Benchmarking logical three-qubit quantum Fourier transform encoded in the Steane code on a trapped-ion quantum computer

• DOI: 10.48550/arxiv.2404.08616
• Publication Date: 2024-04-12
• Authors: Karl Mayer; Ciarán Ryan-Anderson; Natalie Brown; Elijah Durso-Sabina; Charles H. Baldwin; David Hayes; Joan Dreiling; Cameron Foltz; John Gaebler; Thomas M. Gatterman; Justin A. Gerber; Kevin Gilmore; Dan Gresh; Nathan Hewitt; Chandler V. Horst; Jacob Johansen; Tanner Mengle; Michael Mills; Steven A. Moses; Peter Siegfried; Brian Neyenhuis; Juan Miguel Rey Pino; Russell Stutz
• Keywords: Benchmark (surveying); Quantum Fourier transform; Subtractor

We implement logically encoded three-qubit circuits for the quantum Fourier transform (QFT), using [[7,1,3]] Steane code, and benchmark on Quantinuum H2-1 trapped-ion computer. The require multiple logical two-qubit gates, which are implemented transversally, as well non-Clifford single-qubit rotations, performed by non-fault-tolerant state preparation followed a teleportation gadget. First, we individual components randomized benchmarking gate, Ramsey-type experiment $T$ gate. then full QFT circuit, two different methods performing control-$T$, applying it to each basis in set of bases that is sufficient lower bound process fidelity. compare results predictions based component benchmarks.