Synthesis Techniques for Fault-tolerant Quantum Circuit Implementation using the Clifford+ZN-group

Decoherence jeopardizes the entanglement of fragile quantum states, and is among the foremost challenges towards engineering scalable quantum computers. Realizing quantum circuit implementation with small qubit count and shallow circuit depth is necessary due to the linear scaling of decoherence rate with qubit count and circuit depth. Conversely, reasonable correction of small unitary errors can be achieved by using surface codes along with a transversal gate set to protect quantum information from decoherence. In this paper, we analyze and report the upper bound of non-Clifford phase-depth for different mapping schemes and synthesis approaches. We introduce a synthesis methodology based on lookup-table (LUT) networks, wherein the Boolean logic translates into fault-tolerant quantum logic using Clifford+ Z N group with zero ancillary cost. We also present fault-tolerant synthesis techniques for k -LUT network using additional ancillary lines with exponential phase-count and unit phase-depth.