## Low noise transistor microwave amplifiers

A widely varying and critical set of experiments depend on microwave signal processing technology, ranging from searching for the origin of fast radio bursts to investigating the nature of dark matter to the development of near-term quantum computers. While this technology is now relatively mature, present transistor amplifiers remain around a factor of 5 above the standard noise limit set by quantum mechanics. Although superconducting amplifiers operating at the quantum limit are available and in widespread use, they have a number of practical limitations that prohibit their use in many applications.

Our group is studying how to realize transistor microwave amplifiers with noise figure approaching the standard quantum limit. Such devices would find transformative applications in radio telescopes, quantum computers, and other technologies. Key to achieving this goal is assessing the impact of self-heating at cryogenic temperatures on noise as well as microscopic origin of hot electron noise that is associated with the heating of the electron gas in the channel of a transistor. To test predictions that arise from our studies, we work with foundries to fabricate and characterize prototype amplifiers from room temperature down to 4 K.

Image of a custom 4-6 GHz two-stage low-noise n-HEMT MMIC with noise temperature 2.2 K at 5 GHz. We are investigating fundamental noise mechanisms in LNAs with the aim to realize quantum-limited transistor microwave amplifiers.

Measured and predicted intrinsic self-heating of a low noise amplifier versus temperature. Self-heating becomes increasingly important at cryogenic temperatures owing to the freeze-out of the phonons that dissipate heat. [Sch]

[Sch] Schleeh, J., Mateos, J., Íñiguez-de-la-Torre, I. et al. Phonon black-body radiation limit for heat dissipation in electronics. Nature Mater 14, 187–192 (2015) doi:10.1038/nmat4126

## Electronic structure and transport theory in materials

Electronic structure methods now enable diverse properties of materials to be predicted with excellent accuracy. In particular, the calculation of transport properties including electrical and thermal conductivity is now routine, and theory is now able to drive experimental studies. However, the calculation of fluctuational properties such as the spectral noise power have not yet been performed. Such ab-initio calculations would be of considerable value in efforts to decrease the noise of transistor amplifiers discussed above.

We are developing an approach to compute the spectral noise power of a semiconductor from first-principles. The calculation requires computing electron-phonon coupling matrices between the electron and phonon systems, then solving a series of Boltzmann equations. Example results are shown below for GaAs; good agreement is observed with literature measurements on bulk GaAs wafers.

In addition to these efforts, we are also pursuing improvements in numerical methods to compute the electronic structure of materials. While density functional theory is quite accurate for many materials, it remains qualitatively inaccurate for others. For instance, mean-field methods have difficulties treating localized electrons and hence perform poorly for materials exhibiting even moderate correlation and magnetic order. In collaboration with the Chan group at Caltech, we are studying how canonical and equation-of-motion coupled-cluster methods can be adapted to describe the ground and excited states of correlated materials like transition metal oxides. Advances in electronic structure methods aid in the identification of materials with complex electronic structure for use at the heart of detectors.

Schematic of a semiconductor bar with an applied electric field. Electrons undergo collisions with phonons while drifting along the bar, resulting in velocity fluctuations and hence current noise. The spectral noise power of a semiconductor can be computed from first-principles by solving a series of Boltzmann equations with the electron-phonon scattering matrices as input. These calculations provide insight into how to reduce the magnitude of hot electron noise arising from scattering events.

Real space spin density of (a) MnO and (b) NiO. The eg symmetry of the NiO spin density arises from the antiferromagnetic configuration of spins in different atomic planes and the parallel spins in the eg orbitals of NiO. [Gao]

## Quantum simulation and sensing

[Gao] Gao, Y. et al. arXiv:1910.02191v2 (2019)

Controllable quantum systems such as quantum computers based on platforms like superconducting qubits are now a topic of immense interest. In the near-term, the most promising prospects for their application is in quantum simulation, where they may enable the study of highly entangled quantum systems that are out of reach of classical computers. The use of quantum information to improve sensors and detectors is also a nascent field with applications that are yet to be determined.

Our group is generally interested in quantum information as a means to perform quantum simulation and enhance the sensitivity of precision measurement technology. As an example, we have recently contributed to the application of a quantum algorithm to compute ground states and thermal averages of local Hamiltonians known as quantum imaginary time evolution (QITE) via a collaboration with the Chan and Brandao groups at Caltech. This algorithm, developed by the Chan group, enabled the first computation of thermal averages on a quantum computer by the quantum version of minimally entangled typical thermal states (METTS) algorithm. Reducing the quantum resources required to solve a given problem is important given restrictions in gate depth and qubit number of present devices. Some of our present work focuses on adapting methods that exploit symmetries to reduce qubit number and thereby decrease the resources required for QITE. Other work focuses on identifying schemes to create topological states of Hamiltonians in gate-based quantum computers.

Our overarching aim is to explore how devices that manipulate quantum information may be used to both simulate quantum systems of physical interest and as sensors and detectors with noise below the standard quantum limit.

Schematic of the QITE algorithm. Left: Imaginary time evolution by a Hamiltonian term h[m] acting on k qubits can be reproduced by a unitary with domain size D > k. Right: As the state is evolved in imaginary time, the correlation length in the state increases, and therefore the domain size required increases. If the correlation length saturates in imaginary time, the domain size stops growing and QITE can efficiently find the ground state. [Mot]

Energy versus imaginary time from the quantum virtual machine (QVM, red) and quantum processor unit (QPU, blue) of Rigetti for a 2-site Heisenberg model. QITE implemented in the emulator and an actual device approach the exact ground state energy for sufficiently large imaginary time. [Mot]

[Mot] Motta, M., Sun, C., Tan, A.T.K. et al. Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution. Nat. Phys. (2019) doi:10.1038/s41567-019-0704-4