Efficient Implementation of Fault-tolerant 4: 1 Quantum Multiplexer(QMUX) using Clifford plus T-group

Since last couple of years quantum computing has made tremendous advancement towards developing the next generation computing paradigm and much to this cause several investigations already have started to make efficient implementation for quantum logic circuit. By considering several design constraints especially from noisy sources, new design models (like Nearest Neighbor design, Fault-tolerant architecture, single T - depth design) are evolving on daily basis. Focusing on this need, here in this work we show an efficient implementation of Quantum Multiplexer circuit towards realizing the quantum ALU. Two different design models are shown here, where in the first model, we have proposed the ancilla free garbage based implementation of MUX circuit and in the second model, we improve the previous design to make it garbage free. In our design phase, initially we have derived smaller modules and then they are integrated to make the generalized representation. For, ensuring fault-tolerant property in our made designs, we have used the functional power of Clifford +T group. All the made circuits are tested over input vectors and the logical correctness of the designs have been verified individually.