Multilayered logical qubits and synthesized quantum bits

Quantum error correction is likely to be key in obtaining near term quantum advantage. We propose a novel method for providing multiple logical qubits in the correction of quantum errors using classical computers. The core idea of our work is built upon two main pillars: dividing the Hilbert space into reduced Hilbert spaces with individual logical qubits and synthesizing the reduced Hilbert spaces through a mathematical collaborating between classical bits and logical quantum states. We demonstrate that our method supports at least 20 logical qubits in a surface code with a code distance of 3. Furthermore, we generate entangled states of multiple logical qubits from lattice surgery-based surface codes using only physical qubit operations. This approach enables classical computers to support a larger number of logical qubits using less memory and perform faster simulations.