Open Quantum Systems

中文速览 这篇论文提出了一种简单且端到端高效的量子算法，用于制备量子系统的热态和基态。该算法的核心是利用一个主系统与一个可重复使用的单辅助量子比特（作为“热浴”）之间的弱相互作用。算法通过重复执行一个量子通道来实现：该通道包括让系统与辅助比特在特定设计的哈密顿量下共同演化，然后重置辅助比特。论文的关键理论贡献在于，它严谨地证明了这个离散的、物理上易于实现的演化过程，在弱耦合极限下，可以被一个有效的连续时间林德布拉德动力学（Lindblad dynamics）所近似。通过精心设计相互作用的形式、滤波函数以及对耦合的随机化，作者证明了该动力学的不动点能以任意精度逼近目标热态或基态。更重要的是，论文为几个物理上重要的模型（如自由费米子和对易局部哈密顿量）提供了混合时间（mixing time）的多项式界，从而完整地证明了该算法的端到端效率。这种简洁的设计和严格的性能保证使其特别适用于早期的容错量子设备。 English Research Briefing Research Briefing: End-to-End Efficient Quantum Thermal and Ground State Preparation Made Simple 1. The Core Contribution This paper introduces a quantum algorithm for preparing thermal and ground states that is both remarkably simple in its implementation and rigorously proven to be efficient from start to finish. The central thesis is that a carefully engineered, weakly-coupled interaction between a quantum system and a single, reusable ancilla qubit can drive the system to a desired target state. The algorithm’s primary conclusion is that this physically motivated process, which relies only on forward Hamiltonian evolution, effectively simulates a specific Lindblad dynamics whose fixed point correctly approximates the target state and whose convergence time (mixing time) is polynomially bounded for several key physical systems, thereby providing a complete, end-to-end performance guarantee. ...

中文速览 本文提出了一种高效且可高度并行化的经典算法，用于模拟受任意单量子比特噪声影响的n比特量子线路。该算法基于张量网络，其核心思想是将含噪量子系统的状态表示为一组矩阵乘积态（MPS）的系综。关键创新在于，对于作用在任意纯态上的每个单比特噪声过程，算法会选择一种特定的“展开”（即Kraus分解），这种展开能最小化该噪声比特与系统其余部分之间的平均纠缠（即纠缠形成熵）。通过将这个n比特问题映射到一个等效的两比特问题，作者为这种最优展开提供了封闭形式的解析解，从而避免了启发式优化并适用于任何单比特噪声模型。这种方法使得在给定的精度和噪声水平下，能够用更紧凑的MPS来表示量子态。此外，该工作还为这类基于展开的模拟器提供了严格的误差上限，并证明了先前工作中使用的固定展开策略，在其适用的特定噪声模型下，等价于本文方法在随机态上的特例。 English Research Briefing Research Briefing: Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings 1. The Core Contribution This paper introduces a highly general and efficient tensor-network-based algorithm for the classical simulation of one-dimensional noisy quantum circuits. The central thesis is that the simulation’s efficiency can be dramatically improved by strategically choosing how to represent the effect of noise. The primary contribution is a method to select a state-dependent, locally entanglement-optimal unraveling for any single-qubit noise channel. This is achieved by finding the specific Kraus decomposition that minimizes the average von Neumann entanglement (achieving the entanglement of formation) between the noisy qubit and the rest of the system. This approach provides a provably optimal local strategy for reducing the entanglement in the underlying Matrix Product State (MPS) representation, thereby lowering computational cost and improving accuracy for a given bond dimension, and importantly, comes with rigorous, a posteriori error guarantees. ...