NQCP seminar - Gavin Brennen, Macquarie University, Sydney

Non-local interactions as a resource for quantum error correction 

Abstract:  Quantum error correction (QEC) has been described as a process where the effect of errors is reduced by fighting entanglement with entanglement and results over the past decade are converging on the idea that the more non-local the codes the better. I'll describe some recent results on using long range entangling gates natively available in architecture like trapped neutral atoms arrays, to improve the performance of QEC. The first example is a low density parity check code (LDPC), we dub the La-cross code, using a relatively simple non-local extension of the stabilizers for the surface code, where the desired long-range connectivity can be targeted via the Rydberg-blockade mechanism. Below nearest neighbour two qubit errors of ~0.1% these codes outperform comparable sized surface codes in all respects [arXiv:2404.13010]. The second example is permutation invariant (PI) codes which are subspaces of the maximally symmetric space of qubits, i.e. superpositions of Dicke states. PI codes can be processed with the assistance of a non-locally connected bosonic mode, like a microwave/optical cavity mode or motional mode, coupled to the spins. While less studied than stabilizer codes, they offer some advantages including: robustness against unlocated erasure errors, designable transversal gates, and can be used for finite-round error corrected quantum sensing [arXiv:2212.06285].