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

Journal of Physics Conference Series

Optimized realization of Quantum Fourier Transform for domestic DCU accelerator

Ke Ma, Lin Han, Jiandong Shang, Jingming Xie, Hao Zhang

Published Apr 1, 2022• 4 citations
Publisher

Abstract

Abstract Quantum Fourier Transform (QFT) is a key part of quantum algorithms such as Shor algorithm, Grover algorithm, and quantum phase estimation algorithm. The “Songshan” supercomputer system adopts the heterogeneous architecture of domestic CPU+DCU. The simulation implementation of the quantum Fourier transform on the “Songshan” supercomputer can promote the research and optimization of related quantum algorithms. Based on the HIP heterogeneous programming model, this paper first maps the phase shift transformation R gate operation of the QFT transformation to the DCU accelerator, and initially constructs the heterogeneous implementation of QFT on the “Songshan” supercomputer; then, the Hadamard gate transformation operation originally implemented on the host side was implemented on the DCU, which greatly reduces the communication overhead caused by the quantum information data transmission between the CPU and the DCU device; finally, the quantum logic gate is analyzed, and based on the operation of the phase shift transformation R gate on the probability amplitude information in the simulation algorithm, an optimization scheme to improve the activity of the DCU thread is proposed. During the experimental verification process, the realized 28-qubit quantum Fourier transform optimization has achieved 13.440 speedup compared with the serially realized QFT simulation on the CPU. The basic quantum gate optimization method based on DCU acceleration equipment in this paper can provide a reference for the efficient simulation of other quantum algorithms on domestic heterogeneous platforms.

DOI
10.1088/1742-6596/2258/1/012065

Related papers

Quantum Fourier Transform Simulation Based on "Songshan" Supercomputer System

XIE Jing-ming, HU Wei-fang, HAN Lin, ZHAO Rong-cai, JING Li-na

The "Songshan" supercomputer system is a new generation of heterogeneous supercomputer cluster independently developed by China.The CPU and DCU accelerators it carries are all independently developed by my country.In order to expand the scientific computing ecology of the platform and verify the feasibility of quantum computing research on this platform,the paper uses a heterogeneous programming model to implement a heterogeneous version of the quantum Fourier transform simulation on the "Songshan" supercomputer system.The computing hotspots of the program are allocated to run on the DCU;then MPI is used to enable multiple processes on a single computing node to realize the concurrent data transmission and calculation of the DCU accelerator;finally,the hiding of computing and communication prevents the DCU from being in the middle of data transmission.The experiment implements a 44 Qubits-scale quantum Fourier transform simulation on a supercomputing system for the first time.The results show that the heterogeneous version of the quantum Fourier transform module makes full use of the computing resources of the DCU accelerator and achieves 11.594 compared to the traditional CPU version.The speedup ratio is high,and it has good scalability on the cluster.This implementation method provides a reference for the simulation implementation and optimization of other quantum algorithms on the "Songshan" supercomputer system.

•Dec 1, 2021•1 citation

Quantum Fourier Transform Simulation on Sunway TaihuLight

Xiaonan Liu, Lina Jing, Lixin Wang +1 more

Quantum Fourier Transform is a key part of many quantum computing, and it involves phase estimation, ordering and factoring. Especially in large number decomposition, periodic data can be transformed into a normal distribution of probability amplitudes. If Quantum Fourier Transform can be implemented on a large scale, it will be a threat to the security of the current RSA cryptosystem. However, the physical implementation of quantum computers currently faces many difficulties, and it is still far away from quantum computers that can exert huge computing power. Therefore, it can only be simulated by classical computers. This article uses the supercomputer independently developed by China, Sunway TaihuLight, to simulate the Quantum Fourier Transform. Based on the heterogeneous and parallel characteristics of SW26010 processor, 46 qubits Quantum Fourier Transform are simulated using MPI, the acceleration thread library, calculation and communication hiding strategy, with the acceleration ratio reaching 6.45 times.

International Conference on Computer Science & Education (ICCSE)•Aug 1, 2020•2 citations

The Quantum Shor Algorithm Simulated on FPGA

Xin Zhang, Yaqian Zhao, Rengang Li +4 more

Shor algorithm is a key milestone in the quantum computing history. It has greatly promoted the development of quantum computing since it is supposed to crack the RSA cryptosystems. Simulation technology is an important strategy in quantum computing research, but the software simulation can only simulate the final result rather than the behavior and hardware structure. This paper proposes a hardware simulation strategy for quantum Shor algorithm. The hardware simulation is closer to the execution process of quantum computation than software simulation. It helps to understand how quantum computer works more concrete, and guide the design of quantum computer more specifically. According to the workflow of quantum computer, this paper divides the Shor algorithm into quantum part and classical part. In our experiment, the quantum part is simulated on FPGA device, and the classical part is executed on CPU host. FPGA device communicates with CPU through PCIe channel, and realizes the modules of quantum register, Hadamard gate, quantum Fourier transform (QFT), quantum measure and so on. Our experiment support 17 qubit simulation in Intel A10 FPGA device, and the execution performance is consistent with our theoretical analysis.

IEEE International Symposium on Parallel and Distributed Processing with Applications (ISPA)•Dec 1, 2019•13 citations

The Study of Simulation Technique of Quantum Compute and Quantum Fourier Transform

Jiajia Wang, Hanwu Chen, Zhiqiang Li

For discussing the solving methods of NP problems in classical computers and studying the circuit model which is the most representative in quantum computing to simulate the compute processes, this article discussed how to simulate the quantum Fourier transform by using the quantum logic gates, implemented the quantum Fourier transform and constructed the quantum information and compute simulation platform. The experiment introduced the quantum register structure to be the storage medium, which is better than the form of matrix in space. The operation processes adopted the bit manipulation to avoid the mass time for matrix multiplications. The results presented the changes of quantum amplitudes and probabilities of quantum states according to the quantum effect and compared with the approximate quantum Fourier transform. The experimental platform provided a groundwork for the further simulations of other important quantum algorithms and quantum circuits.

International Conference on Computer Supported Cooperative Work in Design (CSCWD)•Apr 1, 2007•3 citations

THEORETICAL FRAMEWORK AND ALGORITHMIC IMPLEMENTATION OF THE QUANTUM FOURIER TRANSFORM AND PHASE ESTIMATION

Medak Srinivas

The Quantum Fourier Transform (QFT)andQuantumPhaseEstimation (QPE)are twofundamental algorithmic frameworks in quantum computation, and they provide the mathematical basis of many exponential-speedup quan tum algorithms, such as Shor’s factoring algorithm and quantum simulation techniques. In this work we present a detailed theoretical and computational study of the Quantum Fourier Transform and its integration in the Quan tum Phase Estimation. The discussion begins with the linear algebraic structure of the Hilbert spaces, the unitary transformations, and the complex vector representations that enable quantum interference and superposition. The QFT is studied as the unitary transform of computational basis states in the amplitudes in the frequency domain by phase rotations and tensor-product decompositions. The efficient circuit implementation in terms of Hadamard and controlled phase gates of this transform is discussed. The advantage of the transform in terms of polynomial time complexity over the classical discrete Fourier transform in some quantum scenarios is discussed.The QFT is implemented and the Quantum Phase Estimation algorithm is proposed to obtain the eigenphase information of the unitary operators. In the report the mathematical representation of QPE is derived by using the controlled unitary evolution, the inverse Fourier transforms and the measurement theory in finite dimensional Hilbert spaces. We discuss the probabilistic interpretation of phase extraction in detail and the convergence properties of the bi nary phase approximation. We also discuss the relation of QPE to eigenvalue problems in quantum mechanics and its applications to Hamiltonian simulation, quantum chemistry, cryptography, and hidden subgroup prob lems.Implementation aspects of these algorithms are studied using quantum circuit representations and oracle based computation models. We also discuss error sensitivity, qubit precision requirements, decoherence limita tions and practical constraints of Noisy Intermediate-Scale Quantum (NISQ) hardware. The work synthesizes the mathematical foundations, computational complexity analysis and physical realizations of the QFT and the QPE, demonstrating how the Fourier-based quantum transformations provide the essential mechanism underlying modern quantum algorithmic speedups and scalable quantum information processing.

Iterative International Publishers eBooks•May 1, 2026•0 citations

Precision Analysis and Hardware Acceleration for Large-Scale Quantum Fourier Transformation on Modern FPGAS

Fangtian Gu, Jiyuan Liu, He Li

With the development of quantum algorithms and practical quantum computing devices, how to efficiently simulate emerging quantum algorithms via quantum circuit simulators on classical parallel-computing hardware platforms has raised more and more interest. The superior customized parallelism and pipeline efficiency over general-purpose processors make FPGAs ideal for large scale quantum algorithms/circuits simulation. Since the quantum Fourier transform (QFT) has been used in many quantum algorithms, such as quantum linear algebra, quantum phase estimation and quantum machine leaning, this paper presented a novel precision analysis and an efficient customized-precision QFT simulator accelerated on AMD Alveo U55C FPGAs. Customized-precision representations via high-level synthesis are employed for QFT implementation with up to 16 qubits, demonstrating up-to 8.3× speedup versus implementations in floating-point arithmetic within an error tolerance of 0.1%.

China Semiconductor Technology International Conference (CSTIC)•Mar 24, 2025•0 citations
Abstract Quantum Fourier Transform (QFT) is a key part of quantum algorithms such as Shor algorithm, Grover algorithm, and quantum phase estimation algorithm. The “Songshan” supercomputer system adopts the heterogeneous architecture of domestic CPU+DCU. The simulation implementation of the quantum Fourier transform on the “Songshan” supercomputer can promote the research and optimization of related quantum algorithms. Based on the HIP heterogeneous programming model, this paper first maps the phase shift transformation R gate operation of the QFT transformation to the DCU accelerator, and initially constructs the heterogeneous implementation of QFT on the “Songshan” supercomputer; then, the Hadamard gate transformation operation originally implemented on the host side was implemented on the DCU, which greatly reduces the communication overhead caused by the quantum information data transmission between the CPU and the DCU device; finally, the quantum logic gate is analyzed, and based on the operation of the phase shift transformation R gate on the probability amplitude information in the simulation algorithm, an optimization scheme to improve the activity of the DCU thread is proposed. During the experimental verification process, the realized 28-qubit quantum Fourier transform optimization has achieved 13.440 speedup compared with the serially realized QFT simulation on the CPU. The basic quantum gate optimization method based on DCU acceleration equipment in this paper can provide a reference for the efficient simulation of other quantum algorithms on domestic heterogeneous platforms.
The "Songshan" supercomputer system is a new generation of heterogeneous supercomputer cluster independently developed by China.The CPU and DCU accelerators it carries are all independently developed by my country.In order to expand the scientific computing ecology of the platform and verify the feasibility of quantum computing research on this platform,the paper uses a heterogeneous programming model to implement a heterogeneous version of the quantum Fourier transform simulation on the "Songshan" supercomputer system.The computing hotspots of the program are allocated to run on the DCU;then MPI is used to enable multiple processes on a single computing node to realize the concurrent data transmission and calculation of the DCU accelerator;finally,the hiding of computing and communication prevents the DCU from being in the middle of data transmission.The experiment implements a 44 Qubits-scale quantum Fourier transform simulation on a supercomputing system for the first time.The results show that the heterogeneous version of the quantum Fourier transform module makes full use of the computing resources of the DCU accelerator and achieves 11.594 compared to the traditional CPU version.The speedup ratio is high,and it has good scalability on the cluster.This implementation method provides a reference for the simulation implementation and optimization of other quantum algorithms on the "Songshan" supercomputer system.
Quantum Fourier Transform is a key part of many quantum computing, and it involves phase estimation, ordering and factoring. Especially in large number decomposition, periodic data can be transformed into a normal distribution of probability amplitudes. If Quantum Fourier Transform can be implemented on a large scale, it will be a threat to the security of the current RSA cryptosystem. However, the physical implementation of quantum computers currently faces many difficulties, and it is still far away from quantum computers that can exert huge computing power. Therefore, it can only be simulated by classical computers. This article uses the supercomputer independently developed by China, Sunway TaihuLight, to simulate the Quantum Fourier Transform. Based on the heterogeneous and parallel characteristics of SW26010 processor, 46 qubits Quantum Fourier Transform are simulated using MPI, the acceleration thread library, calculation and communication hiding strategy, with the acceleration ratio reaching 6.45 times.
Shor algorithm is a key milestone in the quantum computing history. It has greatly promoted the development of quantum computing since it is supposed to crack the RSA cryptosystems. Simulation technology is an important strategy in quantum computing research, but the software simulation can only simulate the final result rather than the behavior and hardware structure. This paper proposes a hardware simulation strategy for quantum Shor algorithm. The hardware simulation is closer to the execution process of quantum computation than software simulation. It helps to understand how quantum computer works more concrete, and guide the design of quantum computer more specifically. According to the workflow of quantum computer, this paper divides the Shor algorithm into quantum part and classical part. In our experiment, the quantum part is simulated on FPGA device, and the classical part is executed on CPU host. FPGA device communicates with CPU through PCIe channel, and realizes the modules of quantum register, Hadamard gate, quantum Fourier transform (QFT), quantum measure and so on. Our experiment support 17 qubit simulation in Intel A10 FPGA device, and the execution performance is consistent with our theoretical analysis.
For discussing the solving methods of NP problems in classical computers and studying the circuit model which is the most representative in quantum computing to simulate the compute processes, this article discussed how to simulate the quantum Fourier transform by using the quantum logic gates, implemented the quantum Fourier transform and constructed the quantum information and compute simulation platform. The experiment introduced the quantum register structure to be the storage medium, which is better than the form of matrix in space. The operation processes adopted the bit manipulation to avoid the mass time for matrix multiplications. The results presented the changes of quantum amplitudes and probabilities of quantum states according to the quantum effect and compared with the approximate quantum Fourier transform. The experimental platform provided a groundwork for the further simulations of other important quantum algorithms and quantum circuits.
The Quantum Fourier Transform (QFT)andQuantumPhaseEstimation (QPE)are twofundamental algorithmic frameworks in quantum computation, and they provide the mathematical basis of many exponential-speedup quan tum algorithms, such as Shor’s factoring algorithm and quantum simulation techniques. In this work we present a detailed theoretical and computational study of the Quantum Fourier Transform and its integration in the Quan tum Phase Estimation. The discussion begins with the linear algebraic structure of the Hilbert spaces, the unitary transformations, and the complex vector representations that enable quantum interference and superposition. The QFT is studied as the unitary transform of computational basis states in the amplitudes in the frequency domain by phase rotations and tensor-product decompositions. The efficient circuit implementation in terms of Hadamard and controlled phase gates of this transform is discussed. The advantage of the transform in terms of polynomial time complexity over the classical discrete Fourier transform in some quantum scenarios is discussed.The QFT is implemented and the Quantum Phase Estimation algorithm is proposed to obtain the eigenphase information of the unitary operators. In the report the mathematical representation of QPE is derived by using the controlled unitary evolution, the inverse Fourier transforms and the measurement theory in finite dimensional Hilbert spaces. We discuss the probabilistic interpretation of phase extraction in detail and the convergence properties of the bi nary phase approximation. We also discuss the relation of QPE to eigenvalue problems in quantum mechanics and its applications to Hamiltonian simulation, quantum chemistry, cryptography, and hidden subgroup prob lems.Implementation aspects of these algorithms are studied using quantum circuit representations and oracle based computation models. We also discuss error sensitivity, qubit precision requirements, decoherence limita tions and practical constraints of Noisy Intermediate-Scale Quantum (NISQ) hardware. The work synthesizes the mathematical foundations, computational complexity analysis and physical realizations of the QFT and the QPE, demonstrating how the Fourier-based quantum transformations provide the essential mechanism underlying modern quantum algorithmic speedups and scalable quantum information processing.
With the development of quantum algorithms and practical quantum computing devices, how to efficiently simulate emerging quantum algorithms via quantum circuit simulators on classical parallel-computing hardware platforms has raised more and more interest. The superior customized parallelism and pipeline efficiency over general-purpose processors make FPGAs ideal for large scale quantum algorithms/circuits simulation. Since the quantum Fourier transform (QFT) has been used in many quantum algorithms, such as quantum linear algebra, quantum phase estimation and quantum machine leaning, this paper presented a novel precision analysis and an efficient customized-precision QFT simulator accelerated on AMD Alveo U55C FPGAs. Customized-precision representations via high-level synthesis are employed for QFT implementation with up to 16 qubits, demonstrating up-to 8.3× speedup versus implementations in floating-point arithmetic within an error tolerance of 0.1%.