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NASA NTRS1972

Classical laser.

In this paper a completely classical model for laser action is discussed. An active medium consisting of classical anharmonic oscillators interacts with a classical electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. The results for the classical model are found to be similar to those for a semiclassical model of the ammonia-beam maser. The conclusion is that laser action is not intrinsically a quantum-mechanical effect. The classical-laser theory as given in this paper can also be applied to the case of the electron-cyclotron maser.

Borenstein, M.↗

NASA NTRS1977

Rotational excitation of linear molecules by collisions with atoms - Comparison of classical and quantum methods

Exact quantum results for the rotational excitation of rigid linear molecules by collisions with atoms are compared with classical trajectory results. The systems studied are CO-He, CS-H2, OCS-H2, HCl-He, and HCl-Ar at collision energies up to 500/cm. Total cross sections and state to state rate constants are compared. The classical results are found to be in good agreement with the quantum results on the average. Differences arising from the existence of purely quantum effects are clearly evident, but consistent and predictable. Two methods of extracting state selective information from moments of the classical distribution are examined and found to be less reliable than the usual histogram method. In conjunction with previous comparisons of classical and quantum results these calculations provide a useful measure of the limitations and reliability of classical trajectories.

Chapman, S.↗

NASA NTRS1995

Exact, E = 0, classical and quantum solutions for general power-law oscillators

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.

Nieto, Michael Martin↗

NASA NTRS2011

Phase-Sensitive Coherence and the Classical-Quantum Boundary in Ghost Imaging

The theory of partial coherence has a long and storied history in classical statistical optics. the vast majority of this work addresses fields that are statistically stationary in time, hence their complex envelopes only have phase-insensitive correlations. The quantum optics of squeezed-state generation, however, depends on nonlinear interactions producing baseband field operators with phase-insensitive and phase-sensitive correlations. Utilizing quantum light to enhance imaging has been a topic of considerable current interest, much of it involving biphotons, i.e., streams of entangled-photon pairs. Biphotons have been employed for quantum versions of optical coherence tomography, ghost imaging, holography, and lithography. However, their seemingly quantum features have been mimicked with classical-sate light, questioning wherein lies the classical-quantum boundary. We have shown, for the case of Gaussian-state light, that this boundary is intimately connected to the theory of phase-sensitive partial coherence. Here we present that theory, contrasting it with the familiar case of phase-insensitive partial coherence, and use it to elucidate the classical-quantum boundary of ghost imaging. We show, both theoretically and experimentally, that classical phase-sensitive light produces ghost imaging most closely mimicking those obtained in biphotons, and we derived the spatial resolution, image contrast, and signal-to-noise ratio of a standoff-sensing ghost imager, taking into account target-induced speckle.

coherence theory↗

DOE OSTI2021

Simultaneous classical and quantum communication scheme based on coherent detection

An improved coherent communication scheme is provided. The coherent communication scheme encodes both classical and quantum information simultaneously using isolated groups of states: classical information is represented by different groups and can be decoded deterministically; and quantum information is represented by highly overlapped states within the same group, thus guaranteeing security. Decoding includes projecting the detection results at the receiver to one of the distinguishable encoding groups first, which allows the classical information to be read out, and then generating a quantum key from the residual randomness. This communications scheme enables simultaneous classical communication and QKD over the same communication channel using the same transmitter and receiver, opening the door to operate QKD in the background of classical communication and at negligible costs.

Qi, Bi↗

DOE OSTI2021

Radiative classical gravitational observables at $ \mathcal{O} $(G 3 ) from scattering amplitudes

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and N =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $ \mathcal{O} $(G 3 ) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Impact of Thermonuclear Reaction Rate Uncertainties on the Identification of Presolar Grains from Classical Novae

Approximately 30%–40% of classical novae generate dust between 20 and 100 days following the eruption. However, there has yet to be a definitive identification of presolar stardust grains originating from classical novae. While multiple studies have suggested a nova origin for specific grains, aligning simultaneously all measured isotopic ratios of a specific grain with those predicted from simulations remains challenging. Using Monte Carlo simulations, this work investigates how uncertainties in thermonuclear reaction rates influence the isotopic ratios predicted in simulations of classical novae, specifically impacting the identification of presolar grains. In particular, we address two questions: (i) What is the impact of uncertainties in reaction rates on the range of isotopic ratios predicted by classical nova simulations? (ii) Which reaction rate uncertainties most significantly influence the predicted abundance ratios in presolar grains? Our results show that current reaction rate uncertainties affect the isotopic ratios of 12 C/ 13 C, 14 N/ 15 N, 16 O/ 17 O, 16 O/ 18 O, 24 Mg/ 25 Mg, 24 Mg/ 26 Mg, 26 Al/ 27 Al, and 28 Si/ 29 Si by less than 20% in either carbon–oxygen or oxygen–neon (ONe) novae, especially when considering the mixing of matter throughout the entire envelope. However, the isotopic ratios of 28 Si/ 30 Si, 32 S/ 33 S, and 32 S/ 34 S in ONe novae are exceptions: their variability greatly exceeds a factor of 2 due to the uncertainties in the reaction rates of 30 P(p,γ) 31 S, 33 S(p,γ) 34 Cl, and 34 S(p,γ) 35 Cl, respectively. These results highlight the significant influence of specific reaction rates on the predicted abundance ratios and underscore the necessity for accurate nuclear measurements to reduce these uncertainties.

Classical novae↗

DOE OSTI2025

Does provable absence of barren plateaus imply classical simulability?

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We collect evidence-on a case-by-case basis-that many commonly used models whose loss landscapes avoid barren plateaus can also admit classical simulation, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing that quantum computers can be essential for collecting data, our analysis sheds doubt on the information processing capabilities of many parametrized quantum circuits with provably barren plateau-free landscapes. We end by discussing the (many) caveats in our arguments including the limitations of average case arguments, the role of smart initializations, models that fall outside our assumptions, the potential for provably superpolynomial advantages and the possibility that, once larger devices become available, parametrized quantum circuits could heuristically outperform our analytic expectations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Classical discrete time crystals

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator–prey models to Faraday waves and a.c.-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially long timescales. Power-law correlations are present along a first-order line, which terminates at a critical point. We analyse the transition by mapping it to the locked-to-sliding transition of a d.c.-driven charge density wave. To conclude, building upon results from the field of probabilistic cellular automata, we conjecture the existence of classical time crystals with true long-range order, where time-translation symmetry is broken out to infinite times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Analytic and numerical vibronic spectra from quasi-classical trajectory ensembles

The truncated Wigner approximation to quantum dynamics in phase space is explored in the context of computing vibronic line shapes for monomer linear optical spectra. We consider multiple model potential forms including a shifted harmonic oscillator with both equal and unequal frequencies on the ground and excited state potentials as well as a shifted Morse potential model. For the equal-frequency shifted harmonic oscillator model, we derive an analytic expression for the exact vibronic line shape that emphasizes the importance of using a quantum mechanical distribution of phase space initial conditions. For the unequal-frequency shifted harmonic oscillator model, we are no longer able to obtain an exact expression for the vibronic line shape in terms of independent deterministic classical trajectories. We show how one can rigorously account for corrections to the truncated Wigner approximation through nonlinear responses of the line shape function to momentum fluctuations along a classical trajectory and demonstrate the qualitative improvement in the resulting spectrum when the leading-order quantum correction is included. Finally, we numerically simulate absorption spectra of a highly anharmonic shifted Morse potential model. We find that, while finite quantization and the dissociation limit are captured with reasonable accuracy, there is a qualitative breakdown of the quasi-classical trajectory ensemble’s ability to describe the vibronic line shape when the relative shift in Morse potentials becomes large. The work presented here provides clarity on the origin of unphysical negative features known to contaminate absorption spectra computed with quasi-classical trajectory ensembles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Possibilistic simulation of quantum circuits by classical circuits

In a breakthrough work, Bravyi, Gosset, and König (BGK) [Science 362, 308 (2018)] unconditionally proved that constant-depth quantum circuits are more powerful than their classical counterparts. Here, their result is equivalent to saying that a particular family of constant-depth quantum circuits takes classical circuits at least Ω⁡(log⁡n) depth to “simulate,” in a certain sense. In our paper, we formalize their sense of simulation, which we call “possibilistic simulation” or “p-simulation,” and construct explicit classical circuits that can p-simulate any depth-d quantum circuit with Clifford and t T-gates in depth O(d+t). Our classical circuits use {NOT,AND,OR} gates of fan-in ≤ 2.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm

The trading of fidelity for scale enables approximate classical simulators such as matrix product states (MPSs) to run quantum circuits beyond exact methods. A control parameter, the so-called bond dimension $\mathcal{χ}$ for MPSs, governs the allocated computational resources and the output fidelity. Here, we characterize the fidelity for the quantum approximate optimization algorithm by the expectation value of the cost function that it seeks to minimize and find that it follows a scaling law $\mathscr{F}$(ln $\mathcal{χ}$/N), where N is the number of qubits. With ln $\mathcal{χ}$ amounting to the entanglement that a MPS can encode, we show that the relevant variable for investigating the fidelity is the entanglement per qubit. Importantly, our results calibrate the classical computational power required to achieve the desired fidelity and benchmark the performance of quantum hardware in a realistic setup. For instance, we quantify the hardness of performing better classically than a noisy superconducting quantum processor by readily matching its output to the scaling function. Moreover, we relate the global fidelity to that of individual operations and establish its relationship with $\mathcal{χ}$ and N. We sharpen the requirements for noisy quantum computers to outperform classical techniques at running a quantum optimization algorithm in speed, size, and fidelity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity

Recent advancements have highlighted the limitations of current quantum systems, particularly the restricted number of qubits available on near-term quantum devices. This constraint greatly inhibits the range of applications that can leverage quantum computers. Moreover, as the available qubits increase, the computational complexity grows exponentially, posing additional challenges. Consequently, there is an urgent need to use qubits efficiently and mitigate both present limitations and future complexities. To address this, existing quantum applications attempt to integrate classical and quantum systems in a hybrid framework. In this study, we concentrate on quantum deep learning and introduce a collaborative classical-quantum architecture called co-TenQu. The classical component employs a tensor network for compression and feature extraction, enabling higher-dimensional data to be encoded onto logical quantum circuits with limited qubits. On the quantum side, we propose a quantum-state-fidelity-based evaluation function to iteratively train the network through a feedback loop between the two sides. co-TenQu has been implemented and evaluated with both simulators and the IBM-Q platform. Compared to state-of-the-art approaches, co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. Additionally, it outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.

42 ENGINEERING↗

DOE OSTI2024

A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the “noise-aware numerical optimization” literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. In conclusion, we study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in scikit-quant.

classical optimizers↗

DOE OSTI2018

Mineralogical, nanostructural, and Ca isotopic evidence for non-classical calcium phosphate mineralization at circum-neutral pH

Growth pathways of calcium (Ca) phosphate minerals are still under debate, but non-classical growth pathways, which encompass any mode of growth involving attachment of primary particles instead of monomer ions, are currently thought to dominate over classical mechanisms under a wide range of growth conditions. Cation desolvation during ion-by-ion growth is associated with the preferential uptake of isotopically light Ca in Ca-bearing phases, so the Ca isotope composition of Ca-bearing minerals can help to elucidate the dominant growth mechanism. Here, we combine stable Ca isotope analysis with mineralogical characterization and nanoscale imaging of growth features to determine for the first time the rate-dependent Ca isotope fractionation during seeded growth of hydroxyapatite (HAP) involving an octacalcium phosphate (OCP) precursor. Our data reveal that growth rates are strongly attenuated by pH, and that Ca isotope fractionation between the solid and growth solution is independent of growth rate between 1.9 × 10 -9 and 2.8 × 10 -8 mol Ca m -2 s -1 . Moreover, nanoscale images of surface topography reveal direct deposition of primary particles on the HAP seed surface following sustained growth, providing visual evidence of a non-classical growth pathway. Together, these findings support the hypothesis that hydroxyapatite growth is dominantly non-classical. The process of cluster nucleation from the bulk solution and attachment of these clusters to the seeded HAP apparently does not involve a significant kinetic isotope effect, which implies that abiogenically formed Ca-phosphates likely preserve the Ca isotope composition of the fluid from which the crystals originated.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Nonlinear solution of classical three-wave interaction via finite-dimensional quantum model

The quantum three-wave interaction, the lowest-order nonlinear interaction in plasma physics, describes energy–momentum transfer between three resonant waves in the quantum regime. We describe how it may also act as a finite-degree-of-freedom approximation to the classical three-wave interaction in certain circumstances. By promoting the field variables to operators, we quantize the classical system, show that the quantum system has more free parameters than the classical system and explain how these parameters may be selected to optimize either initial or long-term correspondence. We then numerically compare the long-time quantum–classical correspondence far from the fixed point dynamics. We discuss the Poincaré recurrence of the system and the mitigation of quantum scrambling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Group-theoretic error mitigation enabled by classical shadows and symmetries

Abstract Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in devices without quantum error correction. To address these challenges simultaneously, we develop a quantum error-mitigation strategy called symmetry-adjusted classical shadows , by adjusting classical-shadow tomography according to how symmetries are corrupted by device errors. As a concrete example, we highlight global U(1) symmetry, which manifests in fermions as particle number and in spins as total magnetization, and illustrate their group-theoretic unification with respective classical-shadow protocols. We establish rigorous sampling bounds under readout errors obeying minimal assumptions, and perform numerical experiments with a more comprehensive model of gate-level errors derived from existing quantum processors. Our results reveal symmetry-adjusted classical shadows as a low-cost strategy to mitigate errors from noisy quantum experiments in the ubiquitous presence of symmetry.

Zhao, Andrew (ORCID:0000000202990277)↗

DOE OSTI2024

Non-classical crystallization in soft and organic materials

Classical nucleation and crystal growth theories describe how nuclei form, become stable after reaching a critical size and then enlarge through monomer attachment. More than two decades ago, non-classical pathways have been proposed for various types of (bio)molecules and materials, which can substantially alter the crystallization kinetics and outcomes. Direct observation of non-classical crystallization of inorganic nanomaterials, including metastable structure-mediated and particle attachment-based pathways that usually occur on the nanoscale, was enabled by in situ liquid-phase electron microscopy. However, it was not until recently that the crystallization dynamics of beam-sensitive soft materials were directly imaged with sufficient spatial resolution, and a level of microstructural understanding of defects and interfaces emerged. This article provides a high-level review of the non-classical crystallization pathways discovered in soft and organic materials and a forward-looking guide for future research. We first analyse how the characteristics of soft materials affect their crystallization pathways and kinetics. We then identify technical approaches to studying the crystallization trajectories of soft materials and discuss strategies to properly select and apply them to different systems. Breakthroughs made in understanding the crystallization of small organic molecules, (bio)macromolecules, colloids and reticular framework materials are examined. Lastly, we provide an outlook on the challenges in elucidating soft material crystallization pathways and the opportunities for assisting the design and synthesis of new materials and structures.

36 MATERIALS SCIENCE↗