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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Saturation and Recurrence of Quantum Complexity in Random Local Quantum Dynamics

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing—in studying the dynamics of quantum many-body systems and the long-time properties of anti–de Sitter black holes. In this context, Brown and Susskind [] conjectured that the complexity of a chaotic quantum system grows linearly in time up to times exponential in the system size, saturating at a maximal value, and remaining maximally complex until undergoing recurrences at doubly exponential times. In this work, we prove the saturation and recurrence of complexity in two models of chaotic time evolutions based on (i) random local quantum circuits and (ii) stochastic local Hamiltonian evolution. Our results advance an understanding of the long-time behavior of chaotic quantum systems and could shed light on the physics of black-hole interiors. From a technical perspective, our results are based on establishing new quantitative connections between the Haar measure and high-degree approximate designs, as well as the fact that random quantum circuits of sufficiently high depth converge to approximate designs. Published by the American Physical Society 2024

Oszmaniec, Michał (ORCID:0000000249466835)↗
DOE OSTI2025

Classical Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. Here, in this Letter, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while nonsymmetric noise leads to highly specific leakage errors that are block diagonal in the symmetry representation. We support our findings with numerical studies of a transverse-field Ising model and a quantum error detecting code subject to spatiotemporally correlated multiaxis noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.

decoherence↗
DOE OSTI2026

Predicting Open Quantum Dynamics with Data-Informed Quantum-Classical Dynamics

We introduce a data-informed quantum-classical dynamics (DIQCD) approach for predicting the evolution of an open quantum system. The equation of motion in DIQCD is a Lindblad equation with a flexible, time-dependent Hamiltonian that can be optimized to fit sparse and noisy data from local observations of an extensive open quantum system. We demonstrate the accuracy and efficiency of DIQCD for both experimental and simulated quantum devices. We show that DIQCD can predict entanglement dynamics of ultracold molecules (calcium fluoride) in optical tweezer arrays. DIQCD also successfully predicts carrier mobility in organic semiconductors (rubrene) with accuracy comparable to nearly exact numerical methods.

Lindblad equation↗
DOE OSTI2025

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein–Tavis–Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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↗
DOE OSTI2026

Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states

Understanding real-time dynamics of interacting quantum fields in curved space-time remains a major theoretical challenge. We employ tensor network methods to study such dynamics using interacting scalar and gauge theories in 1+1 spacetime dimensions, subject to a quench modeling a homogeneously expanding gravitational background. The models considered are the scalar λϕ 4 theory and the Schwinger model, i.e. a Dirac fermion coupled to a U(1) gauge field which is equivalent via bosonization to a scalar field with a cosine self-interaction. In the free scalar limit, both theories reproduce known analytical results, providing a nontrivial numerical validation of bosonization in curved spacetime for the Schwinger model. Our central finding is that self-interactions lead to a suppression of gravitational particle production compared to the free-field case, as evidenced by two-point functions and the spectra of produced particles. We further examine the behavior of entanglement generation and find that interactions suppress entanglement growth in the λϕ 4 theory, while in the Schwinger model, the interplay between suppressed particle production and enhanced inter-particle correlations leads to more complex entanglement behavior. Our results pave the way for further explorations of nonperturbative quantum real-time dynamics of interacting scalar and gauge theories in arbitrary gravitational backgrounds.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements

The adaptive variational quantum dynamics simulation (AVQDS) method performs real-time evolution of quantum states using automatically generated parametrized quantum circuits that often contain substantially fewer gates than Trotter circuits. Here we report an improved version of the method, which we call AVQDS(T), by porting the tiling efficient trial circuits with rotations implemented simultaneously technique. The algorithm adaptively adds layers of disjoint unitary gates to the ansatz circuit so as to keep the McLachlan distance, a measure of the accuracy of the variational dynamics, below a fixed threshold. Here we perform benchmark noiseless AVQDS(T) simulations of quench dynamics in local spin models and compare with an alternative adaptive variational approach on quantum resource requirement. Quantum dynamical simulations implementing realistic noise channels are also reported. Finally, we propose a way to substantially alleviate the measurement overhead of AVQDS(T) while maintaining high accuracy by synergistically integrating quantum circuit calculations on quantum processing units with classical calculations using, e.g., tensor networks to evaluate the quantum geometric tensor. We showcase that this approach enables AVQDS(T) to deliver more accurate results than simulations using a fixed ansatz of comparable final depth for a significant time duration with fewer quantum resources.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Path integral molecular dynamics: A high-fidelity approach to quantum dynamics of electrons

We investigate electron transport in the uniform electron gas using ring-polymer molecular dynamics (RPMD). Working in the weakly coupled, non-degenerate regime, we use RPMD to probe how the onset of quantum diffraction effects at high temperature reshapes electron–electron collisions and leads to a classical-to-quantum crossover in macroscopic transport properties. Static thermodynamics obtained with RPMD are consistent with the weak-coupling equation of state, confirming correct quantum Boltzmann sampling. Real-time transport extracted from mean square displacements exhibits the expected ballistic-to-diffusive transition and a systematic reduction of the electronic self-diffusivity as quantum effects strengthen, due to quantum diffraction modifying electron–electron collisions. Direct ring-polymer scattering simulations reveal diffractive “softening” of binary deflections, providing a micro-to-macro link between collision physics and diffusion. The present study establishes RPMD as a quantitative, trajectory-based tool for electron transport across the classical–quantum crossover and furnishes benchmarks for improving Coulomb-log interpolation models. We outline extensions to multi-component plasmas and a path to incorporate Fermi–Dirac statistics within path-integral dynamics.

Electronic transport↗
DOE OSTI2025

Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. Here, we introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian that maps the evolution to a diffusion problem in a one-dimensional lattice with nearest-neighbor hopping probabilities that are inhomogeneous and time dependent. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

A fractional calculus framework for open quantum dynamics: From Liouville to Lindblad to memory kernels

Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini–Kossakowski–Sudarshan–Lindblad equation uniquely characterizes Markovian completely positive and trace-preserving (CPTP) evolution, many physical platforms display non-Markovian features such as algebraic relaxation and coherence backflow. Fractional calculus provides a natural way to model such long-memory behavior through power-law temporal kernels introduced by fractional time derivatives. Here, we develop a unified framework that embeds fractional master equations within the broader hierarchy of open-system formalisms. The fractional equation forms a structured subclass of memory-kernel models, reduces to the Lindblad form at unit order, and, through Bochner–Phillips subordination, admits a CPTP representation as an average over Lindblad semigroups. Its resolvent structure further connects fractional dynamics to established non-Markovian approaches, including Nakajima–Zwanzig kernels and hierarchical equations of motion, providing a compact surrogate for long-memory effects. This formulation positions fractional calculus as a rigorous and practical language for modeling non-Markovian quantum dynamics in chemical physics and physical chemistry, providing a CPTP-preserving, computationally efficient surrogate for structured condensed-phase environments where long-time memory and dissipation play a central role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum dynamics simulation of the advection-diffusion equation

The advection-diffusion equation is simulated via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive variational quantum dynamics simulation (AVQDS). These schemes were originally developed for the Hamiltonian simulation of many-body quantum systems. The finite-difference discretized operator of the transport equation is formulated as a Hamiltonian and solved without the need for ancillary qubits. Computations are conducted on a quantum simulator (IBM Qiskit Aer) and a superconducting quantum hardware (IBM Fez). The former emulates the latter without the noise. The actual hardware implementation experiences significant noise. The results of the quantum simulator are compared with data from direct numerical simulation (DNS) with infidelities of the order 10 −5 . In the quantum simulator, Trotterization is observed to have the lowest infidelity and is suitable for fault-tolerant computation. The AVQDS algorithm requires the lowest gate count and circuit depth. The VarQTE algorithm is the next best in terms of gate counts, but the number of its optimization variables is directly proportional to the number of qubits. Due to current hardware limitations, Trotterization cannot be implemented, as it has an overwhelmingly large number of operations. Meanwhile, AVQDS and VarQTE can be executed at the hardware level. These algorithms present a new paradigm for computational transport phenomena on quantum computers.

Alipanah, Hirad [Univ. of Pittsburgh, PA (United S↗
DOE OSTI2025

Multiscale Nuclear-Electronic Orbital Quantum Dynamics in Complex Environments

Many renewable energy conversion processes rely on the movement of protons as well as electrons through either electrocatalysis or photoexcitation. The simulation of such processes requires a quantum mechanical description of coupled nuclear-electronic dynamics in a solvent or heterogeneous chemical environment. The overall objective of this project is the development of theoretical and computational capabilities for simulating nuclear-electronic quantum dynamics in complex environments and the creation of high-performance, open-source software. This multiscale framework will enable simulations of the real-time dynamics of nonequilibrium excited state proton-coupled electron transfer, quantum decoherence, vibronic energy transfer, and ultrafast radiolysis, as well as their associated time-resolved multidimensional spectroscopies. An important outcome of this project will be a sustainable, reusable, and interoperable open-source software ecosystem. This software will be designed for emerging exascale and future national leadership computers. Another key outcome will be a multiscale quantum dynamics method and software enabling simulations of nonequilibrium nuclear-electronic quantum dynamics in complex environments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Coherence-Induced Deep Thermalization Transition in Random Permutation Quantum Dynamics

We report a phase transition in the projected ensemble—the collection of postmeasurement wave functions of a local subsystem obtained by measuring its complement. The transition emerges in systems undergoing random permutation dynamics, a type of quantum time evolution wherein computational basis states are shuffled without creating superpositions. It separates a phase exhibiting deep thermalization, where the projected ensemble is distributed over Hilbert space in a maximally entropic fashion (Haar random), from a phase where it is minimally entropic (“classical bit-string ensemble”). Crucially, this deep thermalization transition is invisible to the subsystem’s density matrix, which always exhibits thermalization to infinite temperature across the phase diagram. Through a combination of analytical arguments and numerical simulations, we show that the transition is tuned by the total amount of injected by the input state and the measurement basis, and is exhibited robustly across different microscopic models. Our findings represent a novel form of ergodicity-breaking universality in quantum many-body dynamics, characterized not by a failure of regular thermalization, but rather by a failure of deep thermalization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Valley-Mediated Singlet- and Triplet-Polaron Interactions and Quantum Dynamics in a Doped WSe 2 Monolayer

In doped transition metal dichalcogenides, optically created excitons (bound electron-hole pairs) can strongly interact with a Fermi sea of electrons to form Fermi polaron quasiparticles. When there are two distinct Fermi seas, as is the case in WSe 2 , there are two flavors of lowest-energy (attractive) polarons—singlet and triplet—where the exciton is coupled to the Fermi sea in the same or opposite valley, respectively. Using two-dimensional coherent electronic spectroscopy, we analyze how their quantum decoherence evolves with doping density and determine the condition under which stable Fermi polarons form. Because of the large oscillator strength associated with these resonances, intrinsic quantum dynamics of polarons as well as valley coherence between coupled singlet- and triplet polarons occur on subpicosecond timescales. Surprisingly, we find that a dark-to-bright state conversion process leads to a particularly long-lived singlet polaron valley polarization, persisting up to 200–800 ps. Valley coherence between the singlet- and triplet polaron is correlated with their energy fluctuations. In conclusion, our finding provides valuable guidance for the electrical and optical control of spin and valley indexes in atomically thin semiconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗
DOE OSTI2025

Solid-state platform for cooperative quantum dynamics driven by correlated emission

While traditionally regarded as an obstacle to quantum coherence, recent breakthroughs in quantum optics have shown that the dissipative interaction of a qubit with its environment can be leveraged to protect quantum states and synthesize many-body entanglement. Inspired by this progress, here we set the stage for the—as yet uncharted—exploration of analogous cooperative phenomena in hybrid solid-state platforms. We develop a comprehensive formalism for the quantum many-body dynamics of an ensemble of solid-state spin defects interacting with the magnetic field fluctuations of a common solid-state reservoir. Our framework applies to any solid-state reservoir whose fluctuating spin, pseudospin, or charge degrees of freedom generate magnetic fields. To understand whether correlations induced by dissipative processes can play a relevant role in a realistic experimental setup, we apply our model to a qubit array interacting via the spin fluctuations of a ferromagnetic bath. Our results show that the low-temperature collective relaxation rates of the qubit ensemble can display clear signatures of super- and subradiance, i.e., forms of cooperative dynamics traditionally achieved in atomic ensembles. We find that the solid-state analog of these cooperative phenomena is robust against spatial disorder in the qubit ensemble and thermal fluctuations of the magnetic reservoir, providing a route for their feasibility in near-term experiments. Finally, our work lays the foundation for a multiqubit approach to quantum sensing of solid-state systems and the direct generation of many-body entanglement in spin-defect ensembles. Furthermore, we discuss how the tunability of solid-state reservoirs opens up novel pathways for exploring cooperative phenomena in regimes beyond the reach of conventional quantum optics setups.

NV centers↗
DOE OSTI2026

On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials

Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. Here, in this work, we analyze many-body quantum systems with Coulomb interactions, which are fundamental to electronic and molecular systems. We prove that Trotterization for such unbounded Hamiltonians achieves a 1/4-order convergence rate, with explicit polynomial dependence on the number of particles. The result holds for all initial wavefunctions in the domain of the Hamiltonian, and the 1/4-order convergence rate is optimal, as previous work has numerically demonstrated that it can be saturated by a specific initial ground state. The main challenges arise from the many-body structure and the singular nature of the Coulomb potential. Our proof strategy differs from prior state-of-the-art Trotter analyses, addressing both difficulties in a unified framework. Our analysis treats the Coulomb potential as an unbounded operator without modification or regularization, and does not rely on spatial discretization, making it compatible with both first- and second-quantized circuit constructions.

Fang, Di [Duke Univ., Durham, NC (United States)]↗
DOE OSTI2025

Quantum dynamics of the temporary capture of light atoms by superfluid helium nanodroplets at very low collision energies (≈1–13 meV): the case of the hydrogen atom and its isotopes

The capture dynamics of a H atom and isotopic variants [D, T and Q (hypothetical isotope of mass equal to four times the mass of H)] by a superfluid helium nanodroplet (HeND) has been investigated theoretically. The HeND (T = 0.37 K) is ( 4 He) N=400 and a mean field quantum hybrid approach [TDDFT (helium) + quantum wave packet (H, D, T or Q)] at zero angular momentum, is used to explore a rather wide range of very low initial kinetic energies (E k,0 ≈ 10–150 K). The analysis of the capture mechanism shows the existence of a dynamical barrier and a dynamical minimum that play key roles to understand the time evolution of the capture, especially the former property. In general, the H atom shows a different behavior from the other isotopes, with the behavior of T and Q being very similar to each other and the D atom behaving inbetween H and T. Besides, it is worth noting that, in principle, at the very low initial kinetic energies considered only “short” and “long” lived atom⋯HeND collision complexes are formed, i.e., in the atom-helium nanodroplet collision only the temporary capture of the atom takes place. The different behaviors observed have been interpreted considering the faster motion of the H atom when colliding with ( 4 He) N=400 and the more quantum character of the H behavior both due to its significantly lower mass. As far as we know, this is the first quantum dynamics study carried out on the collision of light atoms with HeNDs at very low energies.

Sternberg, Michael [Argonne National Laboratory (A↗