Resource Optimized Quantum Squaring Circuit
<|reference_start|>Resource Optimized Quantum Squaring Circuit: Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean distance calculation, cryptography, and in finding roots and reciprocals. Quantum circuits could be made fault-tolerant by using error correcting codes and fault-tolerant quantum gates (such as the Clifford + T-gates). However, the T-gate is very costly to implement. Two qubit gates (such as the CNOT-gate) are more prone to noise errors than single qubit gates. Consequently, in order to realize reliable quantum algorithms, the quantum circuits should have a low T-count and CNOT-count. In this paper, we present a novel quantum integer squaring architecture optimized for T-count, CNOT-count, T-depth, CNOT-depth, and $KQ_T$ that produces no garbage outputs. To reduce costs, we use a novel approach for arranging the generated partial products that allows us to reduce the number of adders by 50%. We also use the resource efficient logical-AND gate and uncomputation gate shown in [1] to further save resources. The proposed quantum squaring circuit sees an asymptotic reduction of 66.67% in T-count, 50% in T-depth, 29.41% in CNOT-count, 42.86% in CNOT-depth, and 25% in KQ T with respect to Thapliyal et al. [2]. With respect to Nagamani et al. [3] the design sees an asymptotic reduction of 77.27% in T-count, 68.75% in T-depth, 50% in CNOT-count, 61.90% in CNOT-depth, and 6.25% in the $KQ_T$.<|reference_end|>
@article{sultana2024resource,
    title={Resource Optimized Quantum Squaring Circuit},
    author={Afrin Sultana, Edgard Mu~noz-Coreas},
    journal={arXiv preprint arXiv:2406.01875},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.01875},
    primaryClass={quant-ph cs.AR cs.ET}
}