T-count and Qubit Optimized Quantum Circuit Designs of Carry Lookahead Adder

• URL: http://arxiv.org/abs/2004.01826v1
• Date: Sat, 4 Apr 2020 01:07:50 GMT
• Title: T-count and Qubit Optimized Quantum Circuit Designs of Carry Lookahead Adder
• Authors: Himanshu Thapliyal, Edgard Mu\~noz-Coreas, Vladislav Khalus
• Abstract summary: 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 T-count performance measure has become important in quantum circuit design.
• Score: 0.966840768820136
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 tradeoff 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 performance measure has 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 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. The proposed QCLAs for out-of-place addition achieve average T gate savings of $54.34 \%$ and $37.21 \%$, respectively. The proposed QCLAs for in-place addition achieve average T gate savings of $72.11 \%$ and $35.87 \%$

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