Utility of virtual qubits in trapped-ion quantum computers

TL;DR

This paper introduces the concept of virtual qubits in trapped-ion quantum computers, enabling more efficient algorithms, reduced noise, and enhanced error correction by encoding multiple qubits within individual ions.

Contribution

It proposes a novel method of encoding virtual qubits in ions, simplifying circuit implementation and improving noise resilience in trapped-ion quantum computing.

Findings

Virtual qubits reduce the need for vibrational modes, decreasing noise.

Implementation of algorithms like Bernstein-Vazirani with fewer physical qubits.

Enhanced error correction capabilities using virtual qubits.

Abstract

We propose encoding multiple qubits inside ions in existing trapped-ion quantum computers to access more qubits and to simplify circuits implementing standard algorithms. By using such `virtual' qubits, some inter-ion gates can be replaced by intra-ion gates, reducing the use of vibrational modes of the ion chain, leading to less noise. We discuss specific examples such as the Bernstein-Vazirani algorithm and random circuit sampling, using a small number of virtual qubits. Additionally, virtual qubits enable using larger number of data qubits for an error correcting code, and we consider the repetition code as an example. We also lay out practical considerations to be made when choosing states to encode virtual qubits in $^{137}\mathrm{Ba}^+$ ions, and for preparing states and performing measurements.