Hardware Implementation of Quantum Stabilizers in Superconducting Circuits

Stabilizer operations are at the heart of quantum error correction and are typically implemented in software-controlled entangling gates and measurements of groups of qubits. Alternatively, qubits can be designed so that the Hamiltonian corresponds directly to a stabilizer for protecting quantum information. We demonstrate such a hardware implementation of stabilizers in a superconducting circuit composed of chains of π-periodic Josephson elements. With local on-chip flux and charge biasing, we observe a progressive softening of the energy band dispersion with respect to flux as the number of frustrated plaquette elements is increased, in close agreement with our numerical modeling.