Benchmarking logical three-qubit quantum Fourier transform encoded in the Steane code on a trapped-ion quantum computer
Abstract
We implement logically encoded three-qubit circuits for the quantum Fourier transform (QFT), using the [[7,1,3]] Steane code, and benchmark the circuits on the Quantinuum H2-1 trapped-ion quantum computer. The circuits require multiple logical two-qubit gates, which are implemented transversally, as well as logical non-Clifford single-qubit rotations, which are performed by non-fault-tolerant state preparation followed by a teleportation gadget. First, we benchmark individual logical components using randomized benchmarking for the logical two-qubit gate, and a Ramsey-type experiment for the logical gate. We then implement the full QFT circuit, using two different methods for performing a logical control-, and benchmark the circuits by applying it to each basis state in a set of bases that is sufficient to lower bound the process fidelity. We compare the logical QFT benchmark results to predictions based on the logical component benchmarks.
Cite
@article{arxiv.2404.08616,
title = {Benchmarking logical three-qubit quantum Fourier transform encoded in the Steane code on a trapped-ion quantum computer},
author = {Karl Mayer and Ciarán Ryan-Anderson and Natalie Brown and Elijah Durso-Sabina and Charles H. Baldwin and David Hayes and Joan M. Dreiling and Cameron Foltz and John P. Gaebler and Thomas M. Gatterman and Justin A. Gerber and Kevin Gilmore and Dan Gresh and Nathan Hewitt and Chandler V. Horst and Jacob Johansen and Tanner Mengle and Michael Mills and Steven A. Moses and Peter E. Siegfried and Brian Neyenhuis and Juan Pino and Russell Stutz},
journal= {arXiv preprint arXiv:2404.08616},
year = {2024}
}