Quantum Simulation Logic, Oracles, and the Quantum Advantage
Institutionen för Systemteknik, Linköpings Universitet, 581 83 Linköping, Sweden
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(8), 800; https://doi.org/10.3390/e21080800
Received: 16 May 2019 / Revised: 8 August 2019 / Accepted: 12 August 2019 / Published: 15 August 2019
Query complexity is a common tool for comparing quantum and classical computation, and it has produced many examples of how quantum algorithms differ from classical ones. Here we investigate in detail the role that oracles play for the advantage of quantum algorithms. We do so by using a simulation framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms that solve some problems with the same success probability and number of queries as the quantum algorithms. The framework can be simulated using only classical resources at a constant overhead as compared to the quantum resources used in quantum computation. Our results clarify the assumptions made and the conditions needed when using quantum oracles. Using the same assumptions on oracles within the simulation framework we show that for some specific algorithms, such as the Deutsch-Jozsa and Simon’s algorithms, there simply is no advantage in terms of query complexity. This does not detract from the fact that quantum query complexity provides examples of how a quantum computer can be expected to behave, which in turn has proved useful for finding new quantum algorithms outside of the oracle paradigm, where the most prominent example is Shor’s algorithm for integer factorization.
View Full-Text
▼
Show Figures
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Johansson, N.; Larsson, J.-Å. Quantum Simulation Logic, Oracles, and the Quantum Advantage. Entropy 2019, 21, 800. https://doi.org/10.3390/e21080800
AMA Style
Johansson N, Larsson J-Å. Quantum Simulation Logic, Oracles, and the Quantum Advantage. Entropy. 2019; 21(8):800. https://doi.org/10.3390/e21080800
Chicago/Turabian StyleJohansson, Niklas; Larsson, Jan-Åke. 2019. "Quantum Simulation Logic, Oracles, and the Quantum Advantage" Entropy 21, no. 8: 800. https://doi.org/10.3390/e21080800
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
Search more from Scilit