Adiabatic quantum unstructured search in parallel

TL;DR

This paper develops an optimized adiabatic quantum search schedule that maintains Grover's quadratic speedup, enabling efficient parallelization and robustness against limited coherence times in quantum hardware.

Contribution

It introduces a new adiabatic schedule with rapid endpoint variation, improving success probability and demonstrating potential quantum advantage under resource constraints.

Findings

Schedule preserves quadratic speedup with faster endpoint variation

Numerical simulations show superior probability performance

Protocol achieves desired success probability in near-optimal time

Abstract

We present an optimized adiabatic quantum schedule for unstructured search building on the original approach of Roland and Cerf [Phys. Rev. A 65, 042308 (2002)]. Our schedule adiabatically varies the Hamiltonian even more rapidly at the endpoints of its evolution, preserving Grover's well-known quadratic quantum speedup. In the errorless adiabatic limit, the probability of successfully obtaining the marked state from a measurement increases directly proportional to time, suggesting efficient parallelization. Numerical simulations of an appropriate reduced two-dimensional Schr\"odinger system confirm adiabaticity while demonstrating superior performance in terms of probability compared to existing adiabatic algorithms and Grover's algorithm, benefiting applications with possible premature termination. We introduce a protocol that ensures a marked-state probability at least $p$ in time of order $\sqrt{N}(1+p/\varepsilon)$, and analyze its implications for realistic bounded-resource scenarios. Our findings suggest that quantum advantage may still be achievable under constrained coherence times (where other algorithms fail), provided the hardware allows for them to be sufficiently long.