Continuous quantum measurements with superconducting circuits:Most likely paths and optimal control

University Of Rochester, Rochester NY

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical research and education on measurement and control of a quantum mechanical system using models fabricated from superconductors as artificial quantum systems. Superconductors exhibit unusual properties as compared to ordinary conductors like copper, such as the ability to conduct electricity without dissipation. Quantum mechanics is required to describe tiny objects like electrons and atoms which behave differently than familiar macroscopic objects like baseballs which obey the laws of classical mechanics. The superconducting state made up of many electrons can be described by quantum mechanics at a level of complexity similar to that of a single atom. Unlike observing the trajectory of a baseball, making measurements on a quantum mechanical system changes the system. The research team will theoretically investigate quantum mechanical systems fabricated from superconductors to advance understanding of how a quantum mechanical system changes in time under measurements. This work will be done in collaboration with an experimentalist to perform rigorous experimental checks, and implement the ideas and concepts developed in the course of the theoretical research. The ability to precisely measure, control and guide a quantum system is a critical element of the emerging field of quantum technology. This includes the operation of a quantum computer in which quantum mechanical states would be manipulated to achieve high performance computing. This research is particularly relevant for proposals of quantum computers that utilize superconducting elements as the quantum mechanical bits. This award supports training graduate students involved in this research effort, as well as an outreach activity in which the PI teaches a summer course to high school students. This class teaches students quantum physics at a qualitative level using minimal mathematics, and focuses on hands-on demonstrations, lab tours, as well as classroom lectures. TECHNICAL SUMMARY This award supports theoretical research and education to advance the fundamental understanding of continuous quantum measurement in superconducting transmon qubits. Technological development of superconducting quantum systems has made great strides leading to the fabrication of systems having long coherence times; experiments can continuously measure the stochastic collapse of the wavefunction as well as implement continuous feedback. The quantum trajectory approach to continuous measurement permits instantaneous tracking of the quantum state during individual measurement runs. The research team will systematically investigate the physics of continuous quantum measurement in superconducting transmon qubits. The PI's group has developed a stochastic path integral formalism of continuous quantum measurements that is well suited to investigate and characterize the physical properties of the measurement process. Fixed initial and final states of the quantum system are considered as boundary conditions on the stochastic dynamics, which are imposed by a pre- and post-selection. In this case, an important topic is how the quantum system gets between these two states. In particular, the average or most-likely path through the quantum state space and the distribution of arrival times provide deep insight into the physics of the continuous quantum collapse process. The most-likely paths the quantum state takes through its space will be investigated as well as the distribution of first passage times in the case where the state is pre- and post-selected. This will be done when the quantum system is unitarily changing while it is being measured. Associated questions, such as the dynamical stability properties of the trajectories, are of fundamental importance in the developing area of quantum control. The nonlinear equations of motion for the most likely path indicate (i) there can be cases when there are multiple most likely paths between the boundary conditions, and (ii) the possibility of chaotic behavior, in the sense of exponential sensitivity to initial conditions. This behavior will be explored and characterized. Joint measurements on multiple transmons will also be investigated, as well as the most likely ways to start in a separable state and end in a desired entangled one. This effort will capitalize on new research horizons in this rapidly developing field of condensed matter physics. The PI will collaborate with colleague Irfan Siddiqi's group (UC Berkeley) to test these theories and implement the physics described here in his laboratory.