Logical Qubit Layout Problem for ICM Representation

Abstract

This paper formulates the qubit layout problem for ICM representation which is favorable for topological quantum computation. Observing the properties of braiding operations in a logic circuit model of ICM, we study the potential usefulness of two-dimensional qubit layouts based on this model. We compare and contrast the efficiency of one- and two-dimensional qubit layouts in reducing the logical time steps for topological quantum circuits. This leads us to an approach to find a good gate order for two-dimensional qubit layouts. Indeed, our preliminary experimental results show the effectiveness of two-dimensional qubit layouts.