Accurate estimation of fermionic observables is essential for advancing quantum physics and chemistry. The fermionic classical shadow (FCS) method offers an efficient framework for estimating these observables without requiring a transformation into a Pauli basis. However, the random matchgate circuits in FCS require polynomial-depth circuits with a brickwork structure, which presents significant challenges for near-term quantum devices with limited computational resources. To address this limitation, we introduce an adaptive-depth fermionic classical shadow (ADFCS) protocol designed to reduce the circuit depth while maintaining the estimation accuracy and the order of sample complexity. Through theoretical analysis and numerical fitting, we establish that the required depth for approximating a fermionic observable $H$ scales as $\max\{d^2_{\text{int}}(H)/\log n, d_{\text{int}}(H)\}$ where $d_{\text{int}}$ is the interaction distance of $H$. We demonstrate the effectiveness of the ADFCS protocol through numerical experiments, which show similar accuracy to the traditional FCS method while requiring significantly fewer resources. Additionally, we apply ADFCS to compute the expectation value of the Kitaev chain Hamiltonian, further validating its performance in practical scenarios. Our findings suggest that ADFCS can enable more efficient quantum simulations, reducing circuit depth while preserving the fidelity of quantum state estimations, offering a viable solution for near-term quantum devices.
Fermionic partial tomography via classical shadows
我们提出了一个层析协议，用于估计任何$ k $体约化密度矩阵（$ k $ -RDM）的$ n $模式的费米子态，一个普遍存在的步骤，在近期的量子算法模拟多体物理，化学和材料。我们的方法扩展了经典阴影的框架，一种学习量子态性质集合的随机方法，到费米子环境。我们的采样协议使用随机测量设置所产生的离散组的费米子高斯幺正，实现与线性深度电路。我们证明，估计所有的$ k $ -RDM元素添加剂精度$ \varepsilon $需要的顺序上的$ \binom{n}{k} k^{3/2} \log(n) / \varepsilon^2 $重复状态的准备，这是最佳的对数因子。此外，数值计算表明，我们的协议提供了一个实质性的改进，在恒定的开销为$ k \geq 2 $，相比以前的确定性策略。我们还调整我们的方法，粒子数对称，其中额外的电路深度可以减半的成本大约2-5倍多的重复。
QPU-scale randomized benchmarking via Bell-pair injection
Moth, Switzerland（Moth）；Center for Quantum Computing and Quantum Coherence (QC2), University of Basel, Switzerland（巴塞尔大学量子计算与量子相干中心（QC2））；Moth, United Kingdom（Moth）；ICCMR, University of Plymouth, United Kingdom（普利茅斯大学ICCMR）
Exponentially accurate open quantum simulation via randomized dissipation with minimal ancilla
Mitsubishi UFJ Financial Group, Inc.（三菱UFJ金融集团）；MUFG Bank, Ltd.（三菱UFJ银行）；Quantum Computing Center, Keio University（庆应义塾大学量子计算中心）；Graduate School of Science and Technology, Keio University（庆应义塾大学理工学研究科）；Toyota Motor Corporation（丰田汽车公司）；Department of Applied Physics and Physico-Informatics, Keio University（庆应义塾大学应用物理及物理信息学科）
Parallel classical simulation of noisy shallow circuits: no quantum advantage in 1D
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies（量子技术中心）
Efficient Preparation of Quantum States via Randomized Truncation
QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong（香港大学计算与数据科学学院量子信息与计算倡议）；Shenzhen International Quantum Research Institute（深圳国际量子研究院）；Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University（华南师范大学物理学院原子与亚原子结构及量子控制教育部重点实验室、广东省物质结构与基本相互作用卓越基础研究中心）；Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University（华南师范大学物理前沿研究院量子工程与量子材料广东省重点实验室、粤港量子物质联合实验室）；Center on Frontiers of Computing Studies, Peking University（北京大学计算前沿研究中心）；School of Computer Science, Peking University（北京大学计算机学院）
One-dimensional quantum Gibbs states in constant circuit depth
Massachusetts Institute of Technology（麻省理工学院）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；New York University（纽约大学）；University of Basel（巴塞尔大学）
Quickly extracting fidelity decay rates in random circuit benchmarking experiments
CWI & QuSoft（荷兰数学与计算机科学研究中心与QuSoft）；Quantum Research Center, Technology Innovation Institute（技术研究院量子研究中心）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Johannes Kepler Universität Linz（林茨约翰内斯·开普勒大学）；Rigetti Computing（里吉蒂计算）
Stabilizer-based quantum simulation of fermion dynamics with local qubit encodings
IBM Quantum, IBM Research Europe - Zurich（IBM量子，IBM欧洲苏黎世研究中心）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）
