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IEIE Transactions on Smart Processing and Computing

Exploiting GPU-based Parallelism for Quantum Computer Simulation: A Survey

Sengthai Heng, Tae-Kyung Kim, Youngsun Han

Published Dec 29, 2020• 4 citations
Publisher

Abstract

As the advent of quantum computers comes closer, research on quantum algorithms is actively being conducted in various fields. Quantum computer simulation is mainly employed for the study of quantum algorithms due to the imperfections of quantum computers. Quantum computer simulation using classical computers has encountered significant challenges in emulating quantum algorithms, where computational time and memory usage increase exponentially due to superposition and entanglement. To resolve these problems, there have been many studies to exploit GPU-based parallelism in quantum computer simulation. In this review paper, we present various studies on implementing quantum computer simulations using single or multiple GPUs. We also analyze the performance of these studies in terms of speedup and summarize the simulation methods.

DOI
10.5573/ieiespc.2020.9.6.468

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As the advent of quantum computers comes closer, research on quantum algorithms is actively being conducted in various fields. Quantum computer simulation is mainly employed for the study of quantum algorithms due to the imperfections of quantum computers. Quantum computer simulation using classical computers has encountered significant challenges in emulating quantum algorithms, where computational time and memory usage increase exponentially due to superposition and entanglement. To resolve these problems, there have been many studies to exploit GPU-based parallelism in quantum computer simulation. In this review paper, we present various studies on implementing quantum computer simulations using single or multiple GPUs. We also analyze the performance of these studies in terms of speedup and summarize the simulation methods.
Simulation of quantum computers using classical computers is a hard problem with high memory and computational requirements. Parallelization can alleviate this problem, allowing the simulation of more qubits at the same time or the same number of qubits to be simulated in less time. A promising approach is to exploit the high performance computing capabilities provided by the latest graphical processing units. In this paper we present a parallel implementation of the QC-lib quantum computer simulator on the GPU using the CUDA programming model. The proposed scheme for partitioning the terms that describe the state of a quantum register takes advantage of the specific characteristics of the CUDA memory spaces and allows for an efficient parallelization of the general singe qubit operator. Experimental results indicate that very good speed-ups can be obtained in contrast with the sequential implementation.
Quantum computers are becoming practical for computing numerous applications. However, simulating quantum computing on classical computers is still demanding yet useful because current quantum computers are limited because of computer resources, hardware limits, instability, and noises. Improving quantum computing simulation performance in classical computers will contribute to the development of quantum computers and their algorithms. Quantum computing simulations on classical computers require long performance times, especially for quantum circuits with a large number of qubits or when simulating a large number of shots for noise simulations or circuits with intermediate measures. Graphical processing units (GPU) are suitable to accelerate quantum computer simulations by exploiting their computational power and high bandwidth memory and they have a large advantage in simulating relatively larger qubits circuits. However, GPUs are inefficient at simulating multi-shots runs with noises because the randomness prevents highly parallelization. In addition, GPUs have a disadvantage in simulating circuits with a small number of qubits because of the large overheads in GPU kernel execution. In this paper, we introduce optimization techniques for multi-shot simulations on GPUs. We gather multiple shots of simulations into a single GPU kernel execution to reduce overheads by scheduling randomness caused by noises. In addition, we introduce shot-branching that reduces calculations and memory usage for multi-shot simulations. By using these techniques, we speed up x10 from previous implementations.
Digital quantum computing promises new pathways for problem solving. However, currently available gate-based quantum computers still suffer from short decoherence timings and noisy results. In the meantime, quantum emulators can offer a way to test and refine quantum algorithms. They reproduce classically the behavior of quantum computers at the cost of large memory requirements: the memory needed doubles with each additional qubits emulated. Emulators can be set-up on a large range of machines, from laptops to supercomputers. In this paper, we compare the capabilities of quantum emulators built on the EuroHPC Karolina server using one CPU, one GPU or multiple GPUs in a single node. In terms of the number of qubits emulated, we show that while only 20+ qubits can be emulated using a single CPU, a single GPU brings this number to 30+. We also compare the timing performances, both for randomly generated quantum circuits and for Shor’s factorization algorithm. For randomly generated circuits with same depth and width, the emulators using a GPU and eight GPUs respectively are up to 20 and 180 times faster than the CPU-based emulator. For Shor’s algorithm which can have more than a million gates, the emulators using a GPU and eight GPUs respectively are up to 11 and 20 times faster than the CPU-based emulator. This benchmark of different types of quantum emulators on the Karolina server helps to choose the right parameters and make the most of the Karolina resources for future scientific work involving quantum emulation.
As is intrinsic to the fundamental goal of quantum computing, classical simulation of quantum algorithms is notoriously demanding in resource requirements. Nonetheless, simulation is critical to the success of the field and a requirement for algorithm development and validation, as well as hardware design. GPU-acceleration has become standard practice for simulation, and due to the exponential scaling inherent in classical methods, multi-GPU simulation can be required to achieve representative system sizes. In this case, inter-GPU communications can bottleneck performance. In this work, we present the introduction of MPI into the QED-C Application-Oriented Benchmarks to facilitate benchmarking on HPC systems. We review the advances in interconnect technology and the APIs for multi-GPU communication. We benchmark using a variety of interconnect paths, including the recent NVIDIA Grace Blackwell NVL72 architecture that represents the first product to expand high-bandwidth GPU-specialized interconnects across multiple nodes. We show that while improvements to GPU architecture have led to speedups of over 4.5X across the last few generations of GPUs, advances in interconnect performance have had a larger impact with over 16X performance improvements in time to solution for multi-GPU simulations.
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.
Quantum computing proposes quantum algorithms exponentially faster than their clas- sical analogues when executed by a quantum computer. As quantum computers are currently unavailable for general use, one approach for analyzing the behavior and re- sults of such algorithms is the simulation using classical computers. As this simulation is inefficient due to the exponential growth of the temporal and spatial complexities, solutions for these two problems are essential in order to increase the simulation capa- bilities of any simulator. This work proposes the development of a methodology defined by two main steps: the first consists of the sequential implementation of the abstractions corresponding to the Quantum Processes and Quantum Partial Processes defined in the qGM model for reduction in memory consumption related to multidimensional quantum transformations; the second is the parallel implementation of such abstractions allowing its execution on GPUs. The results obtained by this work embrace the sequential simu- lation of controlled transformations up to 24 qubits. In the parallel simulation approach, Hadamard gates up to 20 qubits were simulated with a speedup of ? 50× over an 8-core parallel simulation, which is a significant performance improvement in the VPE-qGM environment when compared with its previous limitations.