization. But these algorithms execute in a model that…
ROM-based quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less ``magical'', and being more suited to implementing space-efficient computation (i.e. computation using the minimum number of…
Quantum computers promise to surpass the most powerful classical supercomputers when it comes to solving many critically important practical problems, such as pharmaceutical and fertilizer design, supply chain and traffic optimization, or…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
This paper proposes an optimized formulation of the parts of speech tagging in Natural Language Processing with a quantum computing approach and further demonstrates the quantum gate-level runnable optimization with ZX-calculus, keeping the…
We propose a scheme for quantum computation in optical lattices. The qubits are encoded in the spacial wavefunction of the atoms such that spin decoherence does not influence the computation. Quantum operations are steered by shaking the…
Quantum computing is fast evolving as a technology due to recent advances in hardware, software, as well as the development of promising applications. To use this technology for solving specific problems, a suitable quantum algorithm has to…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
The ZX-calculus, and the variant we consider in this paper (ZXH-calculus), are formal diagrammatic languages for qubit quantum computing. We show that it can also be used to describe SU(2) representation theory. To achieve this, we first…
This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information.…
Counting the solutions to Boolean formulae defines the problem #SAT, which is complete for the complexity class #P. We use the ZH-calculus, a universal and complete graphical language for linear maps which naturally encodes counting…
Quantum computing is an emerging technology, promising a paradigm shift in computing, and allowing for speedups in many different problems. However, quantum devices are still in their early stages, most with only a small number qubits. This…
We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial…
Recent developments in the ZX-Calculus have resulted in complete axiomatisations first for an approximately universal restriction of the language, and then for the whole language. The main drawbacks were that the axioms that were added to…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
In this paper, we give a universal completion of the ZX-calculus for the whole of pure qubit quantum mechanics. This proof is based on the completeness of another graphical language: the ZW-calculus, with direct translations between these…
We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus. Specifically, we develop a canonical form in the ZX calculus and…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…