Karl Mayer, Ciarán Ryan-Anderson, Natalie Brown, Elijah Durso-Sabina, Charles H. Baldwin, David Hayes, Joan M. Dreiling, Cameron Foltz, John P. 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 E. Siegfried, et al (3) (Apr 15 2024).
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 $T$ gate. We then implement the full QFT circuit, using two different methods for performing a logical control-$T$, 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.