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Researchers have demonstrated that smoothing the Hamiltonian's temporal profile by ensuring vanishing derivatives significantly reduces infidelity in adiabatic quantum state preparation. This approach improves error scaling from O(ε^n) to O(ε^(n+1)), offering a systematic method to suppress transfer errors in complex many-body systems like Rydberg atom chains. The findings provide a concrete pathway for enhancing the fidelity of quantum algorithms that rely on slow, controlled evolution of system parameters.

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Error in quantum state prep drops as evolution gets smoother

Quantum ZeitgeistOctober 11, 20267 min read

Simulations show end-to-end transfer error in adiabatic evolution can be reduced with smooth Hamiltonian scheduling, scaling as 1/T^(n+1).

Researchers at the University of Copenhagen and Centrum Wiskunde & Informatica have demonstrated a way to systematically reduce errors during the preparation of complex quantum states. Their work, combining numerical calculations with simulations on a Rydberg atom quantum simulator, reveals that smoother changes to the Hamiltonian, specifically, a time-dependent Hamiltonian with vanishing first to nth order derivatives at the beginning and end of a process, can lower infidelity to a scaling of 1/T^(n+1), where T is the evolution time. The team investigated this effect using a one-dimensional mixed-field Ising model and a chain of Rydberg atoms, finding that careful scheduling of the Hamiltonian suppresses end-to-end transfer error. This mathematical relationship demonstrates a systematic way to minimize error by carefully controlling the Hamiltonian’s behavior over time. Numerical calculations and simulations performed on a chain of Rydberg…

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