Demonstrating Record Fidelity for the Quantum Fourier Transform

Abstract

We demonstrate the Parity Architecture on quantum hardware, using the quantum Fourier transform (QFT) as a benchmark. As a result, a record performance in both fidelity and qubit count is achieved using quantum processors with a native CZ-based instruction set. On the IBM Heron r3 chip, a process fidelity of the QFT algorithm of $F\approx 10^{-2}$ for $N=50$ qubits is achieved. The scaling of the speedup compared to previous swap-based methods is super-exponential $\mathcal{O}(\exp (N^2))$. Furthermore, we show that the scaling can be improved further by including iSWAP gates in the instruction set.