Demonstration of high-fidelity entangled logical qubits using transmons

Quantum error correction (QEC) codes are necessary to fault-tolerantly operate quantum computers. However, every such code is inherently limited by its inability to detect logical errors. Here, we propose and implement a method that leverages dynamical decoupling (DD) to drastically suppress logical errors. The key to achieving this is to use the normalizer elements of the QEC code as DD pulses, which we refer to as normalizer dynamical decoupling (NDD). The resulting hybrid QEC-NDD strategy is in principle capable of handling arbitrary weight errors. We test an error detecting version of this strategy using IBM transmon devices and the [[4, 2, 2]] code, demonstrating performance that significantly exceeds the capabilities of using either this code or DD in isolation. We present a method that allows for the detection of logical errors affecting logically encoded Bell states, which, in this case, arise primarily from crosstalk among physical qubits. Building on this, we experimentally demonstrate high-fidelity entangled logical qubits. The fidelities we achieve are beyond-breakeven, i.e., they significantly exceed the corresponding fidelities of unprotected entangled qubits in the same setting.