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Advanced architectures for high-performance quantum networking

As practical quantum networks prepare to serve an ever-expanding number of nodes, there has grown a need for advanced auxiliary classical systems that support the quantum protocols and maintain compatibility with the existing fiber-optic infrastructure. We propose and demonstrate a quantum local area network design that addresses current deployment limitations in timing and security in a scalable fashion using commercial off-the-shelf components. First, we employ White Rabbit switches to synchronize three remote nodes with ultra-low timing jitter, significantly increasing the fidelities of the distributed entangled states over previous work with Global Positioning System clocks. Second, using a parallel quantum key distribution channel, we secure the classical communications needed for instrument control and data management. Therefore, the conventional network that manages our entanglement network is secured using keys generated via an underlying quantum key distribution layer, preserving the integrity of the supporting systems and the relevant data in a future-proof fashion.

97 MATHEMATICS AND COMPUTING↗

Identifiability and characterization of transmon qutrits through Bayesian experimental design

Robust control of a quantum system is essential to utilize the current noisy quantum hardware to its full potential, such as quantum algorithms. To achieve such a goal, a systematic search for an optimal control for any given experiment is essential. The design of optimal control pulses requires accurate numerical models and, therefore, accurate characterization of the system parameters. We present an online Bayesian approach for quantum characterization of qutrit systems, which automatically and systematically identifies optimal experiments that provide maximum information on the system parameters, thereby greatly reducing the number of experiments that need to be performed on the quantum testbed. Unlike most characterization protocols that provide point-estimates of the parameters, the proposed approach is able to estimate their probability distribution. The applicability of the Bayesian experimental design technique was demonstrated on test problems, where each experiment was defined by a parameterized control pulse. In addition to this, we also present an approach for iterative pulse extension, which is robust under uncertainties in transition frequencies and coherence times, and shot noise, despite being initialized with wide uninformative priors. Furthermore, we provide a mathematical proof of the theoretical identifiability of the model parameters and present conditions on the quantum state under which the parameters are identifiable. The proof and conditions for identifiability are presented for both closed and open quantum systems using the Schrödinger equation and the Lindblad master equation, respectively.

97 MATHEMATICS AND COMPUTING↗

Production, quality assurance and quality control of the SiPM Tiles for the DarkSide-20k Time Projection Chamber

The DarkSide-20k dark matter direct detection experiment will employ a 21 m 2 silicon photomultiplier (SiPM) array, instrumenting a dual-phase 50 tonnes liquid argon Time Projection Chamber (TPC). SiPMs are arranged into modular photosensors called Tiles, each integrating 24 SiPMs onto a printed circuit board (PCB) that provides signal amplification, power distribution, and a single-ended output for simplified readout. Tiles are further grouped into Photo-Detector Units (PDUs). This paper details the production of the Tiles and the Quality Assurance and Quality Control (QA-QC) protocol established to ensure their performance and uniformity. The production and QA-QC of the Tiles are carried out at Nuova Officina Assergi (NOA), an ISO-6 clean room facility at LNGS. This process includes wafer-level cryogenic characterisation, precision die attaching, wire bonding, and extensive electrical and optical validation of each Tile. The overall production yield exceeds 83.5%, matching the requirements of the DarkSide-20k production plan. These results validate the robustness of the Tile design and its suitability for operation in a cryogenic environment.

Acerbi, F. [Fondazione Bruno Kessler]↗

CAST Technical Bulletin #002: Time Synchronization for Next Generation Power Delivery

This technical bulletin gives a description of the updated effort on Oak Ridge National Laboratory (ORNL) Center for Alternative Synchronization and Timing (CAST) project’s work investigating a terrestrial-based high precision timing infrastructure intended for time synchronization of the next generation power delivery infrastructures. We will provide a high-level description of the CAST application context, key protocols, critical architectural issues, and how GPS/timing data traverse through the system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Hamilton: Flexible, Open Source $10 Wireless Sensor System for Energy Efficient Building Operation

Sensors for improving building performance are rapidly populating the market, driven in part by the drive to reduce greenhouse gas emissions resulting from energy production as well as improve the interior environment for healthy and more productive spaces. UC Berkeley has led wireless sensor development over the past 25 years (e.g., Telos mote), with the Hamilton (named after Alexander Hamilton on the US $10 bill) as the most recent. The Hamilton sensor was designed as a low-cost high-performance sensor that is modular and interoperable. The objective of the Hamilton project was to create, evaluate and establish the technological foundations for secure and easy to deploy building energy efficiency applications utilizing pervasive, low-cost wireless sensors integrated with traditional Building Management Systems (BMS), consumer-sector building components, and powerful data analytics. The project included iterative hardware design, incorporating a high-performance database (BTrDb, http://btrdb.io/), creating and iterating the development of secure data middleware (BOSSwave, WAVE/WAVEMQ), working with and pushing the development of an open-source tiny operating system RiotOS, and implementing and improving protocols such as Thread/OpenThread and TCP/IP. The hardware benefited from careful design to drive down the cost; the design included a System-on-a-Chip (SoC), chip antenna, single crystal and five passive components. Careful design of the operating system created a low-power design to enable a long life with small batteries. The hardware included several sensors: temperature, radiant temperature, relative humidity, magnetometer, accelerometer, and light, with an optional occupancy (Passive InfraRed) sensor. The project was the basis of several applications, both internal to the research team and other researchers and professionals at other institutions. Several applications used the sensor hardware as the basis for other complex devices. Other applications used the sensors to improve building performance through interoperating with the building Heating Ventilation and Air-Conditioning (HVAC) system, such as using occupancy and/or distributed temperature sensing to reduce HVAC zone energy while still providing thermal comfort and to reduce peak loads in small commercial buildings. We demonstrated cloud-based energy analytics, implemented a schedule and a Model Predictive Controller in a small commercial building to optimize HVAC energy, occupancy and electricity price. Initial integration of these technological innovations was performed through the creation of execution containers containing the WAVE agent and various driver, proxy, or building system function logic. The research added to the understanding of efficient sensor hardware, secure middleware, time-series data management (high performance database), efficient communication protocols, and interoperating with applications and building systems. The project showed the technical effectiveness and economic feasibility of creating a low-cost, modular, and easy-to-deploy sensor. Through conversations with multiple end users, the research team discovered that many customers wanted data management and services in addition to the sensors. HamiltonIOT developed packages of sensors, border router, and data services to provide a seamless “plug-and-play” sensor deployment. Some customers were willing to pay for higher quality sensors (such as light); some customers wanted a robust enclosure (waterproof).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Commercial PV Inverter IEEE 1547.1 Ride-Through Assessments Using an Automated PHIL Test Platform

As more countries seek solutions to their de-carbonization targets using renewable energy (RE) technologies, interconnection standards and national grid codes for distributed energy resources (DER) are being updated to support higher penetrations of RE and improve grid stability. Common grid-code revisions mandate DER devices, such as solar inverters and energy storage systems, ride-through (RT) voltage and frequency disturbances. This is necessary because as the percentage of generation from DER increases, there is a greater risk power system faults will cause many or all DER to trip, triggering a substantial load-generation imbalance and possible cascading blackout. This paper demonstrates for the first time a methodology to verify commercial DER devices are compliant to new voltage, frequency, and rate of change of frequency (ROCOF) RT requirements established in IEEE Std. 1547-2018. The methodology incorporates a software automation tool, called the SunSpec System Validation Platform (SVP), in combination with a hardware-in-the-loop (HIL) system to execute the IEEE Std. 1547.1-2020 RT test protocols. In this paper, the approach is validated with two commercial photovoltaic inverters, the test results are analyzed for compliance, and improvements to the test procedure are suggested.

14 SOLAR ENERGY↗

eCounter: Inline Per-IP Network Monitoring at Millisecond Resolution via eBPF

Scientific data acquisition (SciDAQ) systems are shifting from archive-based workflows to streaming paradigms, where real-time, fine-grained network monitoring becomes essential. While P4-enabled devices offer per-packet in-band observability, they require specialized switches and routers. Host-side tools like Prometheus exporters lack sufficient temporal granularity. To bridge this gap, we present eCounter, a lightweight, hardware-agnostic, inline telemetry agent built on extended Berkeley Packet Filter (eBPF). eCounter captures per-interface ingress and egress traffic, categorized by IP address and protocol, at millisecond to sub-millisecond resolution. In a 100 Gbps environment, it continuously exports up to 3,257 time-series bins per second with only 4% CPU utilization at a 35¿KiB/s data rate. We evaluate eCounter across diverse NIC MTU settings, hook types, CPU architectures and operating systems, and observed negligible impact on concurrent high-throughput streaming applications. Complexity analysis confirms that it can be readily scaled to distributed SciDAQ deployments.

Mei, Xinxin [Computational Sciences and Technology↗

A protocol and analysis of year-long simulations of global storm-resolving models and beyond

We propose a protocol to evaluate and analyze year-long simulations of global storm-resolving models (GSRMs). The proposed protocol complements an earlier 40-day simulation protocol under the DYAMOND (DYnamics of the Atmospheric general circulation Modeled On Non-hydrostatic Domains) project to allow the analysis of the seasonal cycle and associated climatic relevant phenomena. This intercomparison aims to reveal how GSRMs, which can simulate mesoscale convective systems (MCSs) in the global domain, reproduce atmospheric large-scale structures related to convection beyond month-long simulations. The intercomparison for one-year simulations is conducted by either atmosphere-only models or atmosphere–ocean coupled models with atmospheric horizontal mesh sizes less than 5 km. We recommend the continuous four seasons from March 2020 to February 2021 as a target period for the intercomparison but with options for many groups to join more flexibly. The output variables are collected at 0.25° resolution, and archives of a small set of native grid variables are encouraged to analyze tropical cyclones and MCSs. Through the proposed global storm-resolving simulation, we will evaluate the climatological distributions of the atmospheric large-scale circulations, such as the Intertropical Convergence Zone (ITCZ), monsoon, midlatitude jets, their time evolution, and the upscale impacts on them. We present sample analyses from a one-year simulation using the 3.5 km mesh Nonhydrostatic Icosahedral Atmospheric Model (NICAM), revealing the realistic zonal contrast of tropical precipitation, no double ITCZ structure, the reasonable midlatitude jet position and intensity but a weak bias of storm track activities, and a warm bias over the Eurasia during boreal winter. We also clarify the cross-scale interaction, such as the effects of cold pools on mean precipitation over the Maritime Continent through the precipitation diurnal cycle and the effects of resolved gravity waves on midlatitude mean flows. The proposed one-year simulation protocol is referred to as the “Sendai Protocol.” This protocol is not unique or definite for evaluating GSRMs; we prospect a hierarchical set of experiments from short-term to multi-year simulations as GSRM intercomparisons.

54 ENVIRONMENTAL SCIENCES↗

Dark Energy Survey Year 3 results: A 2.7% measurement of baryon acoustic oscillation distance scale at redshift 0.835

We present angular diameter measurements obtained by measuring the position of baryon acoustic oscillations (BAO) in an optimized sample of galaxies from the first three years of Dark Energy Survey data (DES Y3). The sample consists of 7 million galaxies distributed over a footprint of 4100 deg 2 with 0.6 < z photo < 1.1 and a typical redshift uncertainty of 0.03 ( 1 + z ) . The sample selection is the same as in the BAO measurement with the first year of DES data, but the analysis presented here uses three times the area, extends to higher redshift, and makes a number of improvements, including a fully analytical BAO template, the use of covariances from both theory and simulations, and an extensive preunblinding protocol. We used two different statistics; angular correlation function and power spectrum, and validate our pipeline with an ensemble of over 1500 realistic simulations. Both statistics yield compatible results. We combine the likelihoods derived from angular correlations and spherical harmonics to constrain the ratio of comoving angular diameter distance D M at the effective redshift of our sample to the sound horizon scale at the drag epoch. We obtain D M ( z eff = 0.835 ) / r d = 18.92 ± 0.51 , which is consistent with, but smaller than, the Planck prediction assuming flat Λ CDM , at the level of 2.3 σ . The analysis was performed blind and is robust to changes in a number of analysis choices. It represents the most precise BAO distance measurement from imaging data to date, and is competitive with the latest transverse ones from spectroscopic samples at z > 0.75 . When combined with DES 3 x 2 pt + SNIa , they lead to improvements in H 0 and Ω m constraints by ∼ 20 % .

79 ASTRONOMY AND ASTROPHYSICS↗

Experimental-based mechanistic study and optimization of hydrothermal liquefaction of anaerobic digestates

Valorization of agricultural and food waste digestates is crucial for sustainable waste management to reduce environmental impacts and improve the economics of commercial farms. Hydrothermal liquefaction (HTL) of anaerobic digestates was evaluated to recover resources by converting them into carbon-dense biocrude oil and a nutrient-rich HTL aqueous phase (HTL-AP) coproduct. The effects of HTL temperature (280–360 °C), reaction time (10–50 min), feedstock pH (2.5–8.5), digestate salt content (1–5 wt%), and digestate cellulose-to-lignin ratio (0.2–1.8) on energy and nutrient recovery were systematically investigated in a set of well-designed experiments following a half-fractional central composite protocol. Response surface analysis combined with HTL product characterization and comparative literature study produced a comprehensive reaction pathway for HTL of anaerobic digestates. Moreover, this analysis revealed the importance of acidic feedstocks (pH 3.00–5.53), high reaction temperatures (337–360 °C), and reaction times <45 or 45–50 min for digestates with Cel/Lig >1 or <1, for maximizing the energy recovered in biocrude (high carbon yield and low heteroatom content) and the amounts of P, NH 3 –N, and Mg distributed in the HTL-AP. Acidic conditions catalyzed biocrude production, inhibited the Maillard reaction (lowering the nitrogen content in biocrude), and partitioned nutrients into the HTL-AP. Higher reaction temperatures coupled with longer reaction times activated hydro-denitrogenation and deoxygenation reactions to improve biocrude quality. Finally, this work provides not only validated methods to achieve targeted resource recovery for specific feedstock compositions using HTL, but also a comprehensive mechanistic understanding of the HTL of biomass waste for controlling target product characteristics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-Spatial-Resolution Quantitative Chemomechanical Mapping of Organic Composite Cathodes for Sulfide-Based Solid-State Batteries

Understanding the chemo-mechanical behaviors of electrodes, particularly at the electrode/electrolyte interfaces, is critical for improving the performance of all-solid-state batteries. However, due to the instability of electrolyte materials under ambient conditions, such characterizations are challenging, particularly for sulfide-based all-solid-state batteries. Herein, by combining time-of-flight secondary-ion mass spectroscopy (ToF-SIMS) and in-SEM nanoindentation measurements, a systematic quantitative investigation of the chemo-mechanical behaviors of pyrene-4,5,9,10-tetraone (PTO) /Li 6 PS 5 Cl composite cathodes is carried out. Chemical and quantitative mechanical information of the composite cathode were collected with high spatial resolution after developing and implementing an air-free characterization protocol. By directly connecting the Young’s modulus and hardness with the Li distribution in the composite cathode, a comprehensive chemo-mechanical mapping of the PTO/ Li 6 PS 5 Cl composite cathode has been established. Furthermore, this work improves our knowledge of the critical chemo-mechanical phenomena that occur at the cathode/electrolyte interfaces in all-solid-state batteries.

25 ENERGY STORAGE↗

Remote Hardware-in-the-Loop Approach for Microgrid Controller Evaluation

Utilities have been installing microgrids because of the increased resilience and reliability advantages they may provide to the distribution system. A microgrid controller is a critical component in microgrids. It is of great benefit to derisk the installation of microgrid controllers before field deployment. Hardware-in-the-loop (HIL) testing is used by controller developers and utilities to evaluate the controllers under stressful conditions. In this work, a microgrid control function developed by the Synchrophasor Grid Monitoring and Automation (SyGMA) laboratory at the University of California, San Diego is tested in a remote HIL (RHIL) setup. The digital real-time simulation of the detailed microgrid system was operated at the National Renewable Energy Laboratory's Energy Systems Integration Facility. Under such RHIL setup, successful controller operation is contingent on understanding and characterizing the communications channel and in particular network latencies. The novelty of this paper is the proposed use of a RHIL setup that leverages existing power system communications protocols to evaluate the controller in conjunction with the simulation capabilities of a remote facility. The work presented here will provide the complete setup of the HIL evaluation platform, the details of the communications protocols used by the setup for data transfer between the two organizations, test cases developed to evaluate the controller, and the results from the experiments.

controller hardware-in-the-loop↗

NuQKD: A Modular Quantum Key Distribution Simulation Framework for Engineering Applications

Abstract An experimental Quantum Key Distribution (QKD) implementation requires advanced costly hardware, unavailable in most research environments, making protocol testing and performance evaluation complicated. This has been a major motivation for the development of QKD simulation frameworks, to allow researchers to obtain insight before proceeding into practical implementations. Several simulators have been introduced over the recent years. However, only four are publicly available, only one of which models equipment imperfections. Currently, no open‐source simulator includes all following capabilities: channel attenuation modelling, equipment imperfections and effects on key rates, estimation of elapsed time during classical and quantum‐ channel processes, use of truly random binary sequences for qubits and measurement bases, shared ‐bit fraction customization. In this paper, we present NuQKD, an open‐ source modular, intuitive simulator, featuring all the above capabilities. NuQKD establishes communication between two computer terminals, accepts custom user inputs (iterations, raw key size, attacker interception rate etc.) and evaluates the sifted key, Quantum Bit Error Rate (QBER), elapsed communication time, and more. NuQKD capabilities include optical fiber and free ‐space simulation, modeling of equipment/channel imperfections, bitstrings from True Random Number Generators, decoy‐state protocol support, and automated evaluation of performance metrics. We expect NuQKD to enable convenient and accurate representation of actual experimental conditions.

Gkouliaras, Konstantinos↗

Probing Curved Spacetime with a Distributed Atomic Processor Clock

Quantum dynamics on curved spacetime has never been directly probed beyond the Newtonian limit. Although we can describe such dynamics theoretically, experiments would provide empirical evidence that quantum theory holds even in this extreme limit. The practical challenge is the minute spacetime curvature difference over the length scale of the typical extent of quantum effects. Here, we propose a quantum network of alkaline earth (like) atomic processors for constructing a distributed quantum state that is sensitive to the differential proper time between its constituent atomic processor nodes, implementing a quantum observable that is affected by post-Newtonian curved spacetime. Conceptually, we propose to delocalize one clock between three locations by encoding the presence or absence of a clock into the state of the local atoms. By separating three atomic nodes over approximately kilometer-scale elevation differences and distributing one clock between them via a 𝑊 state, we demonstrate that the curvature of spacetime is manifest in the interference of the three different proper times that give rise to three distinct beat notes in our nonlocal observable. We further demonstrate that 𝑁-atom entanglement within each node enhances the interrogation bandwidth by a factor of 𝑁. We discuss how our proposed system can probe new facets of fundamental physics, such as the linearity, unitarity, and probabilistic nature of quantum theory on curved spacetime. Our protocol combines several recent advances with neutral atom and trapped ions to realize a novel quantum probe of gravity uniquely enabled by quantum networks.

Covey, Jacob P. [Univ. of Illinois at Urbana-Champ↗

Cations Control Lipid Bilayer Memcapacitance Associated with Long-Term Potentiation

Phospholipid bilayers can be described as capacitors whose capacitance per unit area (specific capacitance, C m ) is determined by their thickness and dielectric constant–independent of applied voltage. It is also widely assumed that the C m of membranes can be treated as a “biological constant”. Recently, using droplet interface bilayers (DIBs), it was shown that zwitterionic phosphatidylcholine (PC) lipid bilayers can act as voltage-dependent, nonlinear memory capacitors, or memcapacitors. When exposed to an electrical “training” stimulation protocol, capacitive energy storage in lipid membranes was enhanced in the form of long-term potentiation (LTP), which enables biological learning and long-term memory. LTP was the result of membrane restructuring and the progressive asymmetric distribution of ions across the lipid bilayer during training, which is analogous, for example, to exponential capacitive energy harvesting from self-powered nanogenerators. Here, we describe how LTP could be produced from a membrane that is continuously pumped into a nonequilibrium steady state, altering its dielectric properties. During this time, the membrane undergoes static and dynamic changes that are fed back to the system’s potential energy, ultimately resulting in a membrane whose modified molecular structure supports long-term memory storage and LTP. Here, we also show that LTP is very sensitive to different salts (KCl, NaCl, LiCl, and TmCl 3 ), with LiCl and TmCl 3 having the most profound effect in depressing LTP, relative to KCl. This effect is related to how the different cations interact with the bilayer zwitterionic PC lipid headgroups primarily through electric-field-induced changes to the statistically averaged orientations of water dipoles at the bilayer headgroup interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Control-Agnostic Beam Instrumentation with Redis at the Core

Redis isn’t a database — it’s our protocol. Fermilab’s RedisAdapter provides a high-performance, control-system-agnostic bridge between digitized beam data and downstream consumers such as ACNET and EPICS. It forms the foundation of three new software components deployed across MicroTCA-based digitizers: GMMDM, a runtime for memory-mapped data movement from Zynq-based platforms; GRAFE, a front end for Redis-to-ACNET presentation; and GREFE, an EPICS IOC front end. Together, these tools enable modular, standardized instrumentation pipelines. Precision timing is handled via White Rabbit PPS distribution, allowing nanosecond-scale synchronization across crates. This architecture, originally prototyped in Booster BPM systems, is now deployed on modern hardware and designed to meet the performance, modularity, and scalability requirements of the PIP-II era.

Steinkamp, Derek [Fermilab] (ORCID:000900027228626↗

Adaptive Cybersecurity for Distributed Energy Resources (AdCyDER): Online Reinforcement Learning with Stackelberg-Optimized Defenses — Pipeline Architecture, Evaluation Methodology, and Findings from a Synthetic-Data Evaluation

This report documents the design and evaluation of an integrated online-learning pipeline developed within the AdCyDER project for Distributed Energy Resource (DER) cybersecurity. The pipeline couples a Reinforcement Learning (RL) attack classifier — which produces an attack-type probability distribution — with a Stackelberg game-theoretic (GT) defense selector that consumes those distributions alongside SME-encoded priors over (defense, attack) effectiveness pairings and perdefense costs to choose grid-health-preserving defenses. The objective is not attack classification per se but production of distributions that drive effective defense selection through the Stackelberg layer, learned from delayed grid-health feedback rather than labeled attack data. AdCyDER as a whole is broader than the work presented here; this report covers the specific RL/GT loop integration and its evaluation. We present the integrated pipeline (SCADA telemetry with Fronius inverter physics, Suricata IDS, time-windowed aggregation, per-facility LSTM classifier, Stackelberg optimizer, OpenC2 actuators), an experimental campaign of 28 eight-hour iterations across three baseline modes, and a pipeline-ordered diagnostic protocol. The protocol identifies two distinct failure modes within the loop: paired supervised ceilings on the same features establish that the deployed online RL classifier (macro F1 ≈ 0.07) sits at least 4.7× below a same-architecture supervised LSTM (≈ 0.34) and 10–11× below a linear feature-signal ceiling (≈ 0.70–0.79 depending on per-facility isolation), localizing the dominant failure to the training procedure; and the reward signal driving online updates carries weak directional coupling with classifier correctness in the methodology-expected direction (multi-lens convergent: top-decile P(true) records produce more frequent state changes and slightly larger improvements, top-vs-bot Cohen’s 𝑑 ≈ −0.19), but at effect magnitudes too small to drive gradient-based learning at the campaign sample size. The original learning hypothesis is not supported by the data. The primary contributions are the diagnostic methodology — proposed as a transferable falsification protocol for online RL/GT defense pipelines learning from delayed environmental reward — and the open, reproducible experimental infrastructure. We outline reward reformulation as the highest-priority aspirational next step given the underpowered-but-aligned Q6 reading, with hardware-in-the-loop evaluation as the broadest scope-expansion option.

Blakely, Benjamin [Argonne National Laboratory (AN↗

Operator Relaxation and the Optimal Depth of Classical Shadows

Classical shadows are a powerful method for learning many properties of quantum states in a sample-efficient manner, by making use of randomized measurements. Here we study the sample complexity of learning the expectation value of Pauli operators via “shallow shadows,” a recently proposed version of classical shadows in which the randomization step is effected by a local unitary circuit of variable depth t. Here we show that the shadow norm (the quantity controlling the sample complexity) is expressed in terms of properties of the Heisenberg time evolution of operators under the randomizing (“twirling”) circuit—namely the evolution of the weight distribution characterizing the number of sites on which an operator acts nontrivially. For spatially contiguous Pauli operators of weight k, this entails a competition between two processes: operator spreading (whereby the support of an operator grows over time, increasing its weight) and operator relaxation (whereby the bulk of the operator develops an equilibrium density of identity operators, decreasing its weight). From this simple picture we derive (i) an upper bound on the shadow norm which, for depth t~log⁡(k), guarantees an exponential gain in sample complexity over the t=0 protocol in any spatial dimension, and (ii) quantitative results in one dimension within a mean-field approximation, including a universal subleading correction to the optimal depth, found to be in excellent agreement with infinite matrix product state numerical simulations. Our Letter connects fundamental ideas in quantum many-body dynamics to applications in quantum information science, and paves the way to highly optimized protocols for learning different properties of quantum states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗