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International Conference on Computer Science & Education (ICCSE)

Quantum Fourier Transform Simulation on Sunway TaihuLight

Xiaonan Liu, Lina Jing, Lixin Wang, Meiling Wang

Published Aug 1, 2020• 2 citations
Publisher

Abstract

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.

DOI
10.1109/iccse49874.2020.9201643

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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.
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.
Classical simulation of quantum computation is vital for verifying quantum devices and assessing quantum algorithms. We present a new quantum circuit simulator developed on the Sunway TaihuLight supercomputer. Compared with other simulators, the present one is distinguished in two aspects. First, our simulator is more versatile. The simulator consists of three mutually independent parts to compute the full, partial and single amplitudes of a quantum state with different methods. It has the function of emulating the effect of noise and support more kinds of quantum operations. Second, our simulator is of high efficiency. The simulator is designed in a two-level parallel structure to be implemented efficiently on the distributed many-core Sunway TaihuLight supercomputer. Random quantum circuits can be simulated with 40, 75 and 200 qubits on the full, partial and single amplitude, respectively. As illustrative applications of the simulator, we present a quantum fast Poisson solver and an algorithm for quantum arithmetic of evaluating transcendental functions. Our simulator is expected to have broader applications in developing quantum algorithms in various fields.
With the rapid progress made by industry and academia, quantum computers with dozens of qubits or even larger size are being realized. However, the fidelity of existing quantum computers often sharply decreases as the circuit depth increases. Thus, an ideal quantum circuit simulator on classical computers, especially on high-performance computers, is needed for benchmarking and validation. We design a large-scale simulator of universal random quantum circuits, often called “quantum supremacy circuits”, and implement it on Sunway TaihuLight. The simulator can be used to accomplish the following two tasks: 1) Computing a complete output state-vector; 2) Calculating one or a few amplitudes. We target the simulation of 49-qubit circuits. For task 1), we successfully simulate such a circuit of depth 39, and for task 2) we reach the 55-depth level. To the best of our knowledge, both of the simulation results reach the largest depth for 49-qubit quantum supremacy circuits.
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.
A revised version of the massively parallel simulator of a universal quantum computer, described in this journal eleven years ago, is used to benchmark various gate-based quantum algorithms on some of the most powerful supercomputers that exist today. Adaptive encoding of the wave function reduces the memory requirement by a factor of eight, making it possible to simulate universal quantum computers with up to 48 qubits on the Sunway TaihuLight and on the K computer. The simulator exhibits close-to-ideal weak-scaling behavior on the Sunway TaihuLight, on the K computer, on an IBM Blue Gene/Q, and on Intel Xeon based clusters, implying that the combination of parallelization and hardware can track the exponential scaling due to the increasing number of qubits. Results of executing simple quantum circuits and Shor’s factorization algorithm on quantum computers containing up to 48 qubits are presented.
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%.