Dissipative Encoding of Quantum Information
arXiv:2102.04531 · doi:10.26421/QIC21.9-10-2
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.
29 pages, 4 figures
References in corpus (8)
- Subsystem fault tolerance with the Bacon-Shor code
- Quantum memories based on engineered dissipation
- The structure of preserved information in quantum processes
- On Protected Realizations of Quantum Information
- Quantum resources for purification and cooling: fundamental limits and opportunities
- Stochastic Isometries in Quantum Mechanics
- Encoding Subsystem Codes
- Scaling up reservoir engineering for error-correcting codes