Dense Lindblad propagation at the Hilbert-space sizes of near-term transmon control ($d = 3$, $9$, $27$) sits in a regime where cache boundaries, launch overhead, and fixed latency decide which hardware is useful, not peak arithmetic rate. This paper characterizes that regime on two x86 CPUs, two NVIDIA GPUs, and a low-cost FPGA. Each implementation is stated as an algorithm in $d$ with an idealized cost built from separately measured ceilings, and the measured gaps are attributed to specific mechanisms: thread fork/join, the strided read of the propagator, PCI Express (PCIe) transfers, and propagator re-upload. An end-to-end gradient-ascent (GRAPE-style) benchmark against released QuTiP 5.2.3 shows that fast propagation does not imply fast control optimization: the C path wins by up to two orders of magnitude at $d = 3$ but loses at $d = 27$, where the dense LU solve inside the Padé propagator build takes over $90\%$ of the cost. The FPGA contributes a deterministic-latency operating point, $95$ cycles per step at a stress-characterized $108$ MHz with zero cycle spread over $1000$ trials, and its Q1.15 fixed-point drift is measured on the device. The results are a map of operating regimes for the measured grid, with the propagator build, not propagation, as the dominant cost at the largest size.
As progress is made towards the first generation of error-corrected quantum computers, robust characterization and validation protocols are required to assess the noise environments of physical quantum processors. While standard coherence metrics and characterization protocols such as T1 and T2, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multi-qubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introdu…
Noisy quantum circuit simulation with the tensor jump method
Weierstrass Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机性研究所）；Technical University of Munich（慕尼黑工业大学）；Munich Quantum Software Company GmbH（慕尼黑量子软件有限公司）；Software Competence Center Hagenberg GmbH (SCCH)（哈根贝格软件能力中心有限公司）
IBM Research（IBM 研究部）；Trinity Business School（三一商学院）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）；Nanoscale Device Characterization Division, National Institute of Standards and Technology（美国国家标准与技术研究院纳米器件表征部门）；Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU)（材料物理中心 (西班牙国家科研委员会-巴斯克国立大学/阿尔贝塔理工大学)）；Advanced Micro Devices Inc.（超威半导体公司）
Quantum simulation on emerging quantum hardware is a topic of intense interest. While many studies focus on computing ground state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target of study owing to their ubiquity and rich physical behavior. However, their non-unitary dynamics are also not natural to simulate on digital quantum devices. Here, we report algorithms for the digital quantum simulation of the dynamics of open quantum systems governed by a Lindblad equation using adaptations of the quantum imaginary time evolution (QITE) algo…
In this paper, we examine various software and hardware strategies for implementing high-fidelity controlled-Z gate in the large-scale quantum system by solving the system's Hamiltonian with the Lindblad master equation. First, we show that the optimal single-parameter pulse achieved the gate error on the order of $10^{-4}$ for the 40 ns controlled-Z gate in the 4-qubit system. Second, we illustrate that the pulse optimized in the isolated 2-qubit system must be further optimized in the larger-scale system to achieve errors lower than the fault-tolerant threshold. Lastly, we explain that the h…
We prove a maximal velocity bound for the dynamics of Markovian open quantum systems. The dynamics are described by one-parameter semi-groups of quantum channels satisfying the von Neumann-Lindblad equation. Our result says that dynamically evolving states are contained inside a suitable light cone up to polynomial errors. We also give a bound on the slope of the light cone, i.e., the maximal propagation speed. The result implies an upper bound on the speed of propagation of local perturbations of stationary states in open quantum systems.
Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size
Akhiezer Institute for Theoretical Physics, NSC KIPT（阿赫伊泽尔理论物理研究所，NSC KIPT）；Advanced Photonic and Electronic Sciences Division, U.S. Army DEVCOM Army Research Laboratory（美国陆军DEVCOM陆军研究实验室先进光子与电子科学部）；Department of Physics, University of Massachusetts at Boston（马萨诸塞大学波士顿分校物理系）；Education and Research Institute “School of Physics and Technology”, Karazin Kharkiv National University（哈尔科夫国立大学教育与研究所“物理与技术学院”）；Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）
The rapid development in hardware for quantum computing and simulation has led to much interest in problems where these devices can exceed the capabilities of existing classical computers and known methods. Approaching this for problems that go beyond testing the performance of a quantum device is an important step, and quantum simulation of many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods for analogue quantum s…
We present Quantum Belief Propagation (QBP), a Quantum Annealing (QA) based decoder design for Low Density Parity Check (LDPC) error control codes, which have found many useful applications in Wi-Fi, satellite communications, mobile cellular systems, and data storage systems. QBP reduces the LDPC decoding to a discrete optimization problem, then embeds that reduced design onto quantum annealing hardware. QBP's embedding design can support LDPC codes of block length up to 420 bits on real state-of-the-art QA hardware with 2,048 qubits. We evaluate performance on real quantum annealer hardware, …
Modeling the non-equilibrium dissipative dynamics of strongly interacting quantized degrees of freedom is a fundamental problem in several branches of physics and chemistry. We implement a quantum state trajectory scheme for solving Lindblad quantum master equations that describe coherent and dissipative processes for a set of strongly-coupled quantized oscillators. The scheme involves a sequence of stochastic quantum jumps with transition probabilities determined the system state and the system-reservoir dynamics. Between consecutive jumps, the wavefunction is propagated in coordinate space u…
Fast convergence of propagation algorithms for open quantum systems
University of Cambridge（剑桥大学）；Inria, ENS Lyon, UCBL, LIP（法国国家信息与自动化研究所，里昂高等师范学校，里昂第一大学，计算与图像实验室）；Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris（法国国家信息与自动化研究所，巴黎电信学院-信息与通信系，巴黎理工学院）；University of Copenhagen（哥本哈根大学）
Automatic De-Quantization of Quantum Programs Using Constant Propagation
Institute of Software Technology, German Aerospace Center (DLR)（德国航空航天中心软件技术研究所）；Chair for Design Automation, Technical University of Munich（慕尼黑工业大学设计自动化讲席）；Munich Quantum Software Company GmbH（慕尼黑量子软件有限公司）
Hardware-Efficient Ground-State Preparation using Variational Imaginary-Time Majorana Evolution
IQM Quantum Computers GmbH（IQM量子计算机有限公司）；RPTU Kaiserslautern-Landau（莱布尼茨技术大学凯泽斯劳滕-兰道分校）；Universidad Autónoma de Madrid（马德里自治大学）；Technical University of Munich（慕尼黑工业大学）
Silicon carbide is among the leading quantum information material platforms due to the long spin coherence and single-photon emitting properties of its color center defects. Applications of silicon carbide in quantum networking, computing, and sensing rely on the efficient collection of color center emission into a single optical mode. Recent hardware development in this platform has focused on angle-etching processes that preserve emitter properties and produce triangularly shaped devices. However, little is known about the light propagation in this geometry. We explore the formation of photo…
Computational regimes in matrix-product-state-based quantum trajectory simulations
Technical University of Munich（慕尼黑工业大学）；Freie Universität Berlin（柏林自由大学）；Weierstrass Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机性研究所）；Helmholtz-Zentrum Berlin für Materialien und Energie（柏林亥姆霍兹材料与能源中心）；Munich Quantum Software Company GmbH（慕尼黑量子软件有限公司）；Software Competence Center Hagenberg GmbH (SCCH)（哈根贝格软件能力中心有限公司）
