由精确的费曼-弗农（Feynman-Vernon）路径积分推导而来的运动层级方程（hierarchical equations of motion, HEOM），是模拟嵌入热环境的开放量子系统动力学的最强大数值方法之一。但其适用性受限于谱库分布的特定形式以及相对较高的温度。本文解决了这一问题，通过系统聚类等价于优化有理分解的高阶松原（Matsubara）极点，提出了一种在频域中处理量子噪声的有效方法。这一成果将HEOM优雅地拓展至任意温度和极具普适性的库环境，同时兼具高效性、高精度和长时间稳定性。此外，该技术可直接应用于格林函数方法、随机方法和赝模公式等其他替代方法。作为一项极具挑战性的应用，针对零温下亚欧姆自旋-玻色子模型，本研究定量验证了预测关联函数长时间衰减行为的柴巴（Shiba）关系。
英文摘要：
The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems that are embedded in thermal environments. However, its applicability is restricted to specific forms of spectral reservoir distributions and relatively elevated temperatures. Here we solve this problem and introduce an effective treatment of quantum noise in frequency space by systematically clustering higher order Matsubara poles equivalent to an optimized rational decomposition. This leads to an elegant extension of the HEOM to arbitrary temperatures and very general reservoirs in combination with efficiency, high accuracy and long-time stability. Moreover, the technique can directly be implemented in alternative approaches such as Green's function, stochastic, and pseudo-mode formulations. As one highly non-trivial application, for the sub-ohmic spin-boson model at vanishing temperature the Shiba relation is quantitatively verified which predicts the long-time decay of correlation functions.
Single atoms provide an ideal system for utilizing fundamental quantum functions. Their electrons have well-defined energy levels and spin properties. Even more importantly, for a given isotope -- say, $^{12}$C -- all the atoms are identical. This creates a perfect uniformity that is impossible to achieve in macroscopic-size quantum systems. However, herding individual atoms is a very difficult task that requires trapping them with magnetic or optical means and cooling them down to temperatures in the nanokelvin range. On the other hand, the counterpart of single atoms -- the single defects --…
Taming Spacetime Overhead and Design Complexity in Distributed Fault-Tolerant Superconducting Quantum Computation
Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理科学学院）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学上海量子科学研究中心与中科院量子信息科学与技术卓越创新中心）
Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibility
Department of Computer Science and Technology, Tsinghua University, Beijing, China（计算机科学与技术系，清华大学，北京，中国）；Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China（叶阳数学科学中心，清华大学，北京，中国）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 100407, China（燕琦湖北京数学科学与应用研究所，北京，中国）；Department of Mathematics, Tsinghua University, Beijing 100084, China（数学系，清华大学，北京，中国）
Here we show an ultra-low noise regime of operation in a simple quantum memory in warm Rb atomic vapor. By modelling the quantum dynamics of four-level room temperature atoms, we achieve fidelities >90% for single-photon level polarization qubits, clearly surpassing any classical strategy exploiting the non-unitary memory efficiency. This is the first time such important threshold has been crossed with a room temperature device. Additionally we also show novel experimental techniques capable of producing fidelities close to unity. Our results demonstrate the potential of simple, resource-moder…
Microwave receivers using electromagnetically-induced transparency (EIT) in Rydberg atoms have recently demonstrated improved sensitivities. It is not evident how their state-of-the-art electric field sensitivities compare to those achieved using standard electronic receivers consisting of low-noise amplifiers (LNAs) and mixers. In this paper, we show that conventional room-temperature electronic receivers greatly outperform the best demonstrated sensitivities of room-temperature Rydberg electrometers in standard free-space coupled configurations. However, Rydberg-atom receivers can surpass th…
Scaling up trapped-ion quantum computers requires new trap materials to be explored. Here, we present experiments with a surface ion trap made from the high-temperature superconductor YBCO, a promising material for future trap designs. We show that voltage noise from superconducting electrode leads is negligible within the sensitivity $S_V=9\times 10^{-20}\,\mathrm{V}^2\mathrm{Hz}^{-1}$ of our setup, and for lead dimensions typical for advanced trap designs. Furthermore, we investigate the frequency and temperature dependence of electric field noise above a YBCO surface. We find a $1/f$ spectr…
Future quantum photonic networks require coherent optical memories for synchronizing quantum sources and gates of probabilistic nature. We demonstrate a fast ladder memory (FLAME) mapping the optical field onto the superposition between electronic orbitals of rubidium vapor. Employing a ladder level-system of orbital transitions with nearly degenerate frequencies simultaneously enables high bandwidth, low noise, and long memory lifetime. We store and retrieve 1.7-ns-long pulses, containing 0.5 photons on average, and observe short-time external efficiency of 25%, memory lifetime (${1/e}$) of 8…
We report on the use of parametric excitation to coherently manipulate the collective spin state of an atomic vapour at room temperature. Signatures of the parametric excitation are detected in the ground-state spin evolution. These include the excitation spectrum of the atomic coherences, which contains resonances at frequencies characteristic of the parametric process. The amplitudes of the signal quadratures show amplification and attenuation, and their noise distribution is characterized by a strong asymmetry, similarly to those observed in mechanical oscillators. The parametric excitation…
We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Ham…
We present a cryogenic microwave noise source with a characteristic impedance of 50 $Ω$, which can be installed in a coaxial line of a cryostat. The bath temperature of the noise source is continuously variable between 0.1 K and 5 K without causing significant back-action heating on the sample space. As a proof-of-concept experiment, we perform Y-factor measurements of an amplifier cascade that includes a traveling wave parametric amplifier and a commercial high electron mobility transistor amplifier. We observe system noise temperatures as low as $680^{+20}_{-200}$ mK at 5.7 GHz corresponding…
