Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IntechOpen eBooks

Floating-Point Arithmetic with Consistent Rounding on a Quantum Computer

R. Steijl

Published Jun 7, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.5772/intechopen.1005546

Related papers

T-Count Optimized Quantum Circuit Designs for Single-Precision Floating-Point Division

S. S. Gayathri, R. Kumar, Samiappan Dhanalakshmi +2 more

The implementation of quantum computing processors for scientific applications includes quantum floating points circuits for arithmetic operations. This work adopts the standard division algorithms for floating-point numbers with restoring, non-restoring, and Goldschmidt division algorithms for single-precision inputs. The design proposals are carried out while using the quantum Clifford+T gates set, and resource estimates in terms of numbers of qubits, T-count, and T-depth are provided for the proposed circuits. By improving the leading zero detector (LZD) unit structure, the proposed division circuits show a significant reduction in the T-count when compared to the existing works on floating-point division.

Electronics•Mar 17, 2021•26 citations

Hybrid quantum floating-point method for sharp arithmetic

Gabriele Agliardi, Enrico Prati

There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around $90\%$ reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.

quant-pharXiv:2607.06040•Jul 8, 2026•0 citations

Scaling up and down of 3-D floating-point data in quantum computation

Meiyu Xu, Dayong Lu, Xiaoyun Sun

In the past few decades, quantum computation has become increasingly attractive due to its remarkable performance. Quantum image scaling is considered a common geometric transformation in quantum image processing, however, the quantum floating-point data version of which does not exist. Is there a corresponding scaling for 2-D and 3-D floating-point data? The answer is yes. In this paper, we present a quantum scaling up and down scheme for floating-point data by using trilinear interpolation method in 3-D space. This scheme offers better performance (in terms of the precision of floating-point numbers) for realizing the quantum floating-point algorithms than previously classical approaches. The Converter module we proposed can solve the conversion of fixed-point numbers to floating-point numbers of arbitrary size data with [Formula: see text] qubits based on IEEE-754 format, instead of 32-bit single-precision, 64-bit double-precision and 128-bit extended-precision. Usually, we use nearest-neighbor interpolation and bilinear interpolation to achieve quantum image scaling algorithms, which are not applicable in high-dimensional space. This paper proposes trilinear interpolation of floating-point data in 3-D space to achieve quantum algorithms of scaling up and down for 3-D floating-point data. Finally, the quantum scaling circuits of 3-D floating-point data are designed.

Scientific Reports•Feb 17, 2022•6 citations

Efficient Floating Point Arithmetic for Quantum Computers

Raphael Seidel, Nikolay Tcholtchev, Sebastian Bock +2 more

One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of qubits, we can easily reach situations where we pay less than a single quantum gate per data point for data-processing instructions which would be rather expensive in classical computing. Formulating such instructions in terms of quantum gates, however, still remains a challenging task. Laying out the foundational functions for more advanced data-processing is therefore a subject of paramount importance for advancing the realm of quantum computing. In this paper, we introduce the formalism of encoding so called-semi-boolean polynomials. As it turns out, arithmetic Z/2nZ ring operations can be formulated as semi-boolean polynomial evaluations, which allows convenient generation of unsigned integer arithmetic quantum circuits. For arithmetic evaluations, the resulting algorithm has been known as Fourier-arithmetic. We extend this type of algorithm with additional features, such as ancilla-free in-place multiplication and integer coefficient polynomial evaluation. Furthermore, we introduce a tailormade method for encoding signed integers succeeded by an encoding for arbitrary floating-point numbers. This representation of floating-point numbers and their processing can be applied to any quantum algorithm that performs unsigned modular integer arithmetic. We discuss some further performance enhancements of the semi boolean polynomial encoder and finally supply a complexity estimation. The application of our methods to a 32-bit unsigned integer multiplication demonstrated a 90% circuit depth reduction compared to carry-ripple approaches.

arXiv:2112.10537•IEEE Access•Jan 1, 2022•22 citations

Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

José E. Cruz Serrallés, Oluwadara Ogunkoya, Kürkçüo{g}lu, Do{g}a Murat +5 more

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.

arXiv:2510.20145•Oct 23, 2025•0 citations

Efficient Floating-point Division Quantum Circuit using Newton-Raphson Division

S. S. Gayathri, R. Kumar, Samiappan Dhanalakshmi

Abstract The development of quantum algorithms is facilitated by quantum circuit designs. A floating-point number can represent a wide range of values and is extremely useful in digital signal processing. A quantum circuit model to implement the floating-point division problem using the Newton-Raphson division algorithm is proposed in this paper. The proposed division circuit offers a significant savings in T-gates and qubits used in the circuit design when correlated with the state of art works proposed on fast division algorithms. The qubits savings are estimated around 17% and 20%, T-count savings are around 59.03% and 20.31%. Similarly, T-depth savings is estimated around 77.45% and 24.33% over the existing works.

Journal of Physics Conference Series•Sep 1, 2022•5 citations
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.
The implementation of quantum computing processors for scientific applications includes quantum floating points circuits for arithmetic operations. This work adopts the standard division algorithms for floating-point numbers with restoring, non-restoring, and Goldschmidt division algorithms for single-precision inputs. The design proposals are carried out while using the quantum Clifford+T gates set, and resource estimates in terms of numbers of qubits, T-count, and T-depth are provided for the proposed circuits. By improving the leading zero detector (LZD) unit structure, the proposed division circuits show a significant reduction in the T-count when compared to the existing works on floating-point division.
There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around 90%90\%90% reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.
In the past few decades, quantum computation has become increasingly attractive due to its remarkable performance. Quantum image scaling is considered a common geometric transformation in quantum image processing, however, the quantum floating-point data version of which does not exist. Is there a corresponding scaling for 2-D and 3-D floating-point data? The answer is yes. In this paper, we present a quantum scaling up and down scheme for floating-point data by using trilinear interpolation method in 3-D space. This scheme offers better performance (in terms of the precision of floating-point numbers) for realizing the quantum floating-point algorithms than previously classical approaches. The Converter module we proposed can solve the conversion of fixed-point numbers to floating-point numbers of arbitrary size data with [Formula: see text] qubits based on IEEE-754 format, instead of 32-bit single-precision, 64-bit double-precision and 128-bit extended-precision. Usually, we use nearest-neighbor interpolation and bilinear interpolation to achieve quantum image scaling algorithms, which are not applicable in high-dimensional space. This paper proposes trilinear interpolation of floating-point data in 3-D space to achieve quantum algorithms of scaling up and down for 3-D floating-point data. Finally, the quantum scaling circuits of 3-D floating-point data are designed.
One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of qubits, we can easily reach situations where we pay less than a single quantum gate per data point for data-processing instructions which would be rather expensive in classical computing. Formulating such instructions in terms of quantum gates, however, still remains a challenging task. Laying out the foundational functions for more advanced data-processing is therefore a subject of paramount importance for advancing the realm of quantum computing. In this paper, we introduce the formalism of encoding so called-semi-boolean polynomials. As it turns out, arithmetic Z/2nZ ring operations can be formulated as semi-boolean polynomial evaluations, which allows convenient generation of unsigned integer arithmetic quantum circuits. For arithmetic evaluations, the resulting algorithm has been known as Fourier-arithmetic. We extend this type of algorithm with additional features, such as ancilla-free in-place multiplication and integer coefficient polynomial evaluation. Furthermore, we introduce a tailormade method for encoding signed integers succeeded by an encoding for arbitrary floating-point numbers. This representation of floating-point numbers and their processing can be applied to any quantum algorithm that performs unsigned modular integer arithmetic. We discuss some further performance enhancements of the semi boolean polynomial encoder and finally supply a complexity estimation. The application of our methods to a 32-bit unsigned integer multiplication demonstrated a 90% circuit depth reduction compared to carry-ripple approaches.
We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches.
Abstract The development of quantum algorithms is facilitated by quantum circuit designs. A floating-point number can represent a wide range of values and is extremely useful in digital signal processing. A quantum circuit model to implement the floating-point division problem using the Newton-Raphson division algorithm is proposed in this paper. The proposed division circuit offers a significant savings in T-gates and qubits used in the circuit design when correlated with the state of art works proposed on fast division algorithms. The qubits savings are estimated around 17% and 20%, T-count savings are around 59.03% and 20.31%. Similarly, T-depth savings is estimated around 77.45% and 24.33% over the existing works.