Protecting Expressive Circuits with a Quantum Error Detection Code

TL;DR

This paper introduces the Iceberg code, a quantum error detection scheme tailored for current trapped-ion quantum computers, enabling protection of complex circuits with minimal resources and improved error detection capabilities.

Contribution

The paper develops a novel quantum error detection code that is resource-efficient, compatible with existing hardware, and capable of detecting any single-qubit error in trapped-ion systems.

Findings

Successfully protected 8 logical qubits with 256 circuit layers.

Achieved saturation of logical quantum volume $2^8$.

Showed increased error detection effectiveness with more frequent syndrome measurements.

Abstract

A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing quantum computers. In this context we develop a quantum error detection code for implementations on existing trapped-ion computers. By encoding $k$ logical qubits into $k+2$ physical qubits, this code presents fault-tolerant state initialisation and syndrome measurement circuits that can detect any single-qubit error. It provides a universal set of local and global logical rotations that have physical support on only two qubits. A high-fidelity -- though non fault-tolerant -- compilation of this universal gate set is possible thanks to the two-qubit physical rotations present in trapped-ion computers with all-to-all connectivity. Given the particular structure of the logical operators, we nickname it the Iceberg code. We demonstrate the protection of circuits of 8 logical qubits with up to 256 layers, saturate the logical quantum volume of $2^8$, and show the positive effect of increasing the frequency of syndrome measurements within the circuit. These results illustrate the practical usefulness of the Iceberg code to protect expressive circuits on existing trapped-ion quantum computers.