EAGER-QAC-QSA: COLLABORATIVE RESEARCH: QUANTUM SIMULATION OF EXCITATIONS, BRAIDING, AND THE NONEQUILIBRIUM DYNAMICS OF FRACTIONAL QUANTUM HALL STATES

Cuny City College, New York NY

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research on the studies of dynamics of fractional quantum Hall states using a quantum computer. Recently, we have witnessed extensive development in building quantum computing devices. These advances have allowed efficient calculations of the properties of molecular systems of a few electrons, beyond the capabilities of classical computers. On the other hand, interactions among macroscopically large numbers of electrons lead to the emergence of novel states of matter such the fractional quantum Hall effect, which arises when electrons confined to two dimensions are placed in a strong magnetic field. Interestingly, it has been shown recently that there are connections between fractional quantum Hall states and quantum gravity. The understanding of these novel phenomena requires study of the quantum dynamics of many-particle states when driven out of equilibrium. Experimental and numerical investigations of such states are particularly challenging, motivating a completely new approach. The PIs will develop quantum algorithms to simulate and study these concepts using near-term quantum computing devices. This project will create a new table-top setup to explore questions ranging from quantum dynamics to gravity. The educational component of the activity will provide opportunities for undergraduate and graduate students, particularly from underrepresented groups, to learn about quantum computing and gain hands-on computational experience with quantum circuit design using Google's open-source packages. TECHNICAL SUMMARY This award supports theoretical research on the nonequilibrium quench dynamics and the excitations of fractional quantum Hall states using superconducting qubits. Recent advances in quantum computing devices have motivated using them to simulate quantum states. Given the long-standing challenges in studying correlated many-electron phases, it is compelling to explore the possibility of using quantum computers to investigate these states. This project examines fractional quantum Hall states by developing efficient quantum algorithms that can be implemented on near-term quantum computers. Fractional quantum Hall states are significant examples of quantum phases, where topological order arises from strong electron-electron interactions. The understanding of fractional Hall states is primarily based on insightful trial wave functions, conformal field theory methods, exact diagonalization, and the density-matrix renormalization group. Despite extensive efforts, very little is known about the many-body excitation spectrum and the far-from-equilibrium dynamics of these systems. Notably, there has been a new understanding of novel geometric properties of fractional Hall states, which relates them to concepts in gravity. Advances in quantum computing and quantum simulations provide a new avenue to study fractional Hall phases out of equilibrium. In this research, the PIs pursue two particular directions: 1- Quantum algorithms to generate dynamical quantum braiding and observe its signatures in fractional Hall phases. Even in natural quantum Hall systems, controlled generation of topological excitations and observation of quantum braiding have proved quite challenging. This project opens the door to using quantum computers as an experimental platform for realizing quantum braiding. 2- Generating and observing signatures of geometric high-energy excitations, such as the putative emergent graviton in fractional quantum Hall states. To this end, the research utilizes the simulation of nonequilibrium geometric quenches of fractional Hall states on quantum computers. The PIs will use the network available at City College to involve high-school, undergraduate, and graduate students from underrepresented groups in the efforts to develop quantum algorithms. The PIs engage undergraduate students in this research, allowing them to gain authentic experience and independent research credit toward graduation. In particular, both PIs will use publicly available resources from Google AI lab to train the students in using software packages to design quantum algorithms and visualize them in terms of quantum gates. 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.