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Quantum Fourier Transform Simulation Based on "Songshan" Supercomputer System

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

Published Dec 1, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.11896/jsjkx.201200023

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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.
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.
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.
We have developed a new version of the high-performance Jülich universal quantum computer simulator (JUQCS-50) that leverages key features of the GH200 superchips as used in the JUPITER supercomputer, enabling simulations of a 50-qubit universal quantum computer for the first time. JUQCS-50 achieves this through three key innovations: (1) extending usable memory beyond GPU limits via high-bandwidth CPU-GPU interconnects and LPDDR5 memory; (2) adaptive data encoding to reduce memory footprint with acceptable trade-offs in precision and compute effort; and (3) an on-the-fly network traffic optimizer. These advances result in a 16.6-fold speedup over the previous 48-qubit record on the K computer
With the deeply studied of quantum computing by research fellows, the computational complexity and time complexity of quantum algorithms gradually increase. The quantum computing simulator provides an effective platform for the development and verification of quantum algorithms. However, the running time and memory overhead during calculation will increase exponentially with the number of qubits. Therefore, the difficulty of high-speed quantum computing on classical computers will gradually increase. At present, a single node has been unable to meet the resource requirements of the algorithm in the quantum computing process, and it is necessary to expand the memory resources in the multi-node computing cluster. Message passing interface has high performance inter-process communication capabilities, which can balance the data transmission between different hosts. Quantum computing tasks can be distributed on several servers to work together to solve the same problem. Therefore, this paper designs an advanced scheme of deploying quantum computing programs on cloud computing platform to support message exchanging between servers using message passing interface to accelerate quantum computing.
Advances in quantum simulator technology are increasingly required because research on quantum algorithms is becoming more sophisticated and complex. State vector simulation utilizes CPU and memory resources in computing nodes exponentially with respect to the number of qubits; furthermore, in a variational quantum algorithm, the large number of repeated runs by classical optimization is also a heavy load. This problem has been addressed by preparing numerous computing nodes or simulation frameworks that operate effectively. This study aimed to accelerate quantum simulation using two newly proposed methods: to efficiently utilize limited computational resources by adjusting the ratio of the MPI and distributed processing parallelism corresponding to the target problem settings and to slim down the Hamiltonian by considering the effect of accuracy on the calculation result. Ground-state energy calculations of a fermionic model were performed using a variational quantum eigensolver (VQE) on an HPC cluster with up to 1024 FUJITSU Processor A64FX connected to each other by InfiniBand; the processor is also used on supercomputer Fugaku. We achieved 200 times higher speed over VQE simulations and demonstrated 32 qubits ground-state energy calculations in acceptable time. This result indicates that > 30 qubit state vector simulations can be realistically utilized for further research on variational quantum algorithms.
Quantum computing simulation on a classical computer is difficult due to the exponential runtime and memory overhead. Previous work addresses the difficulty by utilizing multiple Graphical Processing Units (GPUs) and multi-node computers. GPUs are efficient for handling runtime issues but have limited total accessible memory space. Meanwhile, the memory of a multi-node computer can be scaled to the petabytes order, but its bandwidth for access from host computers (CPUs) is narrow. To simultaneously accelerate simulation and enlarge the total memory space, we propose a heterogeneous parallelization approach by combining GPUs and CPUs. Our simulator allocates memory to the GPUs first, and then to the CPUs. It thus accelerates simulation by using the full capabilities of the GPUs if memory for the simulation fits in the GPUs on a cluster. Allocating memory to the CPUs reduces benefits of the GPUs but enlarges the capacity of qubits in the simulation. In such case, it can exploit the memory of the GPUs to add one more qubit in the simulation if the size of memory in a node is the power of two (such as 512GB). We show empirical performance evaluations of our simulator in a distributed environment of POWER9.