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The International Journal of High Performance Computing Applications

Improving in situ GPU simulation of quantum computing in the D-GM environment

Anderson Ávila, Renata Reiser, Mauricio Lima Pilla, Adenauer Yamin

Published Jan 16, 2019• 4 citations
Publisher

Abstract

Exponential increase and global access to read/write memory states in quantum computing (QC) simulation limit both the number of qubits and quantum transformations which can be currently simulated. Although QC simulation is parallel by nature, spatial and temporal complexity are major performance hazards, making this a nontrivial application for high performance computing. A new methodology employing reduction and decomposition optimizations has shown relevant results, but its GPU implementation could be further improved. In this work, we develop a new kernel for in situ GPU simulation that better explores its resources without requiring further hardware. Shor’s and Grover’s algorithms are simulated up to 25 and 21 qubits respectively and compared to our previous version, to [Formula: see text] simulator and to ProjectQ framework, showing better results with relative speedups up to 4.38×, 3357.76× and 333× respectively.

DOI
10.1177/1094342018823251

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Exponential increase and global access to read/write memory states in quantum computing (QC) simulation limit both the number of qubits and quantum transformations which can be currently simulated. Although QC simulation is parallel by nature, spatial and temporal complexity are major performance hazards, making this a nontrivial application for high performance computing. A new methodology employing reduction and decomposition optimizations has shown relevant results, but its GPU implementation could be further improved. In this work, we develop a new kernel for in situ GPU simulation that better explores its resources without requiring further hardware. Shor’s and Grover’s algorithms are simulated up to 25 and 21 qubits respectively and compared to our previous version, to [Formula: see text] simulator and to ProjectQ framework, showing better results with relative speedups up to 4.38×, 3357.76× and 333× respectively.
Exponential increase and global access to read/write memory states in quantum computing simulation limit both the number of qubits and quantum transformations that can be currently simulated. Although quantum computing simulation is parallel by nature, spatial and temporal complexity are major performance hazards, making this an important application for HPC. A new methodology employing reduction and decomposition optimizations has shown great results, but its GPU implementation could be further improved. In this work, we intend to do a new implementation for in-situ GPU simulation that better explores its resources without requiring further HPC hardware. Shors and Grovers algorithms are simulated and compared to the previous version and to LIQUi|s simulator, showing better results with relative speedups up to 15.5× and 765.76× respectively.
The exponential increase and global access to read/write memory states in quantum computing simulation limit both the number of qubits and quantum transformations that can be currently simulated. Although quantum computing simulation is parallel by nature, spatial complexity and memory access patterns are major performance hazards. A new methodology employs reduction and decomposition optimizations, exploring properties such as the sparsity of the Id-Operator and the partiality of dense unitary transformations to improve storage and distribution of quantum states. In this work, Shor's and Grover's algorithms are simulated in both CPU and GPU in the Distributed Geometric Machine environment. Additionally, they are compared to LIQUi|〉's results. In all cases, our simulation was faster and allowed for an improved number of qubits when compared to the academic release version of LIQUi|〉, with relative speedups up to 118×.
Currently quantum computers require specialized hardware to be used, until they become more feasibly the testing of quantum algorithms is done by simulation, which is a task of high temporal and spacial complexity. To address this issue, the HybriD-GM simulator, and many others around the world, are under research and improvement, this paper is an ongoing work on improvements for the multi-core support of the HybriD-GM simulator, the experiments are done with the Shor and Grover algorithms, while varying the number of cores and qubits for each, to improve the scalability the removal of critical regions by the usage of tasks and other OpenMP resources is exploited, and the study about the impact of others variables on the simulator is already planned, as well improvements for future works on the GPU, and GPU-CPU approaches and expansion to distributed computing for horizontal scalability of the system.
This paper presents the HybriD-GM model conception, from modeling to consolidation. The D-GM environment is also extended, providing efficient parallel executions for quantum computing simulations, targeted to hybrid architectures considering the CPU and GPU integration. By managing projection operators over quantum structures, and exploring coalescing memory access patterns, the HybriD-GM model enables granularity control, optimizing hardware resources in distributed computations organized as tree data structures. In the HybriD-GM evaluation, simulations of Shor's and Grover's algorithms achieve significant performance improvements in comparison to the previous D-GM version, and also with other related works, for example, LIQUi|⟩ and ProjectQ simulators.
Due to the expansion of transformations and read/write memory states by tensor products in multidimensional quantum applications, the exponential increase in temporal and spatial complexities constitutes one of the main challenges for quantum computing simulations. Simulation of these systems is important in order to develop and test new quantum algorithms. This work presents reduction and decomposition optimizations for the Distributed Geometric Machine environment. By exploring properties as the sparsity of the Identity operator and partiality of dense unitary transformations, better storage and distribution of quantum information are achieved. The main improvements are implemented by decreasing replication and void elements inherited from quantum operators. In the evaluation of this proposal, Shor’s algorithm considering 2n+3 qubits in the order-finding quantum algorithm was simulated up to 25 qubits over CPU, sequentially and in parallel, and over GPU. Results confirm that temporal complexity is reduced. When comparing our implementations running on the same hardware with LIQUi|i, academic release version, our new simulator was faster and allowed for the simulation of more qubits.
The exponential increase in the temporal and spatial complexities is one of the main challenges in the widespread use of quantum algorithm simulation, especially in dense quantum transformations (QTs) such as the Hadamard transformation (H), which has found wide applications in computer and communication science and also comprising the simplest quantum universal set of QTs. The main reason for these costs is the expansion of QTs by using tensor product in multi-dimension quantum applications. In this work, new optimizations for the execution of reduction and decomposition based on the Identity operator are introduced in the Distributed Geometric Machine framework (D-GM). Instead of executing the quantum transformation in a single step, they are divided in sub-quantum transformations and only the values different from Identity transformations are stored. Mixed Partial Processes provide control over the increase in the size of read/write memory states in the calculation of a QT, thus contributing to increase the scalability of applications regarding hardware-GPUs memory limit. In the evaluation of this D-GM extension, Hadamard Transformations were simulated up to 28 qubits applications over a single GPU. Our new simulator is 10, 829χ faster and allows for the simulation of more qubits when compared to our previous implementation running on the same GPU.