(1+1)D 量子元胞自动机与量子神经网络中的耗散量子多体动力学
Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
AI总结：
本文研究了一种结构等价于(1+1)D量子元胞自动机的量子神经网络架构，通过构造局域量子门实现由Lindblad主方程支配的耗散多体动力学，并数值验证了集体效应的参数化控制，为大规模量子神经网络中的机器学习应用奠定基础。
摘要：
经典人工神经网络以感知器为基本单元构建，具有强大的表达能力。本文研究了一种遵循类似范式的量子神经网络架构。它在结构上等价于所谓的(1+1)D量子元胞自动机，即二维量子晶格系统，其动力学在离散时间中进行。连续时间切片之间——或相邻网络层之间——的信息传递由局域量子门控制，这些量子门可被视为经典感知器的量子对应物。沿时间方向，在约化态层面上涌现出有效的耗散演化，而这种动力学的性质由基本门的结构决定。我们展示了如何构造局域幺正门以产生所需的多体动力学，在特定参数区间内该动力学由Lindblad主方程支配。我们通过数值模拟研究了小系统尺寸下的这一现象，并展示了量子元胞自动机内的集体效应如何可以通过参数进行控制。本研究为在大规模量子神经网络中利用大规模涌现现象服务于机器学习目的迈出了一步。
英文摘要：
Classical artificial neural networks, built from perceptrons as their elementary units, possess enormous expressive power. Here we investigate a quantum neural network architecture, which follows a similar paradigm. It is structurally equivalent to so-called (1+1)D quantum cellular automata, which are two-dimensional quantum lattice systems on which dynamics takes place in discrete time. Information transfer between consecutive time slices -- or adjacent network layers -- is governed by local quantum gates, which can be regarded as the quantum counterpart of the classical perceptrons. Along the time-direction an effective dissipative evolution emerges on the level of the reduced state, and the nature of this dynamics is dictated by the structure of the elementary gates. We show how to construct the local unitary gates to yield a desired many-body dynamics, which in certain parameter regimes is governed by a Lindblad master equation. We study this for small system sizes through numerical simulations and demonstrate how collective effects within the quantum cellular automaton can be controlled parametrically. Our study constitutes a step towards the utilisation of large-scale emergent phenomena in large quantum neural networks for machine learning purposes.
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