Logical qubits Qubits 3 Quantum optics 2 Aircraft scheduling 1 Annealing 1 Benchmarking 1 Encoding (symbols) 1 Error correction 1 Error rate 1 Errors 1 Exact cover problem 1 Fault tolerance 1 Fault tolerant schemes 1 Fault-tolerant 1 Fault-tolerant computation 1 Fault-tolerant thresholds 1 High probability 1 Hilbert spaces 1 Hilbert-space reduction 1 Large problems 1 Multi-layered 1 Novel methods 1 Optical demonstrations 1 Optical systems 1 Optimization problems 1 Physical qubits 1 Problem size 1 Processing units 1 Quantum Computing 1 Quantum annealing 1