Lattice surgery-based Surface Code architecture using remote logical CNOT operation

The lattice surgery approach allows for an efficient implementation of universal quantum gate sets with topological quantum error correcting codes that achieve a high threshold and are composed of only the nearest gate operations and low-weight stabilizers. Here, we propose two types of lattice surgery-based logical qubit architectures using the logical remote-controlled-not operation and circuit mapping method. Our architectures enhanced the qubit efficiency, and when combined with our qubit initialization and routing process, they reduced the running time and quantum volume of several quantum circuits by removing time-expensive logical SWAP operations and enabling fast logical CNOT operations. The quantum volume was compared between three cases, one in which the magic state distillation technique was not applied, one in which the multiple magic state distillation circuits are used to reduce the circuit execution time, and the other in which one magic state distillation circuit are used to reduce the number of qubit used.