相关论文: Hypergraph Simplification: Linking the Path-sum Ap…
The ZX-Calculus is a graphical language for quantum mechanics. An axiomatisation has recently been proven to be complete for an approximatively universal fragment of quantum mechanics, the so-called Clifford+T fragment. We focus here on the…
A major challenge for scaling up superconducting quantum computers is unwanted couplings between qubits, which lead to always-on ZZ couplings that impact gate fidelities by shifting energy levels conditional on qubit states. To tackle this…
Graphical languages offer intuitive and rigorous formalisms for quantum physics. They can be used to simplify expressions, derive equalities, and do computations. Yet in order to replace conventional formalisms, rigour alone is not…
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…
Graph homomorphism has been studied intensively. Given an m x m symmetric matrix A, the graph homomorphism function is defined as \[Z_A (G) = \sum_{f:V->[m]} \prod_{(u,v)\in E} A_{f(u),f(v)}, \] where G = (V,E) is any undirected graph. The…
We study the problem of counting the number of homomorphisms from an input graph $G$ to a fixed (quantum) graph $\bar{H}$ in any finite field of prime order $\mathbb{Z}_p$. The subproblem with graph $H$ was introduced by Faben and Jerrum…
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…
A hypergraph ${\cal F}$ is a set family defined on vertex set $V$. The dual of ${\cal F}$ is the set of minimal subsets $H$ of $V$ such that $F\cap H \ne \emptyset$ for any $F\in {\cal F}$. The computation of the dual is equivalent to many…
Current paper introduces a Hypergraph Graph model of data storage which can be represented as a hybrid data structure based on Hypergraph and Graph. The pro-posed data structure is claimed to realize complex combinatorial structures. The…
While the circuit model of quantum computation defines its logical depth or "computational time" in terms of temporal gate sequences, the measurement-based model could allow totally different temporal ordering and parallelization of logical…
We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arising from certain association schemes. The main result is built…
Path-addition is an operation that takes a graph and adds an internally vertex-disjoint path between two vertices together with a set of supplementary edges. Path-additions are just the opposite of taking minors. We show that some classes…
We consider how the Hamiltonian Quantum Computing scheme introduced in [arXiv:1509.01278] can be implemented using a 2D array of superconducting transmon qubits. We show how the scheme requires the engineering of strong attractive…
Graphical calculi are vital tools for representing and reasoning about quantum circuits and processes. Some are not only graphically intuitive but also logically complete. The best known of these is the ZX-calculus, which is an industry…
Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience…
A graph-theoretic parameter, in a form of a function, called the extra-factorial sum is discussed. The main results are presented in ref. [1] (Nastou et al., Optim Lett, 10, 1203-1220, 2016) and the reader is strongly advised to study the…
We introduce the Spin-ZX calculus as an elevation of Penrose's diagrams and associated binor calculus to the level of a formal diagrammatic language. The power of doing so is illustrated by the variety of scientific areas we apply it to:…
We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that…
In this paper, we introduce a technique for contracting (i.e. numerically evaluating) ZX-diagrams whose complexity scales with their rank-width, a graph parameter that behaves nicely under ZX rewrite rules. Given a rank-decomposition of…
The problem of accelerating drug discovery relies heavily on automatic tools to optimize precursor molecules to afford them with better biochemical properties. Our work in this paper substantially extends prior state-of-the-art on…