Poster is on display and will be presented at the poster pitch session.
Running complex quantum algorithms on near-term quantum hardware is hindered by limited qubit connectivity and the resulting SWAP gate overhead. We present a parity code-based approach that facilitates the direct implementation of all-to-all connected circuits—such as the Quantum Fourier Transform (QFT) and Quantum Approximate Optimization Algorithm (QAOA)—on devices with only nearest-neighbor connectivity. By formulating the parity code as a non-error-correcting code, we reduce the required SWAP gates and achieve circuit depths and gate counts comparable to those achievable on fully connected architectures. As a result, we present new all-to-all QAOA and QFT circuits that set new lowest entangling gate counts and circuit depths for these algorithms on linear and ladder topologies. Experiments on state-of-the-art superconducting quantum hardware (IBM Nighthawk) show an order of magnitude improvement in QFT fidelity compared to a standard SWAP-based circuits when going beyond 13 qubits.
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