Simulating many-body quantum spin models with trapped ions
Dissertation Committee Chair: Chris Monroe
Committee: Chris Monroe, Norbert Linke, Alexey Gorshkov, Ronald Walsworth, Mohammad Hafezi
Richard Feynman in 1981 suggested using a quantum machine to simulate quantum mechanics. Peter Shor in 1994 showed that a quantum computer could factor numbers much more efficiently than a conventional one. Since then, the explosion of the quantum information field is attesting to how motivation and funding work miracles. Naturally, this expansion has led to diversification of the devices being developed. The quantum information systems that cannot simulate an arbitrary evolution, but are specialized in a specific set of Hamiltonians, are called quantum simulators. Several such experimental platforms exist, harnessing the luxury of being able to surpass computational abilities of classical computers right now, at the expense of only doing so for a narrow type of problem. Among those systems, ions trapped in vacuum by electric fields and manipulated with light have proved to be a leading platform in emulating quantum magnetism models. In this thesis, I will present experiments that use trapped ions to realize a prethermal discrete time crystal. This exotic phase occurs in non-equilibrium matter subject to an external periodic drive. Normally, the ensuing Floquet heating maximizes the system entropy, leaving us with nothing but a trivial, infinite-temperature state. However, we can parametrically slow down this heating by tuning the drive frequency. During the time window of slow thermalization, we define an order parameter and observe two different regimes, based on whether it spontaneously breaks the discrete time translation symmetry of the drive or it preserves it.
Furthermore, I demonstrate a simple model of electric field noise classically heating an ion in an anharmonic confining potential. As ion traps shrink, this kind of noise may become more significant. And finally, I discuss a handful of error sources relevant in recent simulation experiments. Most notably, these were AC Stark shifts on the qubit levels, manifesting themselves as additional time-dependent terms in our Hamiltonian evolution. As quantum simulation experiments progress to more qubits and complicated sequences, accounting for system imperfections is becoming an integral part of the process.