Real-time Krylov Diagonalisation for Open Quantum Systems

TL;DR

This paper adapts real-time quantum Krylov subspace methods to analyze open quantum systems governed by the Lindblad formalism, demonstrating their effectiveness on a superconducting Kerr resonator.

Contribution

It introduces a novel application of quantum Krylov methods to open systems and estimates the Liouvillian gap in a Kerr Cat qubit regime.

Findings

Successfully applied Krylov methods to a superconducting Kerr resonator.

Estimated the Liouvillian gap in the Kerr Cat qubit regime.

Demonstrated the potential of these methods for open quantum system analysis.

Abstract

In this chapter, we demonstrate how real-time quantum Krylov subspace methods can be adapted to investigate open quantum systems described by the Lindblad formalism. We apply these methods to a two-photon-driven superconducting Kerr resonator and illustrate their use in estimating the Liouvillian gap within the Kerr Cat qubit regime. This is based on work done between November 2025 and January 2026 and on the talk given in early February 2026 at the Kwekfest 2026 conference, to celebrate L.C. Kwek's lifetime achievements.