Error correction 1 Hilbert spaces 1 Hilbert-space reduction Logical qubits 1 Multi-layered 1 Novel methods 1 Quantum entanglement 1 Quantum error 1 Quantum error corrections 1 Quantum optics 1 Quantum simulators 1 Qubits 1 Space reductions 1 Surface code 1 Synthesised 1 Vector spaces 1 quantum error 1 quantum simulator 1 surface code 1