Post-Quantum Error-Correction for Quantum Annealers

We present a general post-quantum error-correcting technique for quantum annealing, called multi-qubit correction (MQC), that views the evolution in an open-system as a Gibs sampler and reduces a set of (first) excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels -- i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy -- and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and also improves the reproducibility of results, compared to recent hardware/software advances in the realm of quantum annealing such as reverse quantum annealing, increased inter-sample delay, and classical pre/post-processing methods.