利用半定规划缓解局部重叠量子层析中的散粒噪声
Mitigating shot noise in local overlapping quantum tomography with semidefinite programming
AI总结：
针对近期量子计算中约化密度矩阵（RDMs）测量易受散粒噪声影响产生非物理结果的问题，提出用多项式规模半定规划施加相容性约束、重构重叠RDMs以缓解噪声的方法，可提升精度与资源效率，适用于变分算法等场景。
AI中文摘要：
约化密度矩阵（RDMs）是量子信息处理中的基础工具，无需以指数级复杂度完整表征量子态，即可计算能量、关联函数等局域可观测量。在近期量子计算场景下，RDMs能提供充足信息，有效设计变分量子算法。然而，其实验估计颇具挑战：需在多个基矢下制备并测量量子态，这一过程资源消耗大，且因测量次数有限产生的散粒噪声，易得到非物理的RDMs。针对该问题，我们提出一种通过在RDMs上重新施加特定物理性约束来缓解散粒噪声的方法。尽管验证RDMs与全局态的相容性是量子梅林-亚瑟（QMA）完全问题，我们对该条件进行了松弛，采用多项式规模的半定规划（SDP）施加特定层级的相容性约束，从模拟数据中重构重叠的RDMs。与无相容性约束的层析相比，在相同测量次数下，我们的方法平均能得到更紧的界。我们将该方法集成到算法冷却流程中，用于制备局域哈密顿量的低能态，验证了其通用性与有效性。对阻挫哈密顿量的模拟显示，该方法在精度和资源效率上均有显著提升，凸显了其在近期量子计算实际应用中的潜力。
英文摘要：
Reduced density matrices (RDMs) are fundamental in quantum information processing, allowing the computation of local observables, such as energy and correlation functions, without the exponential complexity of fully characterizing quantum states. In the context of near-term quantum computing, RDMs provide sufficient information to effectively design variational quantum algorithms. However, their experimental estimation is challenging, as it involves preparing and measuring quantum states in multiple bases--a resource-intensive process susceptible to producing non-physical RDMs due to shot noise from limited measurements. To address this, we propose a method to mitigate shot noise by re-enforcing certain physicality constraints on RDMs. While verifying RDM compatibility with a global state is quantum Merlin-Arthur complete, we relax this condition by enforcing compatibility constraints up to a certain level using a polynomial-size semidefinite program to reconstruct overlapping RDMs from simulated data. Our approach yields, on average, tighter bounds for the same number of measurements compared to tomography without compatibility constraints. We demonstrate the versatility and efficacy of our method by integrating it into an algorithmic cooling procedure to prepare low-energy states of local Hamiltonians. Simulations on frustrated Hamiltonians reveal notable improvements in accuracy and resource efficiency, highlighting the potential of our approach for practical applications in near-term quantum computing.
