Hamiltonian engineering for quantum sensing and quantum simulation

Abstract

Quantum sensing and quantum simulation are emerging areas in quantum science and technology with broad applications. In this thesis, we explore Hamiltonian engineering techniques to build better quantum sensors and quantum simulators. In quantum sensing, advanced control techniques are required to extract all the information available about the sensing target from the sensor. Unfortunately, one major challenge to implementing the optimal control sequence-which extracts the maximum information-is the clock rate of the (classical) hardware used to control the sensor. To overcome this challenge, we develop a novel control technique inspired by quantum simulation ("quantum interpolation") and achieve an effective six picoseconds sampling rate from the hardware-constrained two nanoseconds. This improved sampling rate enables a higher precision in measuring classical fields and the quantum signal arising from a single nuclear spin.

To further improve quantum sensing, we engineer the sensor-target Hamiltonian and make the sensor more sensitive to the target. In particular, we address the challenge that a single sensor cannot be sensitive to all components of a vector DC magnetic field. To overcome this challenge, we modify the sensor Hamiltonian, using an ancillary oscillator, to realize a hybrid magnetometer sensitive to both the longitudinal and the transverse component of a vector DC field. We achieve a nanoscale vector magnetometer with comparable sensitivities for longitudinal and transverse magnetic field components. Finally, we turn to digital quantum simulation, a versatile scheme to study large quantum systems' complex dynamics via controllable quantum devices. In digital quantum simulation, the desired dynamics are approximated by a sequence of elementary gates (Trotterization). Finding a good ordering of gates to achieve high-fidelity simulation is a nontrivial task.

To address this challenge, we develop a geometric picture of Trotter formulas and their errors, from which we were able to find intuitive Trotter formulas providing higher-fidelity simulation compared with the most commonly used Trotter formulas. While the results cover a wide range of applications, this thesis's key insight is that they all emerge from improved control techniques that engineer effective Hamiltonians starting from the natural interactions present in the original quantum system.