Fault-ignorant Quantum Search

Abstract

We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand. We prove lower bounds on the runtime of such algorithms and thereby find that the quadratic speedup is necessarily lost (in our noise models). However, for low but constant noise levels the algorithms we provide (based on Grover's algorithm) still outperform the best noiseless classical search algorithm.

v1: 15+8 pages, 4 figures; v2: 19+8 pages, 4 figures, published version (Introduction section significantly expanded, presentation clarified, results and order unchanged)

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• Using Quantum Switches to Mitigate Noise in Grover's Search Algorithm
• Invariance of success probability in Grover's quantum search under local noise with memory
• Characterizing error propagation in quantum circuits: the Isotropic Index
• A note on the runtime of a faulty Hamiltonian oracle