Verification of Quantum Systems using Barrier Certificates

TL;DR

This paper explores the novel application of barrier certificates, extended to complex variables, for verifying quantum system behaviors using linear programming techniques, demonstrated on simple quantum models.

Contribution

It introduces an extension of barrier certificates to complex variables and develops a linear programming method for their automatic generation in quantum system verification.

Findings

Successfully extended barrier certificates to complex variables

Developed a linear programming approach for certificate generation

Demonstrated effectiveness on simple quantum systems

Abstract

Various techniques have been used in recent years for verifying quantum computers, that is, for determining whether a quantum computer/system satisfies a given formal specification of correctness. Barrier certificates are a recent novel concept developed for verifying properties of dynamical systems. In this article, we investigate the usage of barrier certificates as a means for verifying behaviours of quantum systems. To do this, we extend the notion of barrier certificates from real to complex variables. We then develop a computational technique based on linear programming to automatically generate polynomial barrier certificates with complex variables taking real values. Finally, we apply our technique to several simple quantum systems to demonstrate their usage.