Results for “quantum information architectures & platforms”

DOE OSTI2026

Sparse non-Markovian Noise Modeling of Transmon-Based Multi-Qubit Operations

The influence of noise on quantum dynamics is one of the main factors preventing current quantum processors from performing accurate quantum computations. Sufficient noise characterization and modeling can provide key insights into the effect of noise on quantum algorithms and inform the design of targeted error protection protocols. However, constructing effective noise models that are sparse in model parameters, yet predictive can be challenging. In this work, we present an approach for effective noise modeling of multi-qubit operations on transmon-based devices. Through a comprehensive characterization of seven devices offered by the IBM Quantum Platform, we show that the model can capture and predict a wide range of single- and two-qubit behaviors, including non-Markovian effects resulting from spatiotemporally correlated noise sources. The model’s predictive power is further highlighted through multi-qubit dynamical decoupling demonstrations and an implementation of the variational quantum eigensolver. As a training proxy for the hardware, we show that the model can predict expectation values within a relative error of 0.5%; this is a sevenfold improvement over default hardware noise models. Through these demonstrations, we highlight key error sources in superconducting qubits and illustrate the utility of reduced noise models for predicting hardware dynamics.

open quantum systems & decoherence↗

DOE OSTI2025

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Magnet-superconductor hybrid quantum systems: a materials platform for topological superconductivity

Magnet–superconductor hybrid (MSH) systems have recently emerged as one of the most significant developments in condensed matter physics. This has generated, in the last decade, a steadily rising interest in the understanding of their unique properties. They have been proposed as one of the most promising platforms for the establishment of topological superconductivity, which holds high potential for application in future quantum information technologies. Their emergent electronic properties stem from the exchange interaction between the magnetic moments and the superconducting condensate. Given the atomic-level origin of such interaction, it is of paramount importance to investigate new magnet–superconductor hybrids at the atomic scale. In this regard, scanning tunneling microscopy (STM) and spectroscopy are playing a crucial role in the race to unveil the fundamental origin of the unique properties of MSH systems, with the aim to discover new hybrid quantum materials capable of hosting topologically non-trivial unconventional superconducting phases. In particular, the combination of STM studies with tight-binding model calculations have represented, so far, the most successful approach to unveil and explain the emergent electronic properties of MSHs. The scope of this review is to offer a broad perspective on the field of MSHs from an atomic-level investigation point-of-view. The focus is on discussing the link between the magnetic ground state hosted by the hybrid system and the corresponding emergent superconducting phase. This is done for MSHs with both one-dimensional (atomic chains) and two-dimensional (atomic lattices and thin films) magnetic systems proximitized to conventional s-wave superconductors. We present a systematic categorization of the experimentally investigated systems with respect to defined experimentally accessible criteria to verify or falsify the presence of topological superconductivity and Majorana edge modes. The discussion will start with an introduction to the physics of Yu–Shiba–Rusinov bound states at magnetic impurities on superconducting surfaces. This will be used as a base for the discussion of magnetic atomic chains on superconductors, distinguishing between ferromagnetic, antiferromagnetic and non-collinear magnetic ground states. A similar approach will be used for the discussion of magnetic thin film islands on superconductors. Given the vast number of publications on the topic, we limit ourselves to discuss works which are most relevant to the search for topological superconductivity.

Majorana states↗

DOE OSTI2025

The phase diagram of quantum chromodynamics in one dimension on a quantum computer

The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behaviour of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce colour-neutrality constraints. This work pioneers the quantum simulation of QCD at finite density and temperature for two and three colours, laying the foundation to explore QCD phenomena on quantum platforms.

Quantum information↗

DOE OSTI2026

Multi-purpose quantum laboratories from superconducting circuits

Superconducting circuits (SCs) are the cornerstone of modern quantum technology, enabling scalable computing through coherent control of macroscopic quantum states. Through a legacy that predates modern quantum computing, SCs have emerged as high-precision instruments for discovery. In this review, we highlight the role of SCs as general-purpose quantum laboratories, outlining the emerging landscape of correlated matter-circuit science. We review and unify the capabilities of superconducting quantum hardware across condensed matter, high energy and quantum information sciences. We trace the technical evolution of these architectures, illustrating how their foundational development has culminated in a toolkit for resolving the complexities of macroscopic quantum states.

Arora, Arpit [UCLA, Los Angeles (main); UCLA; Haim↗

DOE OSTI2026

Distributed quantum approximate optimization algorithm on a quantum-centric supercomputing architecture

Quantum approximate optimization algorithm (QAOA) has shown promise in solving combinatorial optimization problems by providing quantum speedup on near-term gate-based quantum computing systems. However, QAOA faces challenges for high-dimensional problems due to the large number of qubits required and the complexity of deep circuits, limiting its scalability for real-world applications. In this study, we present a distributed QAOA (DQAOA), which leverages distributed computing strategies to decompose a large computational workload into smaller tasks that require fewer qubits and shallower circuits than are necessary to solve the original problem. These sub-problems are processed using a combination of high-performance and quantum computing resources. The global solution is iteratively updated by aggregating sub-solutions, allowing convergence toward the optimal solution. We demonstrate that DQAOA can handle considerably large-scale optimization problems (e.g., 1000-bit problem), achieving a high solution quality and short time-to-solution, outperforming existing strategies. Furthermore, we realize DQAOA on a quantum-centric supercomputing architecture, paving the way for practical applications of gate-based quantum computers in real-world optimization tasks. To extend DQAOA’s applicability to materials science, we further develop an active learning algorithm integrated with our DQAOA (AL-DQAOA), which involves machine learning, DQAOA, and active data production in an iterative loop. We successfully optimize photonic structures using AL-DQAOA, indicating that solving real-world optimization problems using gate-based quantum computing is feasible. We expect the proposed DQAOA to be applicable to a wide range of optimization problems and AL-DQAOA to find broader applications in material design.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗

DOE OSTI2026

Optical nanofiber testbeds for benchmarking membrane-waveguide photonic integrated circuit platforms toward on-chip quantum inertial sensing

Recent advances in cold atom interferometry with optical and magnetic atom guides have set the stage for quantum inertial sensors capable of operating in dynamic environments. In this work, we present three key innovations—evanescent-field (EF) atom guides, optical nanofiber testbeds, and membrane-waveguide photonic integrated circuit (PIC) platforms—to advance EF-guided atom interferometry. First, we demonstrate EF atom guides on optical nanofiber testbeds, which serve as performance benchmarks for our membrane-waveguide PIC platforms. Second, we achieve low-power (⁠ ~ 5 mW) guiding of freely moving, laser-cooled 133 Cs atoms in two-color, traveling-wave EF optical dipole traps at the novel, heat-efficient magic wavelengths of 793 and 937 nm (i.e., “793/937-nm EF atom guides”). Concurrently, we design and fabricate membrane-waveguide PIC platforms for these EF atom guides; in our prior work, we showed that these structures safely accommodate 4–6 times the required optical trap power under vacuum and enable dense cold atom generation via magneto-optical trapping in the vicinity of the optical wavguide for efficient loading. Third, we verify preserved atomic coherence via microwave fields and EF-coupled Doppler-free Raman beams; to our knowledge, this is the first report of coherence fringes driven by co-propagating EF-coupled Raman beams with only 150 nW of total optical power. By providing a direct comparison between optical nanofiber testbeds and membrane-waveguide PIC platforms, our results lay critical groundwork for the on-chip realization of EF-guided atom interferometry and the development of fully integrated, compact, lightweight, and low-power quantum accelerometers and gyroscopes.

Orozco, Adrian [Sandia National Laboratories (SNL-↗

DOE OSTI2026

Solid neon as a noise-resilient host for electron qubits above 100 mK

Solid neon can be used as a solid host for single-electron qubits. At temperatures of around 10 mK, electron-on-solid-neon charge qubits exhibit long coherence times and high operation fidelities. However, a systematic characterization of the noise features of such systems is needed for the development of scalable quantum information architectures. Here, in this work, we show that solid neon can be used as a noise-resilient host for electron qubits above 100 mK. We examine the resilience of solid neon against charge and thermal noise when electron-on-solid-neon charge qubits are operated away from the charge-insensitive sweet spot and at elevated temperatures. We show that the extracted high-frequency charge noise density of electron-on-solid-neon qubits, projected as voltage fluctuations on nearby electrodes, is between 10 −4 μV 2 Hz −1 and 10 −6 μV 2 Hz −1 at 0.01 MHz to 1 MHz, which is comparable to common semiconductor hosts. We also show that the electron-on-solid-neon charge qubits operating at frequencies of around 5 GHz can maintain echo coherence times of over 1 μs at temperatures up to 400 mK.

42 ENGINEERING↗

NASA NTRS2026

A Multi-Tier Autonomous Aerial Architecture for Wildfire Detection, Characterization, and Communication in Infrastructure-Denied Environments

Wildfire response depends on how fast an ignition can be confirmed and located, especially in remote regions where ground-based communication and monitoring may be limited. Geostationary sensors provide frequent observations but at kilometer-scale resolution, which is too coarse to resolve small fires in remote terrain. Ground camera networks require sightlines and infrastructure that back-country areas lack. To address these limitations, this work proposes a Multi-Tier Autonomous Wildfire Intelligence System that combines wide-area monitoring with targeted, high-resolution sensing. A solar-powered high-altitude long endurance (HALE) platform operating at approximately 60,000 ft provides persistent wide-area thermal and optical surveillance, running onboard edge inference to screen candidate ignitions and reduce false positives and downlink bandwidth. When a candidate ignition is detected, low-altitude uncrewed aircraft systems (UAS) can be deployed to conduct localized observations, including high-resolution imaging and atmospheric measurements such as wind and plume observation. By combining persistent detection with local sensing, the proposed architecture is designed to provide first responders with timely, high-resolution information about fire location and behavior to aid in emergency decision making.

Wildfire management, UAS, drones↗

DOE OSTI2025

Generalized geometric speed limits for quantum observables

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension ≥3, tighten existing bounds—in some cases by an arbitrarily large multiplicative constant. Our theoretical results are supported by illustrative examples and an experimental demonstration using a superconducting qutrit. We also derive two upper bounds on the generalized quantum Fisher information in terms of the condition number of the density matrix. One of these bounds applies only to coherent dynamics and depends also on the variance of the Hamiltonian. The other bound depends also on the so-called Wigner-Yanase skew information. These bounds generalize well-known bounds on the symmetric logarithmic derivative quantum Fisher information and are tighter than the existing bounds for sufficiently mixed states (e.g., for sufficiently high temperature thermal states).

open quantum systems & decoherence↗

DOE OSTI2026

String-Breaking Dynamics in Quantum Adiabatic and Diabatic Processes

Confinement prohibits isolation of color charges, e.g., quarks, in nature via a process called string breaking : the separation of two charges results in an increase in the energy of a color flux, visualized as a string, connecting those charges. Eventually, creating additional charges is energetically favored, hence breaking the string. Such a phenomenon can be probed in simpler models, including quantum spin chains, enabling enhanced understanding of string-breaking dynamics. A challenging task is to understand how string breaking occurs as time elapses, in an out-of-equilibrium setting. This work establishes the phenomenology of dynamical string breaking induced by a gradual increase of string tension over time. It, thus, goes beyond instantaneous quench processes and enables tracking the real-time evolution of strings in a more controlled setting. We focus on domain-wall confinement in a family of quantum Ising chains. Our results indicate that, for sufficiently short strings and slow evolution, string breaking can be described by the transition dynamics of a two-state quantum system akin to a Landau-Zener process. For longer strings, a more intricate spatiotemporal pattern emerges: the string breaks by forming a superposition of bubbles (domains of flipped spins of varying sizes), which involve highly excited states. We finally demonstrate that string breaking driven only by quantum fluctuations can be realized in the presence of sufficiently long-ranged interactions. This work holds immediate relevance for studying string breaking in quantum-simulation experiments.

Ising model↗

DOE OSTI2026

Self-aligned heterogeneous quantum photonic integration

Integrated quantum photonics holds significant promise for scalable photonic quantum information processing, quantum repeaters, and quantum networks, but its development is hindered by the mismatch between materials hosting high-quality quantum emitters and those compatible with mature photonic technologies. Heterogeneous integration offers a potential solution to this challenge, yet practical implementations have been limited by inevitable insertion losses at material interfaces. Here, we present a self-aligned heterogeneous quantum photonic integration approach that enables near-unity coupling efficiency at the interface. To showcase our approach, we demonstrate Purcell enhancement of a silicon vacancy (SiV) center in diamond induced by a heterogeneous photonic crystal cavity defined by titanium dioxide (TiO 2 ), as well as optical spin control and readout via a TiO 2 photonic circuit. We further show that, when combined with inverse photonic design, our approach enables efficient and broadband collection of single photons from a color center into a heterogeneous waveguide. Our approach is not restricted to SiV centers or TiO 2 ; it has the potential to be broadly applied to integrate diverse solid-state quantum emitters with thin-film photonic devices where conformal deposition is possible. Together, these results establish a practical route to scalable quantum photonic integrated circuits that combine high-quality quantum emitters with technologically mature photonic platforms.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

NASA's Small Spacecraft and Distributed Systems: Development and Demonstration of Technologies Enabling Swarms and New Spacecraft Platforms with AI and Edge Computing

NASA’s Small Spacecraft & Distributed Systems (SSDS) within the Research and Technology Mission Directorate (RTMD) expands U.S. capability to execute unique missions through targeted investment, rapid development, and flight demonstration of small spacecraft technologies applicable to exploration, science and the commercial space sector. SSDS strategically invests in technology development and on-orbit demonstrations executed across NASA, other government agencies, industry, and academia. The program’s University SmallSat Technology Partnerships initiative awards academic researchers with the opportunity to collaborate with NASA to mature innovative technology. Capabilities aligned with RTMD’s technology shortfalls and interests - power, processing, propulsion, sensors, communications, autonomous navigation, architectures, and advanced applications like artificial intelligence (AI), machine learning, and edge computing - are prioritized in SSDS investments. These investments enable distributed, autonomous, and cooperative small spacecraft systems that support swarm missions extending beyond low Earth orbit into cislunar and deep space. This paper highlights representative SSDS flight demonstrations that mature these capabilities to enable a future operational infrastructure needed to support sustained exploration of the Moon and beyond. SSDS’s investment strategy emphasizes rapid development and on-orbit demonstration to validate spacecraft technologies required for swarms and distributed mission architectures. The Starling swarm technology demonstration mission exemplifies this approach by advancing distributed spacecraft autonomy, cooperative operations, and space situational awareness. Extended flight testing and ongoing studies of next generation swarm configurations and on-orbit space traffic monitoring and management continue to inform future swarm designs. DiskSat’s four-spacecraft demonstration mission represents SSDS’s strategic vision to expand the design space for future small spacecraft through its commitment to advance novel platform concepts that can impact how science is performed on orbit. Continuing to invest in future platforms, the notional PY12 concept is a 12-spacecraft swarm hosting neuromorphic processors and is envisioned as an on-orbit testbed for AI, edge computing, and positioning, navigation and timing technologies. SSDS also invests in single-spacecraft technology demonstrations that underpin the success of future swarm missions and accelerate the availability of validated technologies across the small spacecraft ecosystem. Examples of such demonstrations include Pathfinder Technology Demonstrator-3 (PTD-3), which performed high-rate optical communications; PTD-R, which demonstrated a camera capable of simultaneous ultraviolet and short-wave infrared optical sensing; and CAPSTONE, the Cislunar Autonomous Positioning System Technology and Operations Navigation Experiment, which validated autonomous navigation in cislunar space. Collectively, SSDS-funded demonstrations advance capabilities across swarms and illustrate a coordinated investment strategy to mature high-impact technologies required for autonomous, distributed, and cooperative small spacecraft systems for low Earth orbit, cislunar, and deep space applications. Technology demonstrations strengthen SSDS partnerships with industry, academia, and other government agencies, and promote small spacecraft community adoption of capabilities required to close technical gaps for swarm missions.

Jan Stupl↗

DOE OSTI2025

Entanglement Structure of Non-Gaussian States and How to Measure It

Rapidly growing capabilities of quantum simulators to probe quantum many-body phenomena require new methods to characterize increasingly complex states. Here, we present a protocol that constrains quantum states using experimentally measured correlation functions. This method enables measurement of a quantum state’s entanglement structure, opening a new route to study entanglement-related phenomena. Our approach extends Gaussian state parameterizations by systematically incorporating higher-order correlations. We show the protocol’s usefulness in conjunction with current and forthcoming experimental capabilities, focusing on weakly interacting fermions as a proof of concept. Here, the lowest nontrivial expansion quantitatively predicts early time thermalization dynamics, including signaling the onset of quantum chaos indicated by the entanglement Hamiltonian.

Fermi gases↗

NASA NTRSDate not supplied

NASA's Small Spacecraft and Distributed Systems: Development and Demonstration of Technologies Enabling Swarms and New Spacecraft Platforms with AI and Edge Computing

NASA’s Small Spacecraft & Distributed Systems (SSDS) within the Research and Technology Mission Directorate (RTMD) expands U.S. capability to execute unique missions through targeted investment, rapid development, and flight demonstration of small spacecraft technologies applicable to exploration, science and the commercial space sector. SSDS strategically invests in technology development and on-orbit demonstrations executed across NASA, other government agencies, industry, and academia. The program’s University SmallSat Technology Partnerships initiative awards academic researchers with the opportunity to collaborate with NASA to mature innovative technology. Capabilities aligned with RTMD’s technology shortfalls and interests - power, processing, propulsion, sensors, communications, autonomous navigation, architectures, and advanced applications like artificial intelligence (AI), machine learning, and edge computing - are prioritized in SSDS investments. These investments enable distributed, autonomous, and cooperative small spacecraft systems that support swarm missions extending beyond low Earth orbit into cislunar and deep space. This paper highlights representative SSDS flight demonstrations that mature these capabilities to enable a future operational infrastructure needed to support sustained exploration of the Moon and beyond. SSDS’s investment strategy emphasizes rapid development and on-orbit demonstration to validate spacecraft technologies required for swarms and distributed mission architectures. The Starling swarm technology demonstration mission exemplifies this approach by advancing distributed spacecraft autonomy, cooperative operations, and space situational awareness. Extended flight testing and ongoing studies of next generation swarm configurations and on-orbit space traffic monitoring and management continue to inform future swarm designs. DiskSat’s four-spacecraft demonstration mission represents SSDS’s strategic vision to expand the design space for future small spacecraft through its commitment to advance novel platform concepts that can impact how science is performed on orbit. Continuing to invest in future platforms, the notional PY12 concept is a 12-spacecraft swarm hosting neuromorphic processors and is envisioned as an on-orbit testbed for AI, edge computing, and positioning, navigation and timing technologies. SSDS also invests in single-spacecraft technology demonstrations that underpin the success of future swarm missions and accelerate the availability of validated technologies across the small spacecraft ecosystem. Examples of such demonstrations include Pathfinder Technology Demonstrator-3 (PTD-3), which performed high-rate optical communications; PTD-R, which demonstrated a camera capable of simultaneous ultraviolet and short-wave infrared optical sensing; and CAPSTONE, the Cislunar Autonomous Positioning System Technology and Operations Navigation Experiment, which validated autonomous navigation in cislunar space. Collectively, SSDS-funded demonstrations advance capabilities across swarms and illustrate a coordinated investment strategy to mature high-impact technologies required for autonomous, distributed, and cooperative small spacecraft systems for low Earth orbit, cislunar, and deep space applications. Technology demonstrations strengthen SSDS partnerships with industry, academia, and other government agencies, and promote small spacecraft community adoption of capabilities required to close technical gaps for swarm missions.

Jan Stupl↗

DOE OSTI2025

Intermodal microwave-to-optical transduction using silicon-on-sapphire optomechanical ring resonator

Optomechanical and electro-optomechanical systems have emerged as one of the most promising approaches for quantum microwave-to-optical transduction to interconnect distributed quantum modalities for scaling the quantum systems. These systems use suspended structures to increase mode overlap and mitigate loss to achieve high efficiency. However, the suspended design’s poor heat dissipation under strong drive limits the ultimate efficiency. Here, we demonstrate an unsuspended optomechanical ring resonator (OMR) based on the silicon-on-sapphire (SOS) platform for microwave-to-optical frequency conversion. The OMR achieves a triply resonant optical-to-optical conversion with an enhanced coupling rateG b = 3.6 gigahertz per square-root milliwatt at a peak conversion efficiency of 1.2% with 3.6-milliwatt microwave drive power and a microwave-to-optical conversion efficiency of 1.5 × 10 −5 at 10-milliwatt optical drive power. Our results show that the unsuspended SOS platform, which mitigates the thermal effect and is compatible with superconducting qubits, is a promising platform for optomechanical circuitry and quantum transduction.

Science & Technology - Other Topics↗

DOE OSTI2026

Dirac Fermions and Flat Bands in Phosphorus Carbide Nanotubes: Structural and Quantum Phase Transitions in a Quasi-One-Dimensional Material

Chemically realistic quasi-one-dimensional (1D) materials in which Dirac Fermions and highly degenerate flat bands coexist intrinsically at the Fermi level are exceedingly rare, while representing a highly desirable platform for correlated and topological quantum phenomena. Here, in this work, using specialized symmetry-adapted first-principles calculations we predict a new class of nanomaterials─phosphorus carbide nanotubes (P 2 C 3 NTs)─obtained by rolling monolayer P 2 C 3 , a two-dimensional material shown in a previous letter to host “double Kagome bands”. Both armchair and zigzag P 2 C 3 NTs are stable at room temperature and feature the rare coexistence of Dirac crossings and multiple flat bands at the Fermi level inherited from the underlying honeycomb–Kagome lattice, with the flat bands resilient to elastic deformations. Under large strain, the structure transforms from honeycomb–Kagome to “brick-wall”, accompanied by multiple coupled structural and quantum phase transitions. We also uncover localized edge states, spin splitting from vacancies and dopants, and strain-tunable magnetism. Together, these results establish P 2 C 3 NTs as a chemically specific and mechanically tunable 1D material platform with potential applications in quantum hardware and spintronics.

carbon nanotubes↗

DOE OSTI2025

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗