Graphical representation of generalized quantum measurements

Graphical description of Pauli measurements on stabilizer states

We use a graphical representation of stabilizer states to describe, simply and efficiently, the effect of measurements of Pauli products on stabilizer states. This work complements our earlier work [Phys. Rev. A 77, 042307 (2008)], which described in graphical terms the action of Clifford operations on stabilizer states.

Entanglement and Quaternions: The graphical calculus ZQ

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 candidate for an Intermediate Representation; a language that sits between the algorithm designer's intent and the quantum hardware's gate instructions. The ZX calculus, built from generalised Z and X rotations, has difficulty reasoning about arbitrary rotations. This contrasts with the cross-hardware compiler TriQ which uses these arbitrary rotations to exploi…

Graphical Fourier Theory and the Cost of Quantum Addition

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 this paper, we will show that the two calculi are linked by Fourier transform. In particular, we will derive new Fourier expansion rules using the ZH-calculus, and show that we can straightforwardly pass between ZH- and ZX-diagrams using them. Furthermore, we demonstrate that the graphical Fourier expansion of a ZH normal-form corresponds to the standard Fourie…

From probabilistic graphical models to generalized tensor networks for supervised learning

Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motivates the definition of generalized tensor networks where information from a tensor can be copied and reused in other parts of the network. We discuss the relationship between generalized tensor network architectures used in quantum physics, such as string-bond states, and archite…

两个布洛赫球上的纠缠：探索两量子比特稳定子群结构

Entanglement on Two Bloch Spheres: Exploring Two-Qubit Stabilizer Group Structure

本研究借助稳定子形式体系，建立两量子比特态的密度矩阵与双布洛赫球图形表示的关联（二者均源于稳定子群结构），并以此探究最大纠缠态的对称性。

SZX-calculus: Scalable Graphical Quantum Reasoning

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 captures graphically the fundamental properties of quantum mechanics through its complete set of rewrite rules. The ZX-calculus is, however, a low level language, with each wire representing a single qubit. This limits its ability to handle large and elaborate quantum evolutions. We extend the ZX-calculus to registers of qubits and allow compact representati…

Colored props for large scale graphical reasoning

The prop formalism allows representation of processes withstring diagrams and has been successfully applied in various areas such as quantum computing, electric circuits and control flow graphs. However, these graphical approaches suffer from scalability problems when it comes to writing large diagrams. A proposal to tackle this issue has been investigated for ZX-calculus using colored props. This paper extends the approach to any prop, making it a general tool for graphical languages manipulation.

一种图框架用于证明多粒子系统中的引力纠缠熵不等式

A graphical framework for proving holographic entanglement entropy inequalities in multipartite systems

本文提出了一种图框架，用于在多粒子系统中证明引力纠缠熵不等式，并通过定理和示例验证其有效性。