In this research, we create a scalable version of the quantum Fourier transform-based arithmetic circuit to perform addition and subtraction operations on N n-bit unsigned integers encoded in quantum registers, and it is compatible with d-level quantum sources, called qudits. We present qubit- and ququart-based multi-input QFT adders, and we compare and discuss potential benefits such as circuit simplicity and noise sensitivity. The results show that a ququart-based system significantly reduces gate count and improves computational efficiency compared to qubit-based systems. Overall, the findings presented in this study represent a promising step forward in the development of efficient quantum arithmetic circuits, particularly for multi-input operations, with clear advantages for ququart-based systems in reducing gate count, decoherence, and circuit complexity.
In this research, we create a scalable version of the quantum Fourier transform-based arithmetic circuit to perform addition and subtraction operations on N n-bit unsigned integers encoded in quantum registers, and it is compatible with d-level quantum sources, called qudits. We present qubit- and ququart-based multi-input QFT adders, and we compare and discuss potential benefits such as circuit simplicity and noise sensitivity. The results show that a ququart-based system significantly reduces gate count and improves computational efficiency compared to qubit-based systems. Overall, the findings presented in this study represent a promising step forward in the development of efficient quantum arithmetic circuits, particularly for multi-input operations, with clear advantages for ququart-based systems in reducing gate count, decoherence, and circuit complexity.
Abstract The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers , and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance, and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. We analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.
The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor's algorithm, weighted sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM's superconducting qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands' superposed integer states. We analyze performance, and identify the most effective approximation depths for quantum add and quantum multiply within the given context. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges - relevant to signed, unsigned, modular and non-modular versions - that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. We analyze performance trends in our results and speculate on possible future development within this computational paradigm.
In this study, we propose an efficient quantum multiplication approach based on a QFT-assisted parallelized addition scheme. The multiplication stage is implemented using a structure composed entirely of Toffoli gates, which generate partial products. In the second stage, these partial results are accumulated using a QFT-based adder. Unlike conventional QFT-based arithmetic circuits, the proposed design eliminates the repeated application of QFT and inverse QFT (IQFT) operations during intermediate summation processes. This leads to a significant reduction in the total gate count and circuit complexity, enabling a more resource-efficient implementation. To demonstrate the feasibility of the proposed approach, a quantum circuit that performs the multiplication of two 3-bit numbers is designed. The circuit is tested and validated using IBM quantum simulators. The results indicate that the proposed method provides a more efficient alternative to traditional quantum multiplication techniques in terms of gate cost and circuit depth.
In this study, we construct the quantum reversible counterparts of the logical AND, OR, XOR, NOR, and NAND gates. We utilize a quantum Fourier transform (QFT)-based adder circuit that replicates the functionality of a digital half-adder, which computes the sum and carry of two input bits using XOR and AND gates, respectively. To realize different logic gate operations, we apply pre- and post-processing to the QFT-adder using quantum gates, leveraging Boolean algebra properties to enable conversions between various logical functions. Although the number of elementary quantum logic gates increases for a small number of inputs-making the approach appear inefficient at first glance-the overall required qubit count is reduced compared to non-QFT-based designs as the number of inputs increases.
Abstract This study proposes and construct a primitive quantum arithmetic logic unit (qALU) based on the quantum Fourier transform (QFT). The qALU is capable of performing arithmetic ADD (addition) and logic NAND gate operations. It designs a scalable quantum circuit and presents the circuits for driving ADD and NAND operations on two‐input and four‐input quantum channels, respectively. By comparing the required number of quantum gates for serial and parallel architectures in executing arithmetic addition, it evaluates the performance. It also execute the proposed quantum Fourier transform‐based qALU design on real quantum processor hardware provided by IBM. The results demonstrate that the proposed circuit can perform arithmetic and logic operations with a high success rate. Furthermore, it discusses in detail the potential implementations of the qALU circuit in the field of computer science, highlighting the possibility of constructing a soft‐core processor on a quantum processing unit.
This article demonstrates a quantum calculator by experimentally simulating and performing basic arithmetic operations, namely addition, subtraction, multiplication, division on real quantum devices using the IBM Quantum Experience (IBM QE) platform. Two addition algorithms are considered, the classical version, using the Toffoli gate, and using the quantum Fourier transform (QFT). In particular summation with QFT saves memory and time. The task of the work is to build a quantum circuit that performs arithmetic operations between the binary representation of two integers. We then propose a quantum algorithm for converting decimal to binary. This method also allows for massive parallelization during its execution. The addition, subtraction, multiplication, and division functions based on QFT have been improved with some changes. The proposed operations are compared with the closest quantum arithmetic operations. Therefore, we can implement a practical quantum calculator by performing operations on a real quantum computer. The circuits are defined as a kind of quantum adder using a quantum Fourier transform, implemented in Qiskit and demonstrated on one or two copies.