Title: Open and Closed – Two Paths to Quantum Control

Speaker: Poul Jessen
Abstract: Quantum processors of increasing size and sophistication are now available in several hardware implementations and there is hope they may prove useful for classically hard tasks such as quantum simulation. However, their supposed quantum advantage is fundamentally tied to accurate control of entanglement in quantum many body system. It has long been known that such systems also support quantum chaos, in the sense that their time evolution is exponentially sensitive to control errors. This sets up two separate notions of complexity, one related to the nature of the evolving quantum state, and another related to the nature of the system dynamics. Indeed, for a quantum processor operating without error correction, one can expect an inverse relationship between the accessible Hilbert space and the length of time one can meaningfully compute, with those properties playing a role analogous to the width and depth of a quantum circuit. So far, most research has been focused on scaling up the number of qubits, with less attention paid to the fidelity of the output state as one seeks to increase the useful computational depth.

In this presentation I will introduce a unique platform for quantum control and quantum simulation, based on accurate control in a 16-dimensional Hilbert space (isomorphic to 4 qubits) associated with the spins of individual Cs atoms [1]. While not scalable, this small, highly accurate quantum (SHAQ) processor offers tradeoffs that are uniquely suited to the study of dynamical complexity in time. I will briefly introduce the paradigm of optimal control and how it can be optimized for different scenarios, and then discuss applications of the SHAQ processor as a testbed for quantum control and simulation [2,3] on the edge of chaos. If time allows, I will also share a few ideas and results from a project aimed at quantum control and simulation with a different kind of system, consisting of a large collective spin subject to continuous quantum measurement and real-time feedback [4].

[1] B. E. Anderson, H. Sosa-Martinez, C. A. Riofrio, I. H. Deutsch, and PSJ, Phys. Rev. Lett. 114, 240401 (2015).
[2] N. K. Lysne, K. W. Kuper, P. M. Poggi, I. H. Deutsch, and PSJ, Phys. Rev. Lett 124, 230501 (2020).
[3] P. M. Poggi, N. K. Lysne, K. W. Kuper, I. H. Deutsch, and PSJ, PRX-Quantum 1, 020308 (2020).
[4] M. H. Muniz-Arias, P. m. Poggi, PSJ. And I. H. Deutsch, Phys. Rev. Lett. 124, 110503 (2020).