Quantum Computation Using Action Variables

TL;DR

This paper explores a novel approach to quantum computation by encoding qubits into action variables of integrable systems, utilizing resonant control and the quantum KAM theorem for fault tolerance.

Contribution

It introduces a new framework for fault-tolerant quantum computation based on action variables and the quantum KAM theorem, extending harmonic oscillator models.

Findings

Proposes encoding qubits in quantum action variables.

Demonstrates fault-tolerance via the quantum KAM theorem.

Uses Birkhoff normal form as a mathematical framework.

Abstract

Recently, Lloyd and Montangero have made a brief research proposal on universal quantum computation in integrable systems. The main idea is to encode qubits into quantum action variables and build up quantum gates by the method of resonant control. We study this proposal to argue quantum computation using action variables as fault-tolerant quantum computation, whose fault-tolerance is guaranteed by the quantum KAM theorem. Besides, we view the Birkhoff norm form as a mathematical framework of the extended harmonic oscillator quantum computation.