通过插入简单量子通道,解决任意量子电路的梯度消失问题。
Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibility
- 在原电路中插入仅需1个辅助量子比特和4个门的量子通道。
- 可处理多达100量子比特、2400层的热态制备,且参数可训练。
- 对实际噪声鲁棒,适合近期量子硬件应用。
基于参数化量子电路(PQC)的量子算法已在近中期量子设备上实现广泛应用。然而,现有PQC架构面临诸多挑战,其中“梯度消失”现象尤为突出:损失函数随系统规模指数集中,阻碍有效参数优化。为此,我们提出一种通用且硬件友好的方法,可消除任意PQC中的梯度消失问题。具体而言,通过在原始PQC中插入一层易实现的量子通道,每个通道仅需一个辅助量子比特和四个附加门,得到修改后的PQC(MPQC)。该方法保证了MPQC至少与原PQC同等表达能力,并在温和假设下确保无梯度消失。进一步地,通过合理调整结构,可严格证明原PQC中任一参数均可被训练。尤为重要的是,MPQC在真实噪声下仍保持无梯度消失特性,直接适用于近中期量子硬件。数值模拟表明,MPQC能有效消除长达2400层、含100量子比特系统的梯度消失问题;在端到端模拟中,其在寻找复杂哈密顿量基态能量时显著优于传统PQC。
原文摘要 · Abstract (English)
Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face several challenges, among which the ``barren plateaus" phenomenon is particularly prominent. In such cases, the loss function concentrates exponentially with increasing system size, thereby hindering effective parameter optimization. To address this challenge, we propose a general and hardware-efficient method for eliminating barren plateaus in an arbitrary PQC. Specifically, our approach achieves this by inserting a layer of easily implementable quantum channels into the original PQC, each channel requiring only one ancilla qubit and four additional gates, yielding a modified PQC (MPQC) that is provably at least as expressive as the original PQC and, under mild assumptions, is guaranteed to be free from barren plateaus. Furthermore, by appropriately adjusting the structure of MPQCs, we rigorously prove that any parameter in the original PQC can be made trainable. Importantly, the absence of barren plateaus in MPQCs is robust against realistic noise, making our approach directly applicable to near-term quantum hardware. Numerical simulations demonstrate that MPQC effectively eliminates barren plateaus in PQCs for preparing thermal states of systems with up to 100 qubits and 2400 layers. Furthermore, in end-to-end simulations, MPQC significantly outperforms PQC in finding the ground-state energy of a complex Hamiltonian.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。