Protecting expressive circuits with a quantum error detection code

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-initialization 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-although 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 eight logical qubits with up to 256 layers, saturate the logical quantum volume of 28 and show the positive effect of increasing the frequency of syndrome measurements in the circuit. These results illustrate the practical usefulness of the Iceberg code to protect expressive circuits on existing trapped-ion quantum computers. An error detecting code running on a trapped-ion quantum computer protects expressive circuits of eight logical qubits with a high-fidelity and partially fault-tolerant implementation of a universal gate set.