有限测量下多尺度量子态学习的终端寄存器认证
Terminal-Register Certification for Finite-Measurement Learning of Multiscale Quantum States
- Dhirubhai Ambani University（迪鲁巴伊·安巴尼大学）
- Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出一种针对有限测量下多尺度量子态学习的终端寄存器认证方法，通过噪声感知定理和逆MERA拟设，在8量子比特伊辛基态上实现平均保真度0.996886，并验证了架构公平性。
AI中文摘要：
结构化量子态学习不仅依赖于表达力强的拟设，还依赖于一种在有限测量和不完美实现下仍保持意义的操作性认证。我们研究了通过逆二进制多尺度纠缠重整化拟设（MERA）学习一维纯态的过程。在学习过程中，粗粒化过程中移除的量子比特被相干控制，并在终端寄存器处一起测量。我们确认，在匹配的因果操作下，理想的顺序和终端测量方案能产生相同的完整比特串分布，而归一化的后选择会以与前缀接受率成反比的方式放大扰动。一个噪声感知定理为有限次测量认证引入了个体校准的总变差实现预算。该协议在开放边界横向场伊辛基态上进行了评估。一个冻结的8量子比特方案，每次运行使用5.6亿次模拟训练测量，在所有60次保留运行中实现了高于0.99的保真度，平均保真度为0.996886。固定电路鲁棒性验证覆盖了1080个电路噪声单元和6480个置信覆盖行，没有锁定健全性违规。然后，我们通过三项新研究解决了n=16时的架构公平性问题。在120次运行精确梯度多重起始诊断中，MERA在58/60次配对重启中具有更高的保真度，在60/60次中具有更低的远距离误差，尽管没有一次运行满足预先指定的平稳性标准。最后，一个因果锥完备、参数匹配的局部电路实现了2.62倍更大的总门暴露，但在保真度、远距离误差、能量和熵方面输掉了所有30次配对比较。
英文摘要：
Structured quantum-state learning not only depends on an expressive ansatz but also on an operational certificate that stays meaningful with finite measurements and imperfect implementation. We study pure one dimensional states learning by an inverse binary multiscale entanglement renormalization ansatz (MERA). In the learning procedure, the qubits removed during coarse graining are controlled coherently and measured together at the terminal register. We confirm that an ideal sequential and terminal measurement schedule delivers the same complete bit string distribution under matched causal operations, while normalized postselection can amplify perturbations inversely with prefix acceptance. A noise aware theorem introduces an individual calibrated total variation implementation budget to the finite shot certificate. The protocol is estimated on an open boundary transverse field Ising ground state. A frozen 8-qubit schedule using $560$ million simulated training measurements per run achieves fidelity above $0.99$ in all $60$ held-out runs, with a mean fidelity of $0.996886$. 1080 circuit-noise cells and 6480 confidence-coverage rows are covered by fixed-circuit robustness validation without a locked soundness violation. We then address architectural fairness at $n=16$ using three new studies. In a 120-run exact-gradient multistart diagnostic, MERA has higher fidelity in 58/60 paired restarts and lower long-range error in 60/60, although no run met the prespecified stationarity criterion. Finally, a causal cone-complete, parameter matched local circuit achieves $2.62\times$ greater aggregate gate exposure yet loses all 30 paired comparisons in fidelity, long-range error, energy, and entropy.
