Topological self-correcting quantum memory
In this talk, I will give an introduction to the concept of a topological self-correcting quantum memory, which is a hardware approach to fault-tolerant quantum computation. The essence of such an approach is to implement a specific Hamiltonian with intrinsic topological degeneracies, such as the well-known toric-code and surface-code models. The errors in this situation corresponds to creation of anyons and are hence suppressed by energy penalty. In this way, we can let nature itself do the quantum error correction.
However, these exotic Hamiltonians usually involve multi-body interactions and are hence hard to realize. Here, I will mention some of my recent progress on solving this particular problem. I discuss how 4-body spin interactions can emerge in a 2D flat-band lattice with “Aharonov-Bohm cages”, and in the presence of light-matter interactions. Based on such an idea, one can realize the surface-code Hamiltonian in the ultra-strong coupling regime of a circuit-QED lattice, when the interaction strength is comparable to the microwave photon frequency. Two types of 4-body stabilizer interactions are realized by utilizing the electro-magnetic duality in circuit-QED. In such case, the circuit-QED vacuum has topological degeneracies and can be used as a self-correcting quantum memory. An alternative approach without ultra-strong coupling is to simulate the surface-code Hamiltonian in the rotating frame, with side-band driving through modulating the flux penetrating SQUID couplers. Finally, I will mention the problem of finite memory time at non-zero temperature and possible route to circumvent this problem.
College Park, MD 20742