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Semicoherent symmetric quantum processes: Theory and applications
Discovering pragmatic and efficient approaches to construct ε-approximations of quantum operators such as real (imaginary) time-evolution propagators in terms of the basic quantum operations (gates) is challenging. Prior ε-approximations are invaluable, in that they enable the compilation of classical and quantum algorithm modeling of, e.g., dynamical and thermodynamic quantum properties. In parallel, symmetries are powerful tools concisely describing the fundamental laws of nature; the symmetric underpinnings of physical laws have consistently provided profound insights and substantially increased predictive power. In this work, we consider the interplay between the ε-approximate processes and the exact symmetries in a semicoherent context—where measurements occur at each logical clock cycle. Here we draw inspiration from Pascual Jordan's groundbreaking formulation of nonassociative, but commutative, symmetric algebraic form. Our symmetrized formalism is then applied in various domains such as quantum random walks, real-time evolutions, variational algorithm ansatzes, and efficient entanglement verification. Our work paves the way for a deeper understanding and greater appreciation of how symmetries can be used to control quantum dynamics in settings where coherence is a limited resource.
Introducing Quantum Entanglement and Superposition to Secondary School Students Using Portable, Hands-on Exhibits
Historically, the teaching of quantum mechanics has been reserved for advanced undergraduate physics courses, mostly due to how far removed from classical intuition the subject is. Extensive mathematical background is usually a prerequisite for college-level introductory quantum mechanics courses. However, several ways to introduce quantum mechanics at the secondary school level have been suggested and developed. Unlike most other topics in physics, it is difficult to find intuitive examples of quantum phenomena outside of a specialized laboratory; additionally, straightforward hands-on demonstrations, activities, and experiments are somewhat limited.
Molecular axis distribution moments in ultrafast transient absorption spectroscopy: A path toward ultrafast quantum state tomography
In ultrafast time-resolved experiments with gas phase molecules, the alignment of the molecular axis relative to the polarization of the interacting laser pulses plays a crucial role in determining the dynamics following this light–matter interaction. The molecular axis distribution is influenced by the interacting pulses and is intrinsically linked to the electronic coherences of the excited molecules. However, in typical theoretical calculations of such interactions, the signal is either calculated for a single molecule in the molecular frame or averaged over all possible molecular orientations to compare with the experiment. Such averaging removes information about anisotropy in the molecular-axis distribution, even though anisotropic contributions can play a significant role in the measured experimental signal. Here, we calculate the laboratory frame transient electronic first-order polarization [P (1) ] spectra in terms of separated molecular frame and laboratory frame quantities. The laboratory frame polarizations are compared with orientation-averaged quantum master equation calculations, demonstrating that orientation-averaging captures only the isotropic contributions. We show that our formalism also allows us to evaluate the anisotropic contributions to the spectrum. Lastly, we discuss the application of this approach to achieve ultrafast quantum state tomography using transient absorption spectroscopy and field observables in nonlinear spectroscopy.
Seven governing principles in biology
In physical science such as physics and chemistry, there are governing principles that are universal and applicable to all relevant systems, including energy conservation, entropy increase, uncertainty principle in quantum mechanics, and chemical equilibrium. However, what are governing principles in biology that are unique to all living systems? After collecting opinions and thoughts from diverse scientists and engineers all over the world, I summarize seven governing principles or laws in biology: central dogma, evolution, biological robustness, regeneration, reproduction, development, and causality. Some of these are not necessarily unique in biological systems from a reductionist’s point of view (e.g., causality), and others are applicable predominantly to eukaryotes (e.g., reproduction and development). Notably, many engineering systems have mimicked biological systems to enhance their performance. In this perspective article, I discuss these principles to better understand the rules of life and help construct improved engineering systems that we can use and control in an ethical, safe, and rational way.
Lagrangian formulation of nuclear–electronic orbital Ehrenfest dynamics with real-time TDDFT for extended periodic systems
Here, we present a Lagrangian-based implementation of Ehrenfest dynamics with nuclear–electronic orbital (NEO) theory and real-time time-dependent density functional theory for extended periodic systems. In addition to a quantum dynamical treatment of electrons and selected protons, this approach allows for the classical movement of all other nuclei to be taken into account in simulations of condensed matter systems. Furthermore, we introduce a Lagrangian formulation for the traveling proton basis approach and propose new schemes to enhance its application for extended periodic systems. Validation and proof-of-principle applications are performed on electronically excited proton transfer in the o-hydroxybenzaldehyde molecule with explicit solvating water molecules. These simulations demonstrate the importance of solvation dynamics and a quantum treatment of transferring protons. This work broadens the applicability of the NEO Ehrenfest dynamics approach for studying complex heterogeneous systems in the condensed phase.
Geometric phase in coupled cluster theory
It has been well-established that the topography around conical intersections between excited electronic states is incorrectly described by coupled cluster and many other single reference theories (the intersections are “defective”). Despite this, we show both analytically and numerically that the geometric phase effect (GPE) is correctly reproduced upon traversing a path around a defective excited-state conical intersection (CI) in coupled cluster theory. The theoretical analysis is carried out by using a non-Hermitian generalization of the linear vibronic coupling approach. Interestingly, the approach qualitatively explains the characteristic (incorrect) shape of the defective CIs and CI seams. Moreover, the validity of the approach and the presence of the GPE indicate that defective CIs are local (and not global) artifacts. This implies that a sufficiently accurate coupled cluster method could predict nuclear dynamics, including geometric phase effects, as long as the nuclear wavepacket never gets too close to the conical intersections.
Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states
Advances in coherent light sources and development of pump–probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron–nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. Furthermore, this work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.
Non-equilibrium rate theory for polariton relaxation dynamics
We derive an analytic expression of the non-equilibrium Fermi’s golden rule (NE-FGR) expression for a Holstein–Tavis–Cumming Hamiltonian, a universal model for many molecules collectively coupled to the optical cavity. These NE-FGR expressions capture the full-time-dependent behavior of the rate constant for transitions from polariton states to dark states. The rate is shown to be reduced to the well-known frequency domain-based equilibrium Fermi’s golden rule (E-FGR) expression in the equilibrium and collective limit and is shown to retain the same scaling with the number of sites in non-equilibrium and non-collective cases. We use these NE-FGR to perform population dynamics with a time-non-local and time-local quantum master equation and obtain accurate population dynamics from the initially occupied upper or lower polariton states. Furthermore, NE-FGR significantly improves the accuracy of the population dynamics when starting from the lower polariton compared to the E-FGR theory, highlighting the importance of the non-Markovian behavior and the short-time transient behavior in the transition rate constant.
Atomistically resolved hot exciton relaxation dynamics in CdSe quantum dots: Experiment and theory
Semiconductor quantum dots (QDs) are well known to give rise to a quantum confined structure of excitons. Because of this quantum confinement, new physics of hot exciton relaxation dynamics arises. Decades of work using transient absorption (TA) spectroscopy have yielded initial simple observations, such as estimates of the cooling rate from single pump photon energy experiments. More detailed TA experiments employed variable pump photon energies to measure excitonic state-resolved transition rates. These TA measurements, usually the simplest form, have been employed to characterize QDs and their relaxation dynamics to this day. Yet, these TA measurements are fundamentally lacking in their ability to measure energy-resolved hot exciton cooling, which requires observation of the full cooling history through the real excitonic manifold. Here, we employ coherent multi-dimensional spectroscopy (CMDS) to perform an atomistically directed study of hot exciton cooling in CdSe QDs, revealing energy resolved relaxation dynamics. CMDS experiments are compared with simulations and prior TA measurements and simpler theories. Our findings reveal a hot exciton relaxation dynamics landscape. This relaxation dynamics landscape is a linear or sub-linear function of excess energy for different structures of QDs, with a strong size dependence. Our model simulations parameterized by the empirical pseudopotential model reproduces the experimental functional form and the dependence upon QD diameter and shell.
Comparison between explicit and implicit discretization strategies for a dissipative thermal environment
We investigate strategies for simulating open quantum systems coupled to dissipative baths by comparing explicit wave function-based discretization [via multi-layer multi-configuration time-dependent Hartree (ML-MCTDH)] and the implicit density matrix-based master equation method [via tree tensor network hierarchical equations of motion (TTN-HEOM)]. For dissipative baths characterized by exponentially decaying bath correlation functions, the implicit discretization approach of HEOM—rooted in bath correlation function decompositions—proves significantly more efficient than explicit discretization of the bath into discrete harmonic modes. Explicit methods, like ML-MCTDH, require extensive mode discretization to approximate continuum baths, leading to computational bottlenecks. Case studies for two-level systems and a Fenna–Matthews–Olson complex model highlight TTN-HEOM’s superiority in capturing dissipative dynamics with relaxations with a minimal number of auxiliary modes, while the explicit methods are as exact as the HEOM in pure dephasing regimes. This comparison is enabled by the TENSO package, which has both ML-MCTDH and TTN-HEOM implemented using the same computational structure and propagation strategy.
A simple fourth order propagator based on the Magnus expansion in the Liouville space: Application to a Λ-system and assessment of the rotating wave approximation
A simple fourth-order propagator [Ture and Jang, J. Phys. Chem. A 128, 2871 (2024)] based on the Magnus expansion is extended to the Liouville space for both closed-system and Lindbladian open-system quantum dynamics. For both dynamics, commutator free versions of fourth-order propagators are provided as well. These propagators are then applied to the dynamics of a driven Λ-system, where Lindblad terms represent the effect of a photonic bath. For both dynamics, the accuracy of the rotating wave approximation (RWA) for the matter–radiation interaction is assessed. We confirmed reasonable performance of RWA for weak and resonant fields. However, small errors appear for moderate fields and substantial errors can be found for strong fields where coherent population trapping can still be expected. We also found that the presence of bath for open-system quantum dynamics consistently reduces the errors of the RWA. These results provide quantitative information on how the RWA breaks down beyond weak field or for non-resonant cases. Major results are benchmarked against results of our sixth-order ME-based propagator. Finally, we also provide numerical comparison of our algorithms with other fourth-order algorithms for the Λ-system. These confirm reasonable performance of our simple propagators and the improvement gained through commutator-free expressions.
2023 Roadmap on molecular modelling of electrochemical energy materials
New materials for electrochemical energy storage and conversion are the key to the electrification and sustainable development of our modern societies. Molecular modelling based on the principles of quantum mechanics and statistical mechanics as well as empowered by machine learning techniques can help us to understand, control and design electrochemical energy materials at atomistic precision. Therefore, this roadmap, which is a collection of authoritative opinions, serves as a gateway for both the experts and the beginners to have a quick overview of the current status and corresponding challenges in molecular modelling of electrochemical energy materials for batteries, supercapacitors, CO 2 reduction reaction, and fuel cell applications.
Order-by-order uncertainties of nucleon-nucleon Wolfenstein amplitudes in chiral effective field theory
Quantum mechanical invariance principles dictate the most general operator structure that can be present in the nucleon-nucleon (NN) interaction. Five independent operators appear in the on-shell NN amplitude together with five corresponding coefficient functions. The usual choice for these coefficient functions is known as the NN Wolfenstein amplitudes. We analyze the order-by-order convergence of each of the five NN Wolfenstein amplitudes predicted by a semilocal coordinate space potential implementation of chiral effective field theory (𝜒EFT). We do this at laboratory kinetic energies between 25 and 200 MeV for both neutron-proton and proton-proton scattering. Our analysis uses the Gaussian-process methods developed by the BUQEYE Collaboration to describe the contributions of each 𝜒EFT order, and so yields truncation uncertainties for each Wolfenstein amplitude that are correlated across scattering angles. We combine information on the size of different orders in the EFT to infer the 𝜒EFT breakdown scale for each amplitude, finding, on average, Λ 𝑏 between 750 and 800 MeV. Furthermore, with this choice of Λ 𝑏 , the EFT truncation uncertainties cover both higher-order results and empirical Wolfenstein amplitudes well for all orders other than the leading order.
Architecture for Quantum-in-the Loop Real-Time Simulations for Designing Resilient Smart Grids
With the power grid growing more complex every day with the inclusion of new sensors and regulatory approvals that enable end-users and small local developers to participate in the grid, it is becoming challenging for conventional smart grid simulation, emulation, and testing technologies to keep up. In this work, we propose that quantum-encoded real-time simulations can be helpful under the new paradigm and operational circumstances to solve optimization problems for power grids. By leveraging the principles of quantum mechanics, the proposed quantum-in-loop (QIL) framework will enable better and faster optimization solutions based on real-world, real-time data streams, facilitating the real-time planning and operations of electrical grids that rely on millions of distributed sensors and controllers. Furthermore, QIL will allow researchers and engineers to assist utilities in designing, developing, and de-risking algorithms to optimize power grid operation and resilience by considering inputs from millions of grid-connected devices. QIL framework is being developed to have a self-limiting triage mechanism, which will help engineers and practitioners identify fundamental physical limits on quantum processors, revealing what quantum algorithms can and cannot do in utility-specific use cases and must continue to count on classical high-performance computing infrastructure.
How Well Can Quantum Embedding Method Predict the Reaction Profiles for Hydrogenation of Small Li Clusters?
Quantum computing leverages the principles of quantum mechanics in novel ways to tackle complex chemistry problems that cannot be accurately addressed using traditional quantum chemistry methods. However, the high computational cost and available number of physical qubits with high fidelity limit its application to small chemical systems. This work employed a quantum-classical framework which features a quantum active space-embedding approach to perform simulations of chemical reactions that require up to 14 qubits. This framework was applied to prototypical example metal hydrogenation reactions: the coupling between hydrogen and Li 2 , Li 3 , and Li 4 clusters. Particular attention was paid to the computation of barriers and reaction energies. The predicted reaction profiles compare well with advanced classical quantum chemistry methods, demonstrating the potential of the quantum embedding algorithm to map out reaction profiles of realistic gas-phase chemical reactions to ascertain qualitative energetic trends. Additionally, the predicted potential energy curves provide a benchmark to compare against both current and future quantum embedding approaches.
Decoherence Noise on the Superconducting Qubits Training Program
Quantum computing is a growing field with promising applications in a variety of fields such as healthcare, energy consumption, and cryptography. Quantum computing leverages the principles of quantum mechanics - superposition and entanglement. Yet, in the Noisy Intermediate Scale Quantum (NISQ) Era - quantum systems face the major challenge of decoherence due to noise. This era is characterized by low amounts of qubits and high gate error. Decoherence leads to the loss of the quantum information stored in the qubit. Noise occurs with any quantum system that is exposed to the environment. It should also be noted that quantum information can be stored in the cavity - Fermilab specializes in coupling transmons to ultrahigh-Q SRF cavities. The Superconducting Qubits Training Program (SQTP) provides a visualization for beginners in quantum computing. The open quantum system simulated is a superconducting qubit (two-level atom) coupled to a microwave cavity whose excitations are photons. The Rotating Wave Approximation of the Jaynes-Cumming Hamiltonian is used. SQTP utilizes open-source Python-based libraries scQubits, NumPy, and QuTiP alongside the Master Lindblad equation. In this project, we study the different decay behaviors of qubits and cavities with collapse operators.
Harness the power of atomistic modeling and deep learning in biofuel separation
Biofuels offer a remarkable, sustainable energy source for a future of clean energy. The development of efficient biofuel separation plays a crucial role in achieving cost-effective utilization of biofuel. In this chapter, we provide an overview of the recent advancements in atomistic-level modeling and deep learning in the rational design of novel, efficient biofuel separation. The fundamental principles of quantum and statistical mechanics are covered in appropriate detail to highlight their underlying differences in theory. The methodologies of several molecular representations and deep learning algorithms applicable to biofuel separation are briefly demonstrated as well. The applications, successes, and risks of employing density functional theory, ab initio molecular dynamics, classical molecular dynamics, and deep learning are provided to showcase their recent accomplishments in biofuel separation as well as potential improvements in both methodology and application. Lastly, a vision for the future growth of these methods is illustrated.