The multiplier based on quantum Fourier transform
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The multiplier based on quantum Fourier transform AnQi Zhang1 · XueMei Wang1 · ShengMei Zhao1 Received: 12 April 2020 / Accepted: 7 June 2020 © China Computer Federation (CCF) 2020
Abstract In the paper, we first present a quantum multiplier based on quantum Fourier transform (QFT), which is composed by a series of double-controlled phase gates, the control qubits are from the two multipliers, and the controlled qubits are in the ancillary state. By the sequential usage of the double-controlled phase gates, the product could be obtained after the inverse quantum Fourier transform (IQFT) on the final ancillary output state. Then, we further optimize the proposed quantum multiplier. The circuit analysis shows that the proposed multiplier could reduce the number of qubits in ancillary, and the multiplication result of finite qubits can be directly obtained by using fewer quantum gates. The optimization has reduced the resource cost of quantum multiplier greatly. Keywords Multiplier · Quantum Fourier transform · Double-controlled phase gate
1 Introduction In the era of big data processing, due to the rapid innovation of essential technologies, computers or algorithms with the capacity of exascale computation are needed to be built (Shao et al. 2019). Quantum computing is a promising technique (Ying and Feng 2009) due to quantum parallel computations, and has found great applications in computing theory (Wen et al. 2019), search (Chen et al. 2020) and scientific computation (Li et al. 2018; Ye et al. 2019). Moreover, there are quite a few new developments in quantum algorithms (Wang et al. 2020; Zhang and Ni 2020; Shang et al. 2020; Shao et al. 2019) such as quantum machine learning (Hu et al. 2019), factoring (Peng et al. 2019; Wang 2019) and so on, and quantum computing is entering the noisy intermediate-scale quantum (NISQ) period. Circuits implementing reversible modular arithmetic operations are of significant contemporary interest due to their prevalence in important quantum algorithms (Hu * ShengMei Zhao [email protected] AnQi Zhang [email protected] XueMei Wang [email protected] 1
Institute of Signal and Processing, Nanjing university of Posts and Telecommunication, Nanjing, China
et al. 2019; Zhang and Ni 2020; Shor 1994). Multiplier is a very important circuit for the reversible modular arithmetic operations (Akbar et al. 2011; Edrisi Arani and Rezai 2018), and several multiplier have been proposed (Akbar et al. 2011; Edrisi Arani and Rezai 2018; Baugh and Wooly 1973; Kotiyal et al. 2014; Alvarez-Sanchez et al. 2008; Draper et al. 2006; Faraji and Mosleh 2018; Chudasama et al. 2018; Muoz-Coreas and Thapliyal 2018; Panahi et al. 2019). The multiplier proposed in Akbar et al. (2011), was designed by utilizing the modified Baugh–Wooley approach, where 17 AND gates and 8 NOT gates are needed to produce one adder cell, and was achieved significant improvements in terms of quantum cost. Numerous studies of multiplier have been reported using QCA. Chudasama et al. (2018) mainly focu
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