Resource optimized quantum squaring circuit

Afrin Sultana

doi:10.1007/s11227-024-06876-2

Return

Resource optimized quantum squaring circuit

2025-01-13

Afrin Sultana

Edgard Muñoz‐Coreas *

DOI：10.1007/s11227-024-06876-2

Original

Original request for help

Save

Abstract

En 中文

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 KQT 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 Gidney (Quantum 2:74, 2018) 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 KQT with respect to Jayashree et al. (In: 27th International conference on VLSI design, 2014). With respect to Nagamani et al. (Appl Soft Comput 37:1753-1776, 2018) 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 KQT.

Keywords:

Quantum computing

Quantum arithmetic

Squaring operation

Clifford plus T-gates

Quantum circuits