Liam Bond

The aim of this Thesis is to understand and harness hybrid spin-boson systems. Motivated by the prospect of realizing a quantum advantage, in Part One we consider quantum simulations, sensing and state preparation in spin-boson systems. Exactly describing spin-boson systems is often extremely challenging, so in Part Two we develop efficient classical numerical methods for simulating their closed and open quantum dynamics.

We begin Part One in Ch. 1 with a review of trapped-ion systems, a well established spin-boson hardware platform. The theory of ion trapping is introduced, including a detailed treatment of micromotion using Floquet theory. We discuss how a qubit is encoded in each ion’s internal electronic energy levels, and how laser light realizes effective spin-spin interactions that are well-described by an Ising model, enabling quantum simulations of spin-spin models. Finally we review optical tweezers and how they can increase the programmability of the trapped-ion quantum simulator.

In Ch. 2 we numerically study the effect of expected sources of experimental error in quantum simulations with trapped ions in optical tweezers. We show that micromotion should be included when numerically optimizing the tweezer pinning frequencies, while first-order Doppler shifts may be a major source of error along the weaker confinement direction where micromotion is largest. Additional stress and strain forces do not increase the simulator’s programmability, while tweezer intensity noise should be stabilized to the sub-percent level to realize high-fidelity quantum simulations.

In Ch. 3 we continue with the theme of harnessing spin-boson systems, asking how many-body spin-boson systems can be used for displacement sensing. We prove that in terms of the bosonic mode’s occupation, spin-dependent squeezed states are optimal reference states. Specifically, they saturate the Heisenberg limit for estimating a displacement’s amplitude, and for jointly estimating a displacement’s real and imaginary components. With trapped-ion systems in mind, we provide experimentally-realizable measurement schemes that follow Heisenberg scaling. We also introduce a fast and scalable protocol for preparing spin-dependent squeezed states that uses dynamically modulated first-order sideband interactions, achieving a preparation time that scales as 1/√N in systems with N ions. We numerically demonstrate the preparation of 8.7 dB of spin-dependent squeezing 15 times faster than the standard trapped-ion approach using second-order sidebands. The potential applications of our metrology protocols include quantum-logic enabled photon-recoil spectroscopy of molecular and highly charged ions, and searches for physics beyond the Standard Model by sensing a displacement induced by theorized interactions between Standard Model fields and certain forms of dark matter such as axions.

In Ch. 4 we conclude Part One by asking if arbitrary symmetric spin states can be efficiently prepared using only global control. Symmetric spin states are defined as any quantum state that is invariant when two particles are exchanged, while the development of protocols that do not require individual qubit addressing is crucial for platforms where single-qubit addressing is not available, and for reducing experimental demands more broadly. Using a variational quantum circuit built from global rotations and global spin squeezing, we provide numerical evidence and an analytical argument that at most 2N/3 circuit layers are required to prepare arbitrary symmetric states. We highlight the capabilities of our approach by preparing symmetric states that are useful for quantum metrology and quantum error correction. We expect the variational circuit to be immediately realizable on current quantum hardware platforms, and in particular discuss how our protocol can be realized in trapped-ion platforms.

In Part Two we aim to understand hybrid spin-boson systems by developing classical numerical methods for simulating their quantum dynamics. In Ch. 5 we introduce the framework, namely a variational ansatz for the quantum state and the time-dependent variational principle (TDVP) to simulate dynamics. For the ansatz we choose a non-Gaussian state (NGS), specifically a superposition of bosonic Gaussian states (SCS). We also review the study of open quantum systems, including the quantum trajectories method.

In Ch. 6 we study ground-state properties using imaginary-time evolution and non-equilibrium dynamics using real-time evolution. Focusing on the spin-boson model, a paradigmatic model that describes a single spin coupled to a set of bosonic modes, we demonstrate that the ansatz is efficient and controllable even beyond the regime of Ohmic-type couplings. We also use our framework to study bath dynamics, and combine it with optimal control for the fast preparation of near-critical ground states.

In Ch. 7 we extend the NGS and TDVP framework to study open dynamics using quantum trajectories. We study a Holstein-Tavis-Cummings Hamiltonian, a paradigmatic model which in the context of polaritonic chemistry describes low-energy electronic excitations coupled to local molecular vibrations and a collective cavity mode, and features enhanced chemical reaction rates. We benchmark our framework against the truncated Wigner approximation (TWA), showing that there are parameter regimes where the NGS outperforms our TWA implementation. While the NGS framework can be applied to a range of problems, some bottlenecks remain such as a limited number of spins. Possible future applications range from studies of polaritonic chemistry and impurity physics to robust quantum state preparation in hybrid spin-boson systems.