## Transport Phenomena

The theoretical framework to describe the transport of heat, charge, and spin in the solid-state is well-established, but only in the past 10 years have ab-initio methods and computing power advanced sufficiently to compute transport properties from first-principles, free of any adjustable parameters [1-4]. Generally, these methods use density functional theory to calculate electronic band structure or interatomic force constants at zero temperature; scattering rates are then obtained using Fermi’s golden rule. Our focus in recent years has been the development of ab-initio tools to compute the vibrational and thermal transport properties of solids with strong anharmonicity beyond the perturbative regime, as occurs in materials such as PbSe and polyethylene crystals. We continue to advance these methods for increasingly complex, low symmetry crystals, with a particular focus on molecular crystals.

A new research thrust focuses on calculating fluctuational properties by combining ab-initio electronic structure calculations and solutions of the Boltzmann-Langevin equation. These calculations yield the electronic noise spectra of semiconductors used for electronic devices such as microwave amplifiers which are widely used in precision measurement and other fields. Our calculations may provide insight into how hot electron noise may be reduced in the cryogenic microwave amplifiers used for qubit readout in quantum computers. Reduction in the noise figure of these amplifiers is essential to scaling quantum computers to thousands of qubits and more [5].

Another research thrust, primarily experimental in nature, is the investigation of the dynamics of macromolecules under external perturbation. We employ artificial vesicles as a test platform to understand the molecular mechanisms underlying conformational changes to ion channels and transporters due to chemical or optical stimuli [6].

[1] N. Shulumba, O. Hellman, A.J. Minnich. Physical Review Letters, 119:185901, 2017

[2] N. Shulumba, O. Hellman, A.J. Minnich. Physical Review B, 95:014302, 2017

[3] N. Shulumba, B. Latour, A.J. Minnich. Physical Review B, 96:1014310, 2017.

[4] M. Bernardi. The European Physical Journal B, 89(239), 2016.

[5] R.J. Schoelkopf M.H. Devoret. Science, 339:1169–1174, 2013.

[6] D. Fletcher. Dev Cell. 2016 Sep 26; 38(6) 587-589

## Ab-initio Condensed Matter Physics

Density functional theory and the GW method have been remarkably successful at predicting diverse properties of solids, including ground state properties as well as excited state properties such as optical absorption spectra[1,2]. However, well-known deficiencies exist with these methods. For instance, mean-field methods have difficulties treating localized electrons and hence performed poorly for materials exhibiting even moderate correlation and magnetic order[3,4]. Most importantly, traditional ab-initio methods used in condensed matter physics are difficult to systematically improve towards the exact solution within the specified basis set.

In contrast, the quantum chemistry community has developed methods that overcome these limitations, in particular the coupled-cluster method[5], yet these methods have historically been too expensive to apply to the condensed phase. Advances in computing power now put these calculations in reach, as recently demonstrated for semiconductors like Si[6]. We are studying how canonical and equation-of-motion coupled-cluster methods can be adapted for periodic solids to enable the description of excited states, non-adiabatic coupling, and other condensed-phase phenomena with unprecedented accuracy.

[1]. Becke, Axel D. The Journal of chemical physics 140.18 (2014): 18A301.

[2]. Neaton, Jeffrey B., Mark S. Hybertsen, and Steven G. Louie. Physical review letters 97.21 (2006): 216405.

[3]. Cohen, Aron J., Paula Mori-Sánchez, and Weitao Yang. Chemical reviews 112.1 (2011): 289-320.

[4]. Aryasetiawan, F., and O. Gunnarsson. Physical review letters 74.16 (1995): 3221.

[5]. Bartlett, Rodney J., and Monika Musiał. Reviews of Modern Physics 79.1 (2007): 291.

[6]. McClain, James, et al. Journal of chemical theory and computation 13.3 (2017): 1209-1218.

## Quantum Dynamics

Many-body quantum dynamics underlies some of the most physically rich processes in nature including excited state relaxation, non-adiabatic reaction chemistry, many-body localization, the generation of exotic states such as Floquet topological insulators, and many other phenomena at the frontier of research in physics, chemistry, and materials science. In static quantum problems, classical algorithms are often effective because a well-understood physical structure can be exploited to describe only the quantum states that are physically relevant. For instance, it is well-known that local, gapped Hamiltonians satisfy an area law, meaning that the entanglement entropy grows only as the surface area rather than the volume of the region. As a result, physically relevant quantum states are a very small portion of the overall Hilbert space and can thus be represented on classical computers using, for example, tensor networks [1].

Quantum dynamics are far more challenging to compute than static problems because in general, the quantum entanglement of the state grows linearly in time. This means that an exponential number of unentangled states are needed to accurately represent the state [2]. As a result, classical algorithms cannot accurately describe several more exotic quantum dynamical processes.

For these reasons, it is believed that quantum computers may be able to outperform classical computers in the field of quantum dynamics. Near-term quantum computers based on superconducting qubits have made rapid progress and are now increasingly available, though they still face limitations with respect to gate depth and errors. Despite these limitations, near-term (NISQ) devices may still offer a means of performing dynamical calculations that are classically undesirably expensive. On a slightly longer time frame, an exciting prospect with improved hardware is the development of quantum algorithms to solve previously intractable physical problems [3].

Our research in this area focuses on a few areas. First, we aim to identify the limits of tensor network algorithms to simulate quantum dynamics out to long times by combining advances in algorithms with numerical advances for high-performance tensor contractions. Second, we are studying robust algorithms for quantum dynamics based on variational algorithms intended for quantum computers. Such algorithms for real-time dynamics have not yet been implemented on near-term devices, and thus part of our focus will be on the practical implementation of the circuits on emerging hardware. Finally, we are working to characterize the resource requirements and classical-quantum boundary for dynamical simulations of many-body problems on NISQ devices.

[1] F. Verstraete , V. Murg, and J.I. Cirac, Advances in Physics, 57:2, 143-224 (2008)

[2] U. Schollwock, arXiv:1008.3477v2 (2011)

[3] J. Preskill, arXiv:1801.00862v3 (2018)