Related papers: The GHZ/W-calculus contains rational arithmetic
The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics. The language is sound and complete: one can transform a stabilizer ZX-diagram into another one using the graphical rewrite rules if and only…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
ZX-calculus is graphical language for quantum computing which usually focuses on qubits. In this paper, we generalise qubit ZX-calculus to qudit ZX-calculus in any finite dimension by introducing suitable generators, especially a carefully…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
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…
The ZX-calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. We prove that its \pi/4-fragment is not complete, in other words the ZX-calculus is not complete for the so called "Clifford+T…
We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…
Transformations on quantum states form a basic building block of every quantum information system. From photonic polarization to two-level atoms, complete sets of quantum gates for a variety of qubit systems are well known. For multi-level…
Analysis of quantum processes, especially in the context of noise, errors, and decoherence is essential for the improvement of quantum devices. An intuitive representation of those processes modeled by quantum channels are Pauli transfer…
This note presents a simple and unified formulation of the most fundamental structures used in quantum information with qubits, arbitrary dimension qudits, and quantum continuous variables. This \emph{general quantum variables} construction…
We connect partition logic with Generative Logic by translating finite partition logics into Prolog-based Simple Generative Logic Grammars. As a proof of concept, we use the five-atom V-logic L_{12} to generate a modular visual artifact,…
The quantum circuit model is the default for encoding an algorithm intended for a NISQ computer or a quantum computing simulator. A simple graph and through it, a graph state - quantum state physically manifesting an abstract graph…
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 order to realize a Quantum CPU some schemes for executing fundamental mathematical tasks are needed. In this paper we present some quantum circuits which, using elementary arithmetic operations, allow an approximated calculation of…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Quantum circuit cutting refers to a series of techniques that allow one to partition a quantum computation on a large quantum computer into several quantum computations on smaller devices. This usually comes at the price of a sampling…
Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…
Quantum Logic Processors can be implemented with Mach Zehnder Interferometer(MZI) configurations for the Quantum logic operations and gates. In this paper, its implementation for both optical and electronic system has been presented. The…
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…
Quantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac notation difficult to verify. This is why Coecke and Duncan have…