A novel fault-tolerant quantum divider and its simulation

Yuan, Shengjie; Gao, Shengwei; Wen, Chao; Wang, Yuchan; Qu, Hong; Wang, Yan

doi:10.1007/s11128-022-03523-8

Cited by 12 publications

(7 citation statements)

References 18 publications

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“…Key challenges in developing quantum circuit implementations for a divider are the reversibility requirement and fault tolerance, as analyzed by Babu and Mia [18]. The fault-tolerance aspect of a quantum circuit implementation of a floating-point divider was recently addressed by Yuan and their colleagues [13]. Implementations of dividers based on the long division approach perform a series of controlled subtractions for which a comparison operation between two integers encoded by qubit strings is required.…”

Section: Brief Review Of Related Workmentioning

confidence: 99%

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Floating-Point Arithmetic with Consistent Rounding on a Quantum Computer

Steijl

2024

Quantum Information Science - Recent Advances and Computational Science Applications

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Implementation of floating-point arithmetic with consistent rounding is a critical component of many quantum algorithms. Quantum circuit implementations for squaring and division serve as examples here. This work was motivated by ongoing work in developing quantum algorithms for scientific and engineering computing applications, where this type of arithmetic often forms part of the algorithm. A key feature of the work is the use of a reduced-precision floating-point representation of real data specifically designed for near-term future quantum computing hardware with a limited number of qubits (e.g., less than 100) and with an increased level of fault tolerance as compared to current quantum computing hardware. The quantum circuit implementations of the squaring of a floating-point number and the division of two floating-point numbers are detailed here, highlighting similarities in the quantum circuit implementation for the logical steps required for rounding-to-nearest in line with the IEEE 754 standard for the two arithmetic operations. This similarity is an important feature regarding future work where an automated generation of this type of quantum circuit from a set of standard modules and circuit templates is employed.

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Section: Brief Review Of Related Workmentioning

confidence: 99%

“…Recently, a small number of works have focused on quantum algorithms with a floating-point type representation of data. These works include research on floatingpoint arithmetic [8][9][10][11][12][13] as well as research on data encoding and representation of quantum images [14,15].…”

Section: Introductionmentioning

confidence: 99%

Floating-Point Arithmetic with Consistent Rounding on a Quantum Computer

Steijl

2024

Quantum Information Science - Recent Advances and Computational Science Applications

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“…The type of quantum comparator circuits introduced by Xia et al [33] is well-suited to the requirements of the present work since it involves a minimum number of auxiliary qubits. It was also recently used in the work of Yuan et al [37], where the design of a fault-tolerant implementation of quantum divider was considered.…”

Section: Exemplar Circuit: Integer Dividermentioning

confidence: 99%

Quantum Circuit-Width Reduction through Parameterisation and Specialisation

2023

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As quantum computing technology continues to develop, the need for research into novel quantum algorithms is growing. However, such algorithms cannot yet be reliably tested on actual quantum hardware, which is still limited in several ways, including qubit coherence times, connectivity, and available qubits. To facilitate the development of novel algorithms despite this, simulators on classical computing systems are used to verify the correctness of an algorithm, and study its behaviour under different error models. In general, this involves operating on a memory space that grows exponentially with the number of qubits. In this work, we introduce quantum circuit transformations that allow for the construction of parameterised circuits for quantum algorithms. The parameterised circuits are in an ideal form to be processed by quantum compilation tools, such that the circuit can be partially evaluated prior to simulation, and a smaller specialised circuit can be constructed by eliminating fixed input qubits. We show significant reduction in the number of qubits for various quantum arithmetic circuits. Divide-by-n-bits quantum integer dividers are used as an example demonstration. It is shown that the complexity reduces from 4n+2 to 3n+2 qubits in the specialised versions. For quantum algorithms involving divide-by-8 arithmetic operations, a reduction by 28=256 in required memory is achieved for classical simulation, reducing the memory required from 137 GB to 0.53 GB.

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“…In the case of multiplication, there are several different works in the literature that have progressively optimized resources in terms of quantum gates, noise tolerance, or delay cost [22][23][24][25][26][27]. In the case of division, there are currently also several published works that, as with multiplication, have progressively optimized the use of the scarce resources currently available for quantum computers [6,[28][29][30][31][32]. The need for these two operations is justified by the fact that they are involved in quantum algorithms focused on maximization of objective functions, quantum image processing, or the evaluation of transcendental functions [33][34][35].…”

Section: State-of-the-art In Quantum Circuit Design For Arithmetic Op...mentioning

confidence: 99%

Efficient design of a quantum absolute-value circuit using Clifford+T gates

Orts

Ortega

Combarro

et al. 2022

Preprint

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Current quantum computers have a limited number of resources and are heavily affected by internal and external noise. Therefore, small, noise-tolerant circuits are of great interest. With regard to circuit size, it is especially important to reduce the number of required qubits. Concerning to fault-tolerance, circuits entirely built with Clifford+T gates allow the use of error correction codes. However, the T-gate has an excessive cost, so circuits with a high number of T-gates should be avoided. This work focuses on optimising in such terms an operation that is widely used in larger circuits and algorithms: the calculation of the absolute-value of two's complement encoded integers. The proposed circuit reduces by more than half the number of required T gates with respect to the best circuit currently available in the literature. Moreover, our proposal is the circuit that requires the fewest qubits for such an operation.

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A novel fault-tolerant quantum divider and its simulation

Cited by 12 publications

References 18 publications

Floating-Point Arithmetic with Consistent Rounding on a Quantum Computer

Floating-Point Arithmetic with Consistent Rounding on a Quantum Computer

Quantum Circuit-Width Reduction through Parameterisation and Specialisation

Efficient design of a quantum absolute-value circuit using Clifford+T gates

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