Quantum Metropolis-Hastings is implemented in quantum circuits via penalized qubitized walks with spectral filtering, where specific modifications are shown to be essential for recovering correct stationary behavior.
Instead, it realises a Dirichlet kernel [22], corresponding to a sharply peaked response at phase 0 with small side lobes
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Quantum Metropolis-Hastings via Penalised Qubitized Walks: Spectral Filtering and Circuit Implementation
Quantum Metropolis-Hastings is implemented in quantum circuits via penalized qubitized walks with spectral filtering, where specific modifications are shown to be essential for recovering correct stationary behavior.