Quantum Logical States and Operators for Josephson-like Systems

TL;DR

This paper develops an algebraic framework for Josephson-like quantum systems, constructing logical states and operators suitable for quantum information processing using two-boson algebra techniques.

Contribution

It introduces a formal algebraic description of Josephson systems and constructs robust logical states and operators for quantum computing applications.

Findings

Logical codewords are even and odd coherent states, resistant to shifts.

Logical operators are expressed via two-boson algebra operators.

The scheme is relevant for quantum information processing.

Abstract

We give a formal algebraic description of Josephson-type quantum dynamical systems, i.e., Hamiltonian systems with a cos theta-like potential term. The two-boson Heisenberg algebra plays for such systems the role that the h(1) algebra does for the harmonic oscillator. A single Josephson junction is selected as a representative of Josephson systems. We construct both logical states (codewords) and logical (gate) operators in the superconductive regime. The codewords are the even and odd coherent states of the two-boson algebra: they are shift-resistant and robust, due to squeezing. The logical operators acting on the qubit codewords are expressed in terms of operators in the enveloping of the two-boson algebra. Such a scheme appears to be relevant for quantum information applications.