New Avenues in Quantum Computing: Beyond Quantum Circuits with Trapped-Ion Qubits

Trapped ions are a leading quantum technology for quantum computation and simulation, with the capability to
solve computationally hard problems and deepen our understanding of complex quantum systems. The quantum
circuit model is the central paradigm for quantum computation, enabling the realization of various quantum
algorithms by application of multiple one- and two-qubit entangling operations. However, the typical number of
entangling operations required by this model increases exponentially with the number of qubits, making it difficult
to apply to many problems.
In my presentation, I will discuss new methods for realizing quantum gates and simulations that go beyond the
quantum circuit model. I will first describe a single-step protocol for generating native, -body interactions between
trapped-ion spins, using spin-dependent squeezing. Next, I will present a preparation of novel phases of matter
using simultaneous and reconfigurable spin-spin interactions. Lastly, I will explore new avenues to harness the
long-lived phonon modes in trapped-ion crystals for simulating complex bosonic and spin-boson models that are
difficult to solve using classical methods. The presented techniques could push the performance of trapped-ion
systems to solve problems that are currently beyond their reach.