Resource Optimized Quantum Squaring Circuit

• URL: http://arxiv.org/abs/2406.01875v1
• Date: Tue, 4 Jun 2024 01:04:01 GMT
• Title: Resource Optimized Quantum Squaring Circuit
• Authors: Afrin Sultana, Edgard Muñoz-Coreas,
• Abstract summary: Quantum squaring operation is useful building block in implementing quantum algorithms. Quantum circuits could be made fault-tolerant by using error correcting codes and fault-tolerant quantum gates. In this paper, we present a novel integer squaring architecture optimized for T-count, CNOT-count, T-depth, CNOT-depth, and $KQ_T$ that produces no garbage outputs.
• Score: 0.7673339435080445
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $KQ_T$.

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