Engineering exotic phases for topologically-protected quantum computation by emulating quantum dimer models

TL;DR

This paper explores engineering quantum devices using quantum dimer models to achieve topologically protected qubits, analyzing the feasibility, temperature constraints, and practical challenges in implementation with Josephson junction arrays and cold atomic gases.

Contribution

It introduces a nonperturbative ENCORE method to design quantum devices for topological quantum computation and assesses the impact of additional interactions on device feasibility.

Findings

Optimal temperatures below 1 mK require extra interactions not in standard models.

Long operational times are needed due to small energy scales in cold atom implementations.

Realization of topological phases demands large interaction scales and careful engineering.

Abstract

We use a nonperturbative extended contractor renormalization (ENCORE) method for engineering quantum devices for the implementation of topologically protected quantum bits described by an effective quantum dimer model on the triangular lattice. By tuning the couplings of the device, topological protection might be achieved if the ratio between effective two-dimer interactions and flip amplitudes lies in the liquid phase of the phase diagram of the quantum dimer model. For a proposal based on a quantum Josephson junction array [L. B. Ioffe {\it et al.}, Nature (London) {\bf 415}, 503 (2002)] our results show that optimal operational temperatures below 1 mK can only be obtained if extra interactions and dimer flips, which are not present in the standard quantum dimer model and involve three or four dimers, are included. It is unclear if these extra terms in the quantum dimer Hamiltonian destroy the liquid phase needed for quantum computation. Minimizing the effects of multi-dimer terms would require energy scales in the nano-Kelvin regime. An alternative implementation based on cold atomic or molecular gases loaded into optical lattices is also discussed, and it is shown that the small energy scales involved--implying long operational times--make such a device impractical. Given the many orders of magnitude between bare couplings in devices, and the topological gap, the realization of topological phases in quantum devices requires careful engineering and large bare interaction scales.