近日，法国巴黎理工学院的Ugo Nzongani与法国土伦大学的Giuseppe Di Molfetta等人合作取得一项新进展。他们发现狄拉克量子在四面体上行走。相关研究成果已于2024年10月16日在国际知名学术期刊《物理评论A》上发表。

据悉，离散时间量子行走（QWs）是单个量子粒子在晶格上的传输模型。它们的演化由因果性和局部幺正算符驱动。QWs是量子模拟基础物理的强大工具，因为其中一些具有连续极限，可收敛于众所周知的物理偏微分方程，如狄拉克方程或薛定谔方程。

在本文中，研究人员展示了如何在四面体空间中演化的量子行走（QW）中恢复（3+1）维狄拉克方程。这为在弯曲时空中模拟狄拉克方程铺平了道路。这也为在自旋网络上传播物质提供了一个有序方案，这对于圈量子引力理论具有重要意义，因为在该理论中物质的传播一直是一个未解决的问题。

附：英文原文

Title: Dirac quantum walk on tetrahedra

Author: Ugo Nzongani, Nathanal Eon, Iván Márquez-Martín, Armando Pérez, Giuseppe Di Molfetta, Pablo Arrighi

Issue&Volume: 2024/10/16

Abstract: Discrete-time quantum walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental physics, as some of them have a continuum limit converging to well-known physics partial differential equations, such as the Dirac or the Schrdinger equation. In this paper, we show how to recover the Dirac equation in (3+1) dimensions with a QW evolving in a tetrahedral space. This paves the way to simulate the Dirac equation on a curved space-time. This also suggests an ordered scheme for propagating matter over a spin network, of interest in loop quantum gravity, where matter propagation has remained an open problem.

DOI: 10.1103/PhysRevA.110.042418

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.042418