Interfacing digital and analog quantum systems

Objective

Quantum simulation provides us with a powerful set of tools to control and observe complex many-body phenomena. On the one hand, analog quantum simulators have given us a new window on the real-time dynamics of interacting quantum systems. On the other hand, digital quantum computers promise more advanced investigations, ranging from the preparation of many-body eigenstates to the enhanced learning of their properties. While experimental advances in quantum error correction are making this vision more concrete, the digital simulation of many-body Hamiltonians is still prohibitively costly. A compelling perspective lies in interfacing error-corrected digital devices and analog quantum systems that naturally implement the Hamiltonian of interest. However, the one-to-one coupling between physical degrees of freedom and logical qubits, composed of many physical qubits, is fundamentally challenging. This proposal aims to achieve such interfaces via a bottom-up approach. Starting from physically relevant two-body interactions, I will design new quantum algorithms for quantum simulation that couple analog and early fault-tolerant quantum systems. This will be done by combining tools from quantum optics, robust Hamiltonian engineering, and the theory of quantum algorithms and error correction. This route will enable rigorous assessment of hardware requirements, laying the foundations for future experimental implementations. In this way, this project will achieve (1) end-to-end approaches to analyse many-body wavefunctions with early fault-tolerant quantum computers and (2) state preparation protocols based on analog Hamiltonian evolution controlled by logical qubits. The result will be a new generation of experiments leveraging the full potential of quantum computers to manipulate and probe artificial quantum matter.