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International Conference for High Performance Computing, Networking, Storage and Analysis (SC)

Density Matrix Quantum Circuit Simulation via the BSP Machine on Modern GPU Clusters

Ang Li, Omer Subasi, Xiu Yang, Sriram Krishnamoorthy

Published Nov 1, 2020• 40 citations
Publisher

Abstract

As quantum computers evolve, simulations of quantum programs on classical computers will be essential in validating quantum algorithms, understanding the effect of system noise, and designing applications for future quantum computers. In this paper, we first propose a new multi-GPU programming methodology called MG-BSP which constructs a virtual BSP machine on top of modern multi-GPU platforms, and apply this methodology to build a multi-GPU density matrix quantum simulator called DM-Sim. We propose a new formulation that can significantly reduce communication overhead, and show that this formula transformation can conserve the semantics despite noise being introduced. We build the tool-chain for the simulator to run open standard quantum assembly code, execute synthesized quantum circuits, and perform ultra-deep and largescale simulations. We evaluated DM-Sim on several state-of-the-art multi-GPU platforms including NVIDIA's PascaUVolta DGX1, DGX-2, and ORNL's Summit supercomputer. In particular, we have demonstrated the simulation of one million general gates in 94 minutes on DGX-2, far deeper circuits than has been demonstrated in prior works. Our simulator is more than 10x faster with respect to the corresponding state-vector quantum simulators on GPUs and other platforms. The DM-Sim simulator is released at: http:llgithub.comlpnnllDM-Sim.

DOI
10.1109/sc41405.2020.00017

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As quantum computers evolve, simulations of quantum programs on classical computers will be essential in validating quantum algorithms, understanding the effect of system noise, and designing applications for future quantum computers. In this paper, we first propose a new multi-GPU programming methodology called MG-BSP which constructs a virtual BSP machine on top of modern multi-GPU platforms, and apply this methodology to build a multi-GPU density matrix quantum simulator called DM-Sim. We propose a new formulation that can significantly reduce communication overhead, and show that this formula transformation can conserve the semantics despite noise being introduced. We build the tool-chain for the simulator to run open standard quantum assembly code, execute synthesized quantum circuits, and perform ultra-deep and largescale simulations. We evaluated DM-Sim on several state-of-the-art multi-GPU platforms including NVIDIA's PascaUVolta DGX1, DGX-2, and ORNL's Summit supercomputer. In particular, we have demonstrated the simulation of one million general gates in 94 minutes on DGX-2, far deeper circuits than has been demonstrated in prior works. Our simulator is more than 10x faster with respect to the corresponding state-vector quantum simulators on GPUs and other platforms. The DM-Sim simulator is released at: http:llgithub.comlpnnllDM-Sim.
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Quantum circuit simulation is crucial for the development of quantum algorithms, particularly given the high cost and noise limitations of physical quantum hardware. While full-state quantum circuit simulation is commonly employed for prototyping and debugging, it poses challenges because of the exponential increase in simulation time for large quantum systems. In this work, we propose an extensible framework designed to enhance simulation performance by optimizing both data locality and computational efficiency, thereby addressing these challenges. This framework is seamlessly integrated with an optimizer that restructures quantum circuits and a simulator that adjusts execution strategies for various quantum operations. For the newly developed components, merge booster and diagonal detector, the underlying algorithms are inspired by the principles of quantum entanglement and gate fusion, as well as by the limitations identified in existing third-party simulation libraries. The experiments were conducted on eight DGX-H100 workstations, each equipped with eight NVIDIA H100 GPUs, employing both gate-level and circuit-level benchmarks. The results indicate a speedup of up to 160 times for circuit-level benchmarks and an acceleration of up to 34 times for diagonal-heavy gate-level benchmarks compared to existing simulators. The proposed methodologies are anticipated to deliver more robust and faster quantum circuit simulations, thereby fostering the advancement of novel quantum algorithms.
This paper presents techniques for theoretically and practically efficient and scalable Schrödinger-style quantum circuit simulation. Our approach partitions a quantum circuit into a hierarchy of subcircuits and simulates the subcircuits on multi-node GPUs, exploiting available data parallelism while minimizing communication costs. To minimize communication costs, we formulate an Integer Linear Program that rewards simulation of "nearby" gates on "nearby" GPUs. To maximize throughput, we use a dynamic programming algorithm to compute the subcircuit simulated by each kernel at a GPU. We realize these techniques in Atlas, a distributed, multi-GPU quantum circuit simulator. Our evaluation on a variety of quantum circuits shows that Atlas outperforms state-of-the-art GPU-based simulators by more than 2×\times× on average and is able to run larger circuits via offloading to DRAM, outperforming other large-circuit simulators by two orders of magnitude.
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.
This paper presents techniques for theoretically and practically efficient and scalable Schrödinger-style quantum circuit simulation. Our approach partitions a quantum circuit into a hierarchy of subcircuits and simulates the subcircuits on multinode GPUs, exploiting available data parallelism while minimizing communication costs. To minimize communication costs, we formulate an Integer Linear Program that rewards simulation of “nearby” gates on “nearby” GPUs. To maximize throughput, we use a dynamic programming algorithm to compute the subcircuit simulated by each kernel at a GPU. We realize these techniques in Atlas, a distributed, multi-GPU quantum circuit simulator. Our evaluation on a variety of quantum circuits shows that Atlas outperforms state-of-the-art GPU-based simulators by more than 2×2 \times2× on average and is able to run larger circuits via offloading to DRAM, outperforming other large-circuit simulators by two orders of magnitude.
Simulating the behavior of quantum circuits on classical computers are one of the widely used approaches for current quantum computing device and quantum algorithm research. State-vector simulators keep all the quantum states in main memory, thus consuming a large amount of memory and resulting in great memory access and communication overhead far longer than calculation time. Many classical simulators, such as QuEST, are designed by serial execution of quantum gates without using the data locality, and all amplitudes need to be exchanged. Such a gate-unaware full data communication scheme forces powerful computation such as GPUs to spend a lot of time on waiting for data transmission. In this paper, we propose a gate-aware on-demand communication quantum simulation framework to optimize communication overhead. A quantum circuit partition method through gate fusion is first proposed to avoid unnecessary communications. Moreover, a on-demand data communication scheme is proposed to optimize data transfer among computation nodes. Based on these designs, a prototype has been implemented on QuEST. We evaluated on an 8-node cluster with four NVIDIA Tesla V100 GPUs on each node and our designs can achieve 3.0x-15.6x speedup compared to QuEST for 32-34-qubit quantum systems. Moverover, it can scale to simulate 37-qubit quantum system instead of 34-qubit quantum system for QuEST.