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1. Quantum algorithms for escaping from saddle points

   https://doi.org/10.22331/q-2021-08-20-529  

   Zhang, Chenyi; Leng, Jiaqi; Li, Tongyang (August 2021, Quantum)

   null (Ed.)

   We initiate the study of quantum algorithms for escaping from saddle points with provable guarantee. Given a function f : R n → R , our quantum algorithm outputs an ϵ -approximate second-order stationary point using O ~ ( log 2 ⁡ ( n ) / ϵ 1.75 ) queries to the quantum evaluation oracle (i.e., the zeroth-order oracle). Compared to the classical state-of-the-art algorithm by Jin et al. with O ~ ( log 6 ⁡ ( n ) / ϵ 1.75 ) queries to the gradient oracle (i.e., the first-order oracle), our quantum algorithm is polynomially better in terms of log ⁡ n and matches its complexity in terms of 1 / ϵ . Technically, our main contribution is the idea of replacing the classical perturbations in gradient descent methods by simulating quantum wave equations, which constitutes the improvement in the quantum query complexity with log ⁡ n factors for escaping from saddle points. We also show how to use a quantum gradient computation algorithm due to Jordan to replace the classical gradient queries by quantum evaluation queries with the same complexity. Finally, we also perform numerical experiments that support our theoretical findings. 

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

   https://doi.org/10.1063/5.0243535  

   Mondal, M Elious; Vamivakas, A Nickolas; Cundiff, Steven T; Krauss, Todd D; Huo, Pengfei (January 2025, The Journal of Chemical Physics)

   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. 

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3. DL_POLY Quantum 2.0: A modular general-purpose software for advanced path integral simulations

   https://doi.org/10.1063/5.0197822  

   London, Nathan; Limbu, Dil K; Momeni, Mohammad R; Shakib, Farnaz A (April 2024, The Journal of Chemical Physics)

   DL_POLY Quantum 2.0, a vastly expanded software based on DL_POLY Classic 1.10, is a highly parallelized computational suite written in FORTRAN77 with a modular structure for incorporating nuclear quantum effects into large-scale/long-time molecular dynamics simulations. This is achieved by presenting users with a wide selection of state-of-the-art dynamics methods that utilize the isomorphism between a classical ring polymer and Feynman’s path integral formalism of quantum mechanics. The flexible and user-friendly input/output handling system allows the control of methodology, integration schemes, and thermostatting. DL_POLY Quantum is equipped with a module specifically assigned for calculating correlation functions and printing out the values for sought-after quantities, such as dipole moments and center-of-mass velocities, with packaged tools for calculating infrared absorption spectra and diffusion coefficients. 

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4. Efficient simulation of ultrafast quantum nonlinear optics with matrix product states

   https://doi.org/10.1364/OPTICA.423044  

   Yanagimoto, Ryotatsu; Ng, Edwin; Wright, Logan_G; Onodera, Tatsuhiro; Mabuchi, Hideo (October 2021, Optica)

   Ultrashort pulses propagating in nonlinear nanophotonic waveguides can simultaneously leverage both temporal and spatial field confinement, promising a route towards single-photon nonlinearities in an all-photonic platform. In this multimode quantum regime, however, faithful numerical simulations of pulse dynamics naïvely require a representation of the state in an exponentially large Hilbert space. Here, we employ a time-domain, matrix product state (MPS) representation to enable efficient simulations by exploiting the entanglement structure of the system. To extract physical insight from these simulations, we develop an algorithm to unravel the MPS quantum state into constituent temporal supermodes, enabling, e.g., access to the phase-space portraits of arbitrary pulse waveforms. As a demonstration, we perform exact numerical simulations of a Kerr soliton in the quantum regime. We observe the development of non-classical Wigner-function negativity in the solitonic mode as well as quantum corrections to the semiclassical dynamics of the pulse. A similar analysis of ${\mathrm{\chi <\#comment/>}}^{\left(2\right)}$simultons reveals a unique entanglement structure between the fundamental and second harmonics. Our approach is also readily compatible with quantum trajectory theory, allowing full quantum treatment of propagation loss and decoherence. We expect this work to establish the MPS technique as part of a unified engineering framework for the emerging field of broadband quantum photonics. 

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5. A neural network protocol for electronic excitations of N -methylacetamide

   https://doi.org/10.1073/pnas.1821044116  

   Ye, Sheng; Hu, Wei; Li, Xin; Zhang, Jinxiao; Zhong, Kai; Zhang, Guozhen; Luo, Yi; Mukamel, Shaul; Jiang, Jun (June 2019, Proceedings of the National Academy of Sciences)

   UV absorption is widely used for characterizing proteins structures. The mapping of UV spectra to atomic structure of proteins relies on expensive theoretical simulations, circumventing the heavy computational cost which involves repeated quantum-mechanical simulations of excited-state properties of many fluctuating protein geometries, which has been a long-time challenge. Here we show that a neural network machine-learning technique can predict electronic absorption spectra of N -methylacetamide (NMA), which is a widely used model system for the peptide bond. Using ground-state geometric parameters and charge information as descriptors, we employed a neural network to predict transition energies, ground-state, and transition dipole moments of many molecular-dynamics conformations at different temperatures, in agreement with time-dependent density-functional theory calculations. The neural network simulations are nearly 3,000× faster than comparable quantum calculations. Machine learning should provide a cost-effective tool for simulating optical properties of proteins. 

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