Quantum circuit designs of carry lookahead adder optimized for T-count T-depth and qubits

Quantum circuits of arithmetic operations such as addition are needed to implement quantum algorithms in hardware. Quantum circuits based on Clifford+T gates are used as they can be made tolerant to noise. The trade -off of gaining fault tolerance from using Clifford+T gates and error-correcting codes is the high implementation overhead of the T gate. As a result, the T-count and T-depth performance measures have become important in quantum circuit design. Due to noise, the risk for errors in a quantum circuit computation increases as the number of gate layers (or depth) in the circuit increases. As a result, low depth circuits such as quantum carry lookahead adders (QCLA)s have caught the attention of researchers. This work presents two QCLA designs each optimized with emphasis on T-count and T-depth or qubit cost, respectively. In-place and out-of-place versions of each design are shown. The proposed QCLAs are compared against the existing works in terms of T-count and T-depth. The proposed QCLAs for out-of-place addition achieve average T-count savings of 54.34% and 37.21%, respectively. The proposed QCLAs for out-of-place addition achieve up to a 33.33% reduction in T-depth. The proposed QCLAs for in-place addition achieve average T-count savings of 65.31% and 30.63%, respectively. When compared to existing works, the proposed QCLAs for in-place addition achieves T-depth savings ranging from 33.33% to 95.56%.

Automated summary

This study focuses on the performance measures of T-count and T-depth in quantum circuit design. Researchers have paid attention to low depth circuits like QCLA designs, and proposed optimized solutions. By comparing with existing works, it is evident that the proposed QCLAs have made significant improvements in terms of T-count and T-depth.