Dissipative Encoding of Quantum Information

TL;DR

This paper formalizes dissipative quantum encoding using Markovian dynamics, demonstrating finite-time convergence and robustness advantages over unitary methods, with applications to stabilizer codes like the toric code.

Contribution

It introduces a framework for dissipative quantum encoding with finite-time convergence and robustness, applicable to stabilizer codes and overcoming limitations of unitary encoding.

Findings

Finite-time dissipative encoders can be constructed for stabilizer codes.

Dissipative encoders exhibit robustness against initialization errors.

Application to Kitaev's toric code illustrates practical relevance.

Abstract

We formalize the problem of dissipative quantum encoding, and explore the advantages of using Markovian evolution to prepare a quantum code in the desired logical space, with emphasis on discrete-time dynamics and the possibility of exact finite-time convergence. In particular, we investigate robustness of the encoding dynamics and their ability to tolerate initialization errors, thanks to the existence of non-trivial basins of attraction. As a key application, we show that for stabilizer quantum codes on qubits, a finite-time dissipative encoder may always be constructed, by using at most a number of quantum maps determined by the number of stabilizer generators. We find that even in situations where the target code lacks gauge degrees of freedom in its subsystem form, dissipative encoders afford nontrivial robustness against initialization errors, thus overcoming a limitation of purely unitary encoding procedures. Our general results are illustrated in a number of relevant examples, including Kitaev's toric code.