Tensor network theory and quantum simulation are, respectively, the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions. With the example of hybrid tree tensor networks, we demonstrate efficient quantum simulation using a quantum computer whose size is significantly smaller than the one of the target system. We numerically benchmark our method for finding the ground state of 1D and 2D spin systems of up to $8\times 8$ and $9\times 8$ qubits with operations only acting on $8+1$ and $9+1$ qubits, respectively. Our approach sheds light on simulation of large practical problems with intermediate-scale quantum computers, with potential applications in chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.

中文翻译：

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使用混合张量网络进行量子模拟

张量网络理论和量子模拟分别是理解量子多体物理的关键经典计算方法和量子计算方法。在这里，我们介绍了混合张量网络的框架，其构建块由可测量的量子态和经典可收缩张量组成，继承了它们在多体波函数的有效表示中的独特特征。以混合树张量网络为例，我们使用尺寸明显小于目标系统的量子计算机来演示高效的量子模拟。我们对我们的方法进行数值基准测试，以找到高达 1D 和 2D 自旋系统的基态$8\times 8$ 和 $9\times 8$ 操作仅作用于的量子位 $8+1$ 和 $9+1$分别为量子位。我们的方法阐明了使用中型量子计算机模拟大型实际问题，在化学、量子多体物理学、量子场论和量子引力思想实验中具有潜在应用。