Design of a Fault-Tolerant BCD to Excess-3 Code Converter Using Clifford+T Quantum Gates
Sandip Das, Shankar Prasad Mitra, Sushmita Chaudhari, Riya Sen · 2026
Quantum computing has the potential to transform modern computation by offering exponential advantages in areas such as cryptography, optimization, and intelligent data processing. To effectively realize these advantages, particularly in fault-tolerant and Noisy Intermediate-Scale Quantum (NISQ) environments, quantum circuits must be both resource-efficient and error-resilient. This paper presents a novel Binary-Coded Decimal (BCD) to Excess-3 code converter designed exclusively using the Clifford+T gate set, which is widely supported by fault-tolerant quantum hardware. The proposed design eliminates conventional 4-bit reversible adder-based implementations and instead employs an optimized logic structure based on Clifford+T-decomposed Peres gates. By leveraging Temporary Logical-AND gates and CNOT operations, the circuit achieves reduced T-count, circuit depth, and quantum cost as key metrics in fault-tolerant quantum computation. Functional correctness is verified through IBM Qiskit, Version 2.1 simulations for all valid BCD inputs. The proposed converter serves as a scalable and hardware-compatible arithmetic building block for resource-aware and AI-oriented quantum architectures.