Clifford plus T-based implementation of fault-tolerant quantum circuits over XOR-Majority Graph

To build a scalable quantum computer that is sufficiently large to solve classically intractable problems is one of the biggest engineering quests of current times. But, the fragility of quantum states with short coherence time and vulnerability of quantum components towards external noise becomes an immense challenge to the physical implementation. Thus, the fault-tolerant architecture over the quantum error-correcting code (qecc) such as Surface code in optimal logical level are most desirable and can be achieved transversely using Clifford+T-group. However, the T-gate has high latency. In this paper, we introduce a template matching scheme over the Xor-Majority Graphs to realize a high scalable fault-tolerant quantum circuit. The proposed methodology is validated with multiple quantum benchmarks achieving an improvement of 71.98%, and 78.33% on average T - count, and T - depth respectively over state-of-art, and at the same time completely avoiding any ancillary input. When ancillary inputs are permitted, an improvement of 92.77% on T - depth is obtained.