通过虚拟Rz实现适用于偏微分方程的低深度、抗噪声量子态制备
Low-Depth and Noise-Resilient Quantum State Preparation for Partial Differential Equations via Virtual Rz
AI总结：
针对NISQ和早期FTQC硬件，提出了支持虚拟Rz的低深度量子态制备电路，可实现高理想与噪声保真度，优于精确态制备基线。
AI中文摘要：
制备具有平滑实振幅的量子态是耗散偏微分方程（PDE）量子求解器（如LCHS）中的关键子例程，其中离散化的正权重必须编码进振幅中。精确态制备分解在理想情况下可达到单位保真度，但其两量子比特深度会快速增长，进而在噪声中等规模量子（NISQ）硬件上导致严重的保真度损失。我们提出了一种低深度、硬件感知的变分拟设，专门针对阻尼PDE动力学典型的平滑、弱纠缠、近实目标分布。该电路使用一层局部Ry旋转生成实振幅，最近邻CZ纠缠层引入有限纠缠，以及额外的Rz旋转，这些Rz旋转以帧更新的形式虚拟实现。虚拟Rz操作不添加物理脉冲，也不增加电路时长，在不增大门 footprint 的前提下提供额外自由度；在模拟中，它们被视为理想情况以隔离其优势。从张量网络视角来看，这种交替结构将态限制为低键维度的矩阵乘积态（MPS），与目标平滑性匹配（对于3量子比特，键维度≤2）。我们使用COBYLA优化参数以最小化非保真度，并与精确态制备（Qiskit）和RealAmplitudes（CZ）基线进行基准测试。在代表NISQ和早期容错量子计算（FTQC） regime 的去极化噪声下，所提出的单层电路在O(n)深度下实现了高理想保真度，且比更深的精确构造具有显著更高的噪声保真度。在相干噪声扫描中，虚拟Rz参数吸收系统相位误差和轴不匹配，在宽误差范围内保持近单位保真度。这些结果表明，支持虚拟Rz的低深度电路为NISQ和早期FTQC硬件上的PDE求解器提供了实用、抗噪声的态制备原语。
英文摘要：
Preparing smooth real-amplitude quantum states is a key subroutine in quantum solvers for dissipative PDEs, such as LCHS, where discretized positive weights must be encoded into amplitudes. Exact state-preparation decompositions can reach unit fidelity ideally, but their two-qubit depth grows quickly and causes severe fidelity loss on NISQ hardware. We propose a low-depth, hardware-aware variational ansatz tailored to smooth, weakly entangled, near-real target distributions typical of damped PDE dynamics. The circuit uses one layer of local Ry rotations to generate real amplitudes, a nearest-neighbor CZ entangling layer to introduce limited entanglement, and additional Rz rotations implemented virtually as frame updates. Virtual Rz operations add no physical pulses and do not increase circuit duration, providing extra degrees of freedom without enlarging the gate footprint; in simulation they are treated as ideal to isolate their benefit. From a tensor-network viewpoint, the alternating structure restricts the state to a low-bond-dimension MPS, matching the target smoothness (for 3 qubits, bond dimension <= 2). We optimize parameters with COBYLA to minimize infidelity and benchmark against exact state preparation (Qiskit) and a RealAmplitudes (CZ) baseline. Under depolarizing noise representative of NISQ and early fault-tolerant regimes, the proposed single-layer circuit achieves high ideal fidelity with O(n) depth and substantially higher noisy fidelity than deeper exact constructions. In coherent-noise sweeps, virtual Rz parameters absorb systematic phase errors and axis mismatch, maintaining near-unity fidelity over a wide error range. These results indicate that virtual-Rz-enabled, low-depth circuits provide a practical, noise-resilient state-preparation primitive for PDE solvers on NISQ and early FTQC hardware.
