Noisy simulations of Quantum Walk and Quantum Walk search via Quantum Cellular Automata on a semiconducting spin processor emulator

In this work we map NISQ-friendly implementations of the non-interacting QCA to a circuit Quantum Electrodynamics (cQED) hardware. We perform both noiseless and noisy simulations of the QCA one particle sector, namely the Quantum Walk, on N-cycles and NxN torus graphs. Moreover, in such a framework we also investigate the searching problem. The noiseless simulations are conducted with the Qiskit Aer simulator, while the noisy simulations with C12 Quantum Electronics in-house noisy emulator, Callisto. We benchmark the performance of our implementations by analyzing the simulations via relevant metrics and quantities such as the state count distributions, the Hellinger Fidelity, the l1 distance, the hitting time, and success probability. Our results demonstrate that the QCA framework, in combination with cQED processors, holds promise as an effective platform for early NISQ implementations of Quantum Walk and Quantum Walk Search algorithms.