Year: 2014
Type: article
Abstract: Quantum states can, in a sense, be thought of as generalizations of classical probability distributions, but are more powerful than probability distributions when used for computation or communication. Quantum speedup therefore requires some feature of quantum states that classical probability distributions lack. One such feature is interference. We quantify interference and show that there can be no quantum speedup due to a small number of operations incapable of generating large amounts of interference (although large numbers of such operations can, in fact, lead to quantum speedup). Low-interference operations include sparse unitaries, Grover reflections, short-time and low-energy Hamiltonian evolutions, and the Haar wavelet transform. Circuits built from such operations can be classically simulated via a Monte Carlo technique making use of a convex combination of two Markov chains. Applications to query complexity, communication complexity, and the Wigner representation are discussed.
Source: Physical Review A
Author: Dan Stahlke
Institution: Carnegie Mellon University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2067606087