2D Qubit Layout Optimization for Topological Quantum Computation

Abstract

Nowadays,Topological quantum computation is considered to be one of the most promising methods in realizing the future of quantum computation. The circuit model for topological quantum computation differs from the conventional quantum circuit model even in the logic level; which is multiple CNOT gates can only be performed at the same time if the order of qubits satisfies a certain property. Thus, there has been a wide research to find a good qubit order in one-dimension to satisfy such a property for topological quantum computation. This paper proposes a new method by using two-dimensional qubit layouts for topological quantum computation in order to reduce the computational time steps instead of one-dimensional qubit layouts used by the conventional computer. The general idea is to find a good two-dimensional qubit layout, so our propose is to find the best set of one-dimensional qubit layouts exactly by solving a minimum clique partition problem, and by then we will find the best two-dimensional layout that can embed as many of one-dimensional layouts as possible. The further task may need a very time-consuming(exponential number of) enumerations because we try to find the best possible solution by using an efficient graph structure called πDDs. Indeed, despite this, we still could not find a solution for larger cases more than 16 qubits (4x4 layout) case in our preliminary experiment. Thus, we also implement an SA-based method in order to find a good two-dimensional qubit layout for a reasonable time. Our preliminary experiment shows that the SA-based method works very well for larger cases.