arXiv 2403.134862024-03-20quant-ph

张量量子编程

Tensor Quantum Programming

A. Termanova, Ar. Melnikov, E. Mamenchikov, N. Belokonev, S. Dolgov, A. Berezutskii, R. Ellerbrock, C. Mansell, M. Perelshtein

备注：: 17 pages, 13 figures

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AI总结：

本文提出张量量子编程方法，利用量子计算机处理高阶张量的优势，开发了将矩阵乘积算符编码至量子电路的算法，在多达50个量子比特上验证了有效性，为构建实用量子算法奠定基础。

摘要：

运行量子算法通常涉及实现包含大量多量子比特门的复杂量子电路，以至于应对实际应用的挑战显得令人生畏。迄今为止，尚无实验成功展示出量子优势，因为通过使用张量网络算法，在经典计算机上可以轻松地充分复现这些结果。此外，即使在理论上也不清楚这些优势究竟根植于量子系统中的何处，因为通常与量子算法相关的对数复杂度同样存在于基于张量网络的算法中。在本文中，我们提出了一种名为Tensor Quantum Programming（张量量子编程）的新方法，该方法利用张量网络进行混合量子计算。我们的核心洞察是，基于张量网络的算法的主要挑战在于其高阶数（键维数）。量子计算为这一挑战提供了潜在的解决方案，因为理想的量子计算机能够表示任意高阶数的张量，这与经典计算机形成对比，从而指明了通往量子优势的道路。虽然基于张量的向量编码和状态读出是已知程序，但直接在量子设备上执行矩阵向量乘法所需的矩阵编码仍然未能解决。在此，我们开发了一种算法，将Matrix Product Operators（矩阵乘积算符）编码到量子电路中，其深度线性依赖于量子比特的数量。该算法在多达50个量子比特上，针对微分方程、优化问题和量子化学中经常遇到的几个矩阵展示了有效性。我们将这项工作视为迈向创建真正实用的量子算法的初步步伐。

英文摘要：

Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully demonstrated a quantum advantage due to the ease with which the results can be adequately replicated on classical computers through the use of tensor network algorithms. Additionally, it remains unclear even in theory where exactly these advantages are rooted within quantum systems because the logarithmic complexity commonly associated with quantum algorithms is also present in algorithms based on tensor networks. In this article, we propose a novel approach called Tensor Quantum Programming, which leverages tensor networks for hybrid quantum computing. Our key insight is that the primary challenge of algorithms based on tensor networks lies in their high ranks (bond dimensions). Quantum computing offers a potential solution to this challenge, as an ideal quantum computer can represent tensors with arbitrarily high ranks in contrast to classical counterparts, which indicates the way towards quantum advantage. While tensor-based vector-encoding and state-readout are known procedures, the matrix-encoding required for performing matrix-vector multiplications directly on quantum devices remained unsolved. Here, we developed an algorithm that encodes Matrix Product Operators into quantum circuits with a depth that depends linearly on the number of qubits. It demonstrates effectiveness on up to 50 qubits for several matrices frequently encountered in differential equations, optimization problems, and quantum chemistry. We view this work as an initial stride towards the creation of genuinely practical quantum algorithms.

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