Related papers: Beyond Penrose tensor diagrams with the ZX calculu…
Optimizing quantum circuits is a key challenge for quantum computing. The PyZX compiler broke new ground by optimizing circuits via the ZX calculus, a powerful graphical alternative to the quantum circuit model. Still, it carries no…
In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum…
Systematic discovery of optimization paths in quantum circuit simplification remains a challenge. Today, ZX-calculus, a computing model for quantum circuit transformation, is attracting attention for its highly abstract graph-based…
The ZX-calculus is a convenient formalism for expressing and reasoning about quantum circuits at a low level, whereas the recently-proposed ZH-calculus yields convenient expressions of mid-level quantum gates such as Toffoli and CCZ. In…
Multipartite quantum scenarios are a significant and challenging resource in quantum information science. Tensors provide a powerful framework for representing multipartite quantum systems. In this work, we introduce the role of…
This paper is intended to describe twistors via the paravector model of Clifford algebras and to relate such description to conformal maps in the Clifford algebra over R(4,1), besides pointing out some applications of the pure spinor…
This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tensor eigenvalue problems to the tensor-train framework. As an…
We propose a quantum programming language that generalizes the $\lambda$-calculus. The language is non-linear; duplicated variables denote, not cloning of quantum data, but sharing a qubit's state; that is, producing an entangled pair of…
A graphical representation of supersymmetry is presented. It clearly expresses the chiral flow appearing in SUSY quantities, by representing spinors by {\it directed lines} (arrows). The chiral suffixes are expressed by the directions (up,…
Mapping fermionic systems to qubits on a quantum computer is often the first step for algorithms in quantum chemistry and condensed matter physics. However, it is difficult to reconcile the many different approaches that have been proposed,…
In the N=1 four-dimensional new-minimal supergravity framework, we supersymmetrise the coupling of the scalar kinetic term to the Einstein tensor. This coupling, although introduces a non-minimal derivative interaction of curvature to…
ZW-calculus is a useful graphical language for pure qubit quantum computing. It is via the translation of the completeness of ZW-calculus that the first proof of completeness of ZX-calculus was obtained. A d-level generalisation of qubit…
Graphical languages are a convenient shorthand to represent computation, with rewrite rules relating one graph to another. In contrast, proof assistants rely heavily on inductive datatypes, particularly when giving semantics to embedded…
The ZX-calculus is a graphical language for reasoning about quantum computation using ZX-diagrams, a certain flexible generalisation of quantum circuits that can be used to represent linear maps from $m$ to $n$ qubits for any $m,n \geq 0$.…
We present and benchmark a quantum computing approach to calculate the two-dimensional coherent spectrum (2DCS) of high-spin models. Our approach is based on simulating their real-time dynamics in the presence of several magnetic field…
Spin-geometrical projections, from the study of the human universe onto the study of the self-organizing brain, are herein leveraged to address certain concerns raised in latest neuroscience research, namely (i) the extent to which neural…
This paper presents a novel approach to quantum architecture search by integrating the techniques of ZX-calculus with Genetic Programming (GP) to optimize the structure of parameterized quantum circuits employed in Quantum Machine Learning…
We introduce a ZX-like diagrammatic language devoted to manipulating real matrices - and rebits -, with its own set of axioms. We prove the necessity of some non trivial axioms of these. We show that some restriction of the language is…
We review the present state of the art in using the endohedral fullerenes N@C60 and P@C60 as qubits in a spin quantum computer. After a brief introduction to spin quantum computing, we first discuss the rich spin structure of these…
Besides tensor contractions, one of the most pronounced computational bottlenecks in the non-orthogonally spin-adapted forms of the quantum chemistry methods CCSDT and CCSDTQ, and their approximate forms---including CCSD(T) and…