Quantum Merkle Trees
Lijie Chen, Ramis Movassagh
Quantum
Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes any classical code and explicitly constructs the corresponding QEC code. Our framework can be seen to generalize the CSS codes, and goes beyond the stabilizer formalism (Fig. 1). A concrete advantage is that the desirable properties of a classical code are automatically incorporated in the design of the resulting quantum code. We reify the theory by various illustrations some of which outperform the best previous constructions. We then introduce a local quantum spinchain Hamiltonian whose ground space we analytically completely characterize. We utilize our framework to demonstrate that the ground space contains explicit quantum codes with linear distance. This side-steps the Bravyi-Terhal no-go theorem.
Lijie Chen, Ramis Movassagh
Quantum
Jesse Michel, Sushruth Reddy, et al.
Journal of Complex Networks
Ramis Movassagh, Jeffrey Schenker
Commun. Math. Phys.
Ramis Movassagh, Leo P. Kadanoff
Journal of Statistical Physics