Noise-Induced Sampling of Alternative Hamiltonian Paths in Quantum Adiabatic Search

TL;DR

This paper investigates how noise-induced sampling of different Hamiltonian paths affects the performance of quantum adiabatic search in solving NP-Complete problems, revealing that noise generally slows down the process but may improve scaling under certain conditions.

Contribution

It introduces a numerical analysis of noise effects on Hamiltonian path variation in quantum adiabatic search, highlighting potential performance benefits from path alterations.

Findings

Noise slows down QuAdS performance.

A downward shift in scaling exponent occurs for N > 12.

Altered Hamiltonian paths may improve scaling under noise.

Abstract

We numerically simulate the effects of noise-induced sampling of alternative Hamiltonian paths on the ability of quantum adiabatic search (QuAdS) to solve randomly generated instances of the NP-Complete problem N-bit Exact Cover 3. The noise-averaged median runtime is determined as the noise-power and number of bits N are varied, and power-law and exponential fits are made to the data. Noise is seen to slowdown QuAdS, though a downward shift in the scaling exponent is found for N > 12 over a range of noise-power values. We discuss whether this shift might be connected to arguments in the literature that suggest that altering the Hamiltonian path might benefit QuAdS performance.