# Modular Quantum Computation in a Trapped Ion System

## TL;DR

This paper demonstrates the first modular quantum computation in a trapped ion system by implementing a quantum API that allows clients to estimate the trace of a server-provided unitary, enabling scalable and parallel quantum algorithms.

## Contribution

It introduces a quantum API for modular quantum computation and demonstrates its functionality using trapped ion technology, advancing scalable quantum computing.

## Key findings

- Successful implementation of a quantum API for trace estimation
- First demonstration of modular quantum computation in a trapped ion system
- Pioneering techniques for coherent qubit swapping within motional states

## Abstract

Modern computation relies crucially on modular architectures, breaking a complex algorithm into self-contained subroutines. A client can then call upon a remote server to implement parts of the computation independently via an application programming interface (API). Present APIs relay only classical information. Here we implement a quantum API that enables a client to estimate the absolute value of the trace of a server-provided unitary $U$. We demonstrate that the algorithm functions correctly irrespective of what unitary $U$ the server implements or how the server specifically realizes $U$. Our experiment involves pioneering techniques to coherently swap qubits encoded within the motional states of a trapped \Yb ion, controlled on its hyperfine state. This constitutes the first demonstration of modular computation in the quantum regime, providing a step towards scalable, parallelization of quantum computation.