Quantum Dynamics

Canh Minh Do, Tsubasa Takagi, Kazuhiro Ogata

While constructing practical quantum computers by big companies remains a challenge, the application of quantum communication and cryptography has made remarkable progress. Therefore, it is crucial to verify quantum protocols before they can be trusted in safety and security-critical applications. We have proposed Basic Dynamic Quantum Logic (BDQL) to formalize and verify sequential models of quantum protocols with a support tool developed in Maude. However, BDQL does not support concurrency in its formalization. This article introduces Concurrent Dynamic Quantum Logic (CDQL), an extension of BDQL, to formalize and verify concurrent models of quantum protocols. CDQL is more expressive than BDQL by considering concurrent behavior and communication among participants in quantum protocols. Since CDQL is a conservative extension of BDQL, we extend the syntax of BDQL to CDQL and make a transformation from CDQL to BDQL without interrupting the semantics of BDQL. We also extend the implementation of BDQL to support CDQL, making a new support tool in Maude. The new support tool is equipped with a lazy rewriting strategy to make the verification process significantly faster. Several quantum communication protocols are successfully formalized and verified in BDQL/CDQL, demonstrating the effectiveness of our automated approach and tool in verifying quantum protocols.

George Androulakis, Duncan Wright

Linearity of a dynamical entropy means that the dynamical entropy of the n-fold composition of a dynamical map with itself is equal to n times the dynamical entropy of the map for every positive integer n. We show that the quantum dynamical entropy introduced by Słomczyński and Życzkowski is nonlinear in the time interval between successive measurements of a quantum dynamical system. This is in contrast to Kolmogorov-Sinai dynamical entropy for classical dynamical systems, which is linear in time. We also compute the exact values of quantum dynamical entropy for the Hadamard walk with varying Lüders-von Neumann instruments and partitions.

Walter E Thirring

Günter Mahler A, Volker A. Weberruß

Jincheng Zhang

This paper introduces the Dynamic Quantum State Prediction Algorithm (DQPA), a novel approach to quantum state prediction that leverages the inherent dynamism of quantum states. Traditional methods often rely on static models, while DQPA dynamically analyzes and predicts quantum system evolution, ultimately aiming for more precise control and optimization within quantum computation. We detail the core mechanisms of DQPA, emphasizing its ability to mitigate error and computational complexity through the observation of quantum state transitions. This research explores the potential of DQPA to significantly advance the capabilities of quantum algorithms.