Hexagonal matching codes with two-body measurements

Abstract

Matching codes are stabilizer codes based on Kitaev's honeycomb lattice model. The hexagonal form of these codes are particularly well-suited to the heavy-hexagon device layouts currently pursued in the hardware of IBM Quantum. Here we show how the stabilizers of the code can be measured solely through 2-body measurements that are native to the architecture. Though the subsystem code formed by these measurements has a trivial code space, the sequence in which they are measured allows the desired logical subspace to be preserved. This therefore achieves a result similar to the recently introduced Floquet codes, but via a completely different method. The process is then run on 27 and 65 qubit devices, to compare results with simulations for a standard error model. It is found that the results correspond well to simulations where the noise strength is similar to that found in the benchmarking of the devices. The best devices show results consistent with a noise model with an error probability of around $1.5\%-2\%$.

Nonlocal correlations in noisy multiqubit systems simulated using matrix product operators

“…The setup with alternating-frequency qubits on a plaquette is motivated by currently deployed IBM Quantum devices [45] accessible via the cloud using Qiskit [46], whose time-dependent Hamiltonian can be programmed [47]. In those devices the qubit connectivity is that of a "heavy-hexagonal" lattice [48,49], which consists of connected qubit plaquettes. Typically, the fixed-frequency qubits are purposefully chosen to have different frequencies for neighboring ones in order to reduce unwanted interactions, and the design of qubit frequency patterns and their effect on the dynamics is an active field of research [50][51][52].…”