Collaborative Research: Fractional quantum Hall effect on noisy quantum computers

Nontechnical Summary

This award supports theoretical research on using quantum computers to investigate the fractional quantum Hall state, a quantum state of matter that can emerge when electrons are confined to two dimensions and placed in a strong magnetic field. Fractional quantum Hall states have unusual properties, for example, excitations that have a charge that is a fraction of the electron charge.

These excitations may be anyons which are in a sense in between the usual classification of quantum particles as either fermions, for example electrons, or bosons, for example quanta of light. In some cases, these particles can significantly change the quantum state simply by moving two particles around each other. The properties of the fractional quantum Hall state can be discussed in terms of topological and geometrical properties.

Recent advancements in quantum computing provide a unique opportunity to generate and study natural quantum phenomena in controllable quantum platforms. This project leverages these advancements to explore on available quantum computers, several challenging problems related to the quantum Hall effect, aiming to demonstrate critical signatures of topological and geometrical characteristics of fractional Hall states.

This project can in this way turn current quantum computers into a laboratory for conducting experiments on fractional quantum Hall physics, allowing us to study phenomena that are difficult to access through traditional experimental methods.

Through comprehensive curriculum development, the project seeks to integrate quantum computing concepts throughout undergraduate education and train a new generation of students who are proficient in using quantum computing resources. The project's outreach and educational initiatives will create new resources to showcase the application of quantum computers in addressing real-world physics problems.

These materials will mainly target high school and undergraduate students from underrepresented backgrounds, aiming to boost student enrollment and promote diversity in the future workforce. Technical Summary

This award supports research on using existing noisy quantum computers as synthetic experimental platforms to investigate various phenomena in quantum Hall systems. The project is focused on three thrusts:

(a) Designing a quantum circuit for simulating braiding and verifying the quasihole statistics for non-Abelian fractional quantum Hall states.

(b) Implementing nonequilibrium quantum quenches that probe the bosonic and fermionic collective neutral modes of the Moore-Read state on the quantum computer.

(c) Developing and running quantum algorithms that measure the Hall viscosity of the Laughlin state and probe its robustness to disorder.

This project enables the investigation of novel topological and geometric characteristics of fractional Hall states using noisy quantum computers. Quantum algorithms will be created and implemented to generate complex ground states and perform adiabatic and nonadiabatic quantum evolution. The PIs will use a general theoretical framework based on quasi-one-dimensional models of fractional quantum Hall states obtained from Landau orbitals in a spatially anisotropic cylinder.

This requires reduced registers to use physical qubits efficiently, and provides efficient variational circuit architectures for implementing the three thrusts above.

Additionally, the project includes an education program that focuses on curriculum development to incorporate quantum computing modules for solving physical problems into undergraduate-level physical chemistry, solid state, and quantum mechanics courses. There will also be outreach presentations to high-school students and underrepresented undergraduate students through the NSF Center for Research Excellence in Science and Technology at the City College of New York.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.