John Gamble

Quantum low-density parity-check (qLDPC) codes are a class of quantum error-correction (QEC) codes with low-weight parity-checks that each require only a few two-qubit gates to implement. In recent years, qLDPC codes have gained popularity, as concrete code constructions have been found that outperform the surface code, and correspondingly performant practical decoders have been built. An outstanding challenge, however, remains that their Tanner graphs are not 2D-local thereby necessitating entangling gates to operate on distant qubits on a 2D device. Trapped-ion and neutral-atom qubits possess the ability to move qubits around when necessary – i.e. “flying qubits” – obviating the need for long-range gates. Here we report on an explicit layout that leverages flying qubits, that is very low-overhead for many families of cyclic codes (including the most promising qLDPC instances found to-date). Crucially, our layout eschews more complicated qubit permutations, and instead favours the cyclic shift a simple re-ordering of qubits along a loop that can be realized in depth 1 even on current generation devices. This contrasts significantly with layouts on fixed qubits that depend on a large number of long-range (and more error-prone) hardware couplers for long-distance gates. We also report on two competitive new sets of cyclic qLDPC codes that we constructed. The first is a set of Bivariate-Bicycle (BB) codes with lower weight parity-checks and higher minimum distance while maintaining the same length and encoding rate as comparable BB codes in. Second, we also constructed new Hypergraph Product (HGP) codes, that significantly outperform previously state-of-the-art HGP instances that were optimized by machine-learning methods. Both sets of new codes are efficiently implementable with our cyclic layout with syndrome circuits of fixed depth, made up of alternating layers of parallel gates and only a very small number of cyclic shifts. Combining competitive new qLDPC codes alongside a simple layout implementable on existing hardware, our work suggest a concrete and practical path towards a fault-tolerant quantum computer.