一种用于量子门合成的储层计算方法
A Reservoir Computing Approach to Quantum Gate Synthesis
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中文总结 AI 辅助
研究提出基于分组储层计算的方法用于量子门合成，利用魏 - 诺曼分解，证明其重构动力学保持酉性并推导误差界。该方法在单比特门集上表现良好，适用于有限维硬件平台，还讨论了多比特合成途径。
中文摘要 AI 辅助
量子门合成对于在实际硬件上实现量子算法至关重要，但现有方法通常计算量很大。在此，我们引入一种基于储层计算的新方法，即分组储层计算，它是一种用于学习时间动态的高效机器学习范式，其训练简化为单个线性回归，以减少所需资源。该方法基于魏 - 诺曼分解，能紧凑描述演化过程。我们证明通过构造重构动力学始终保持酉性，并推导出形式误差界以确立该策略的理论有效性。在标准单比特门集上，训练后的网络单次就能生成控制脉冲，八个基准门的平均保真度为0.94；用于热启动基于梯度的优化时，它能将普通梯度上升达到目标保真度所需的迭代次数大致减半，所以关键指标是达到该阈值的时间而非固定预算后的最终精度。由于其通用形式，该方法适用于任何有限维硬件平台，最后一节讨论了多比特合成的途径。
英文摘要
Quantum gate synthesis is essential for implementing quantum algorithms on real hardware, yet existing methods are often computationally demanding. Here, we introduce a novel approach based on reservoir computing, which we name Group Reservoir Computing, an efficient machine-learning paradigm for learning temporal dynamics whose training reduces to a single linear regression, to reduce the resources required. The method is grounded in the Wei--Norman decomposition, which provides a compact description of the evolution. We prove that the reconstructed dynamics always remain unitary by construction and derive formal error bounds that establish the theoretical validity of the strategy. On the standard single-qubit gate set the trained network produces a control pulse in a single pass, with mean fidelity 0.94 across the eight benchmark gates; used to warm-start gradient-based optimization, it roughly halves the number of iterations that plain gradient ascent needs to reach a target fidelity, so that the relevant figure of merit is the time to reach that threshold rather than the final accuracy after a fixed budget. Owing to its general formulation, the method applies to any finite-dimensional hardware platform; the route to multiqubit synthesis is discussed in the closing section.
