相关论文: Well-tempered ZX and ZH Calculi

We introduce diagrammatic differentiation for tensor calculus by generalising the dual number construction from rigs to monoidal categories. Applying this to ZX diagrams, we show how to calculate diagrammatically the gradient of a linear…

Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of…

We introduce here a new axiomatisation of the rational fragment of the ZX-calculus, a diagrammatic language for quantum mechanics. Compared to the previous axiomatisation introduced in [8], our axiomatisation does not use any metarule , but…

Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path…

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…

We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams…

We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on the completeness of the graphical ZX…

$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular…

Quantum circuit optimization - the process of transforming a quantum circuit into an equivalent one with reduced time and space requirements - is crucial for maximizing the utility of current and near-future quantum devices. While most…

With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…

The ZH-calculus is a graphical calculus for linear maps between qubits that allows a natural representation of the Toffoli+Hadamard gate set. The original version of the calculus, which allows every generator to be labelled by an arbitrary…

We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…

In this paper, we use the twisted regular representation theory of vertex operator algebras to construct bimodules over twisted Zhu algebras, extending Haisheng Li's work in untwisted scenarios. Moreover, a conjecture of Dong and Jiang on…

Interaction nets are a graphical model of computation, which has been used to define efficient evaluators for functional calculi, and specifically lambda calculi with patterns. However, the flat structure of interaction nets forces pattern…

This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…

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 introduce the first complete and approximatively universal diagrammatic language for quantum mechanics. We make the ZX-Calculus, a diagrammatic language introduced by Coecke and Duncan, complete for the so-called Clifford+T quantum…

Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser…

In these notes we present preliminary results on quantum-like algorithms where tensor product is replaced by geometric product. Such algorithms possess the essential properties typical of quantum computation (entanglement, parallelism) but…

Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…