Interference versus success probability in quantum algorithms with imperfections
arXiv:0711.1513 · doi:10.1103/PhysRevA.77.022318
Abstract
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We consider systematic unitary errors, random unitary errors, and decoherence processes. We show that unitary errors which destroy the interference destroy the efficiency of the algorithm, too. However, unitary errors may also create useless additional interference. In such a case the total amount of interference can increase, while the efficiency of the quantum computation decreases. For decoherence due to phase flip errors, interference is destroyed for small error probabilities, and converted into destructive interference for error probabilities approaching one, leading to success probabilities which can even drop below the classical value. Our results show that in general interference is necessary in order for a quantum algorithm to outperform classical computation, but large amounts of interference are not sufficient and can even lead to destructive interference with worse than classical success rates.
21 pages, 16 figures
References in corpus (11)
- Quantum Mechanics helps in searching for a needle in a haystack
- Quantum Algorithms Revisited
- Tight bounds on quantum searching
- On the role of entanglement in quantum computational speed-up
- Characterizing Entanglement
- Efficient classical simulation of the semi-classical Quantum Fourier Transform
- A Quantitative Measure of Interference
- Classical simulability and the significance of modular exponentiation in Shor's algorithm
- Role of interference in quantum state transfer through spin chains
- Quantum Computing of Poincare Recurrences and Periodic Orbits
- Distribution of interference in random quantum algorithms