Eigenpath Traversal by Poisson-Distributed Phase Randomisation

Learn about a groundbreaking quantum computation framework presented at the 19th Conference on Theory of Quantum Computation (TQC 2024) through this 23-minute conference talk. Explore a novel approach based on the quantum Zeno effect that parallels Adiabatic Quantum Computation (AQC), utilizing randomized dephasing operations determined by a Poisson process to track eigenspace associated with specific eigenvalues. Discover how this framework leads to optimal time complexity bounds of O(1/Δ) with minimal problem-specific requirements, and see its practical applications in achieving optimal scaling for both the Grover problem (O(N^1/2)) and the Quantum Linear System Problem (O(κ\log(1/ε))). Delve into the mathematical foundations through a derived differential equation for fidelity and understand how eigenstate filtering optimizes error tolerance scaling, presented by researchers Joseph Cunningham and Jérémie Roland at OIST, Japan.