Classical/Quantum Mix

Shi Wang, Hendra I. Nurdin, Guofeng Zhang +1 more

The purpose of this paper is to formulate and solve a synthesis problem for a class of linear quantum equations that may describe mixed quantum-classical systems. We propose a standard model for mixed quantum-classical linear stochastic systems for the design process, which can present the internal structure of a mixed quantum-classical system. Physical realizability conditions are derived for the standard model to ensure that it can correspond to a physical system. Furthermore, a network synthesis theory for a mixed quantum-classical system of the standard form has been developed. An example is given to illustrate the results.

F. G. Major

Shi Wang, Hendra I. Nurdin, Guofeng Zhang +1 more

The purpose of this paper is to formulate and solve a synthesis problem for a class of linear quantum equations that may describe mixed quantum-classical systems. A general model and a standard model for mixed quantum-classical linear stochastic systems are proposed for our design processes and then we show how the former may be transformed into the latter, which can clearly present the internal structure of a mixed quantum-classical system. Physical realizability conditions are derived separately for the two models to ensure that they can correspond to physical systems. Furthermore, a network synthesis theory is developed for a mixed quantum-classical system of the standard form and an example is given to illustrate the theory. Index Terms — linear stochastic system, mixed quantum-classical linear stochastic system, quantum system, network synthesis theory, physical realizability condition. I.

Edmund Marr

Simon Apers, Alain Sarlette, Francesco Ticozzi

Quantum walks have been linked to acceleration in various information processing tasks, and proposed as a possible model for quantum-enhanced behavior in biological systems.These links and acceleration claims have been made with various levels of detail.Here we consider discrete-time quantum walks, and focus on the task of mixing, i.e., distributing the state over a graph.Previous papers have observed that the so-called coined quantum walks can accelerate mixing on certain graphs with respect to the optimal classical Markov chain.We here show that the same speedup can be attained with a classical process, if a similar classical coin is added.We establish a precise correspondence between the mixing performance of quantum walks and such "lifted walks" for all (finite) graphs, and thereby improve known bounds on quantum walk mixing time.We conclude that the advantage of quantum walks with respect to classical processes is not in the mixing speed of the optimal design.However, a notable quantum advantage might reside in the fact that the mixing speed obtained with suboptimal designs, due to for instance limited graph knowledge, appears to be generically faster.

Nicolaas P. Landsman