# Minnich Group

# CALIFORNIA INSTITUTE OF TECHNOLOGY

## 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 the 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

## Transport and fluctuation phenomena in semiconductors

A microscopic understanding of electron transport and fluctuations is essential to creating low-noise instruments. Ab-initio methods, in which transport properties are computed with knowledge of only the atomic elements and positions in a crystal, now enable the routine computation of transport properties like electrical and thermal conductivity. However, the calculation of fluctuational properties such as the spectral noise power that are of direct importance to technology are minimally developed within the ab-initio formalism.

We have developed the first 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 calculations of the spectral noise power are shown for GaAs. Key features are observed, including the anisotropy of the noise despite the cubic symmetry of the crystal and the roll-off as the frequency becomes comparable to momentum scattering rates.

Computed power spectral density (PSD) of longitudinal (||, dashed orange line) and transverse (⊥, dotted orange line) current density fluctuations versus frequency at E = 500 V cm−1 , along with the Nyquist-Johnson prediction for E = 0 (solid black line). [Cho]

## Quantum simulation

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.

Our group is exploring the capabilities of these near-term quantum computers as well as investigating the effect of undesired interactions such as cross-talk on the logical error rate of error correction schemes. As an example, we have recently reported the first hardware calculations on dynamic correlation functions, spectral functions, and other quantities at finite temperature on up to 4 qubits. This calculation employed the quantum imaginary time evolution (QITE) developed at Caltech along with a number of other error mitigation schemes. In particular, we have developed a systematic means to reduce the quantum resources required for QITE by exploiting symmetries in the Hamiltonian.

Our overarching aim is to explore and expand the capabilities of near-term quantum hardware for quantum simulation through development of algorithms and the execution of error correction schemes on actual hardware.

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]

Finite-temperature dynamical properties of the four-site tranverse-field Ising model (TFIM) with J = 3, h = 1 at β = 0.2. QITE is performed with a time step of ∆τ = 0.05 and recompiled D = 2 unitaries. Real and imaginary parts of the finite-temperature dynamical correlation function versus real time t. Raw hardware data are post-processed by phase-and-scale correction. [Sun]