Quantum Property Preservation

TL;DR

This paper develops a general theory for quantum property preservation (QPP), enabling continuous Hamiltonian control to maintain specific properties of open quantum systems, offering a complementary approach to existing quantum error correction and dynamical decoupling methods.

Contribution

It formalizes QPP, characterizes controllability under various noise channels, and introduces geometric and control-theoretic insights into property preservation in open quantum systems.

Findings

QPP can be achieved via smooth Hamiltonian control without measurement.

Classification of properties as controllable, uncontrollable, or trivially controllable.

Identification of control Hamiltonian singularities and breakdown times.

Abstract

Quantum property preservation (QPP) is the problem of maintaining a target property of a quantum system for as long as possible. This problem arises naturally in the context of open quantum systems subject to decoherence. Here, we develop a general theory to formalize and analyze QPP. We characterize properties encoded as scalar functions of the system state that can be preserved time-locally via continuous control using smoothly varying, time-dependent control Hamiltonians. The theory offers an intuitive geometric interpretation involving the level sets of the target property and the stable and unstable points related to the noise channel. We present solutions for various noise channels and target properties, which are classified as trivially controllable, uncontrollable, or controllable. In the controllable scenario, we demonstrate the existence of control Hamiltonian singularities and breakdown times, beyond which property preservation fails. QPP via Hamiltonian control is complementary to quantum error correction, as it does not require ancilla qubits or rely on measurement and feedback. It is also complementary to dynamical decoupling, since it uses only smooth Hamiltonians without pulsing and works in the regime of Markovian open system dynamics. From the perspective of control theory, this work addresses the challenge of tracking control for open quantum systems.