Creation, verification, and scalability of decoherence-free subspaces and noiseless subsystems on superconducting qubits

Decoherence-free subspaces/noiseless subsystems (DFS/NS) preserve quantum information by identifying subspaces/subsystems of the Hilbert space that remain unaffected by decoherence. Identifying DFS/NS codes under collective decoherence is well-understood, and the resultant codes support scalable and universal quantum computation. While most experimental systems, including superconducting qubit-based devices, do not decohere collectively, it is possible to engineer the conditions for collective decoherence using dynamical decoupling (DD) sequences. We report on the creation and verification of DD assisted DFS/NS codes on quantum processors provided by the IBM Quantum Experience. We compare the performance of a DFS/NS encoded qubit with its unprotected counterpart. We show that qubit lifetime can be improved substantially using DD assisted DFS/NS codes. Furthermore, we exploit gate set tomography to characterize logical error channels and estimate logical gate error rates for the DFS/NS encoding. When combined with an analysis of qubit lifetimes for multiple simultaneously encoded qubits, we obtain a comprehensive picture of DFS/NS feasibility and scalability on near-term quantum processors.