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%.