提出新方法同时提升量子电路的表达力与可训练性
How to find expressible and trainable parameterized quantum circuits?
- 基于方差浓度边界，给出可训练性的明确保证
- 发现表达力与可训练性存在负相关，指导电路设计
- 在真实量子机上验证，用更少参数实现高精度
参数化量子电路（PQC）能否系统构造出既具表达力又可训练，仍是开放问题。高度表达的电路常出现梯度消失，而部分可训练方案则可被经典高效模拟。本文推导出估计PQC代价函数方差的有限样本、维度无关集中界，获得明确可训练性保障。在常见量子线路结构中，观察到可训练性与表达力存在负相关，与理论一致。基于此，提出基于属性的线路搜索框架，用于发现兼具两者特性的电路。在真实量子计算机上验证其可行性，并应用于变分量子算法。识别出有效维度更高的量子神经网络线路，使用超过6倍更少的参数；在氢分子（H₂）的变分量子本征求解（VQE）中，达到类似UCCSD的精度，但电路复杂度显著降低。
原文摘要 · Abstract (English)
Whether parameterized quantum circuits (PQCs) can be systematically constructed to be both trainable and expressive remains an open question. Highly expressive PQCs often exhibit barren plateaus, while several trainable alternatives admit efficient classical simulation. We address this question by deriving a finite-sample, dimension-independent concentration bound for estimating the variance of a PQC cost function, yielding explicit trainability guarantees. Across commonly used ansätze, we observe an anticorrelation between trainability and expressibility, consistent with theoretical insights. Building on this observation, we propose a property-based ansatz-search framework for identifying circuits that combine trainability and expressibility. We demonstrate its practical viability on a real quantum computer and apply it to variational quantum algorithms. We identify quantum neural network ansätze with improved effective dimension using over $6 \times$ fewer parameters, and for VQE on $\mathrm{H}_2$ we achieve UCCSD-like accuracy at substantially reduced circuit complexity.
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