Observation of quantum-field-theory dynamics on a spin-phonon quantum computer: Experiment

Simulating real-time non-equilibrium dynamics of bosonic quantum field theories will give essential insights into high-energy particle collisions and the nature of the early universe. Although these simulations are intractable for classical computers, quantum computers provide a possible way forward. However, there are several challenges that inhibit bosonic simulations on quantum computers. One of these is the high cost of mapping bosons onto qubits. In a fully-digital scheme, the infinite-dimensional Hilbert space of bosons is truncated and mapped onto a finite number of qubits, leading to truncation error, large gate depth, and high qubit overhead. We bypass these problems by using a hybrid digital-analog scheme, where the bosons are mapped onto the motional modes of a trapped-ion quantum computer. We use this scheme to simulate non-equilibrium dynamics of a (1+1)D Yukawa model, which describes the interaction between scalar and fermionic fields. We find excellent agreement with theoretical expectations, even for high bosonic occupations, in a first experimental demonstration of this scheme. This work pushes the capabilities of hybrid quantum computing and opens the way towards simulating gauge theories on spin-boson systems. In this talk, we present our experimental capability and results, with a preceding talk covering the theoretical foundations of this work.