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IEEE Congress on Evolutionary Computation (CEC)

Optimizing D-GM quantum computing by exploring parallel and distributed quantum simulations under GPUs arquitecture

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

Published Jul 1, 2016• 10 citations
Publisher

Abstract

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.

DOI
10.1109/cec.2016.7748342

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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.
The D-GM execution environment improves distributed simulation of quantum algorithms in heterogeneous computing environments comprising both multi-core CPUs and GPUs. The main contribution of this work consists in the optimization of the environment VirD-GM, conceived in three steps: ( i ) the theoretical studies and implementation of the abstractions of the Mixed Partial Process defined in the qGM model, focusing on the reduction of the memory consumption regarding multidimensional QTs; ( ii ) the distributed/parallel implementation of such abstractions allowing its execution on clusters of GPUs; ( iii ) and optimizations that predict multiplications by zero-value of the quantum states/transformations, implying reduction in the number of computations. The results obtained in this work embrace the distribute/parallel simulation of Hadamard gates up to 21 qubits, showing scalability with the increase in the number of computing nodes.
One of the main obstacles for the adoption of quantum algorithm simulation is the exponential increase in temporal and spatial complexities, due to the expansion of transformations and read/write memory states by using tensor product in multi-dimension applications. Reduction and decomposition optimizations via the Id-operator provide a smart and appropriate storage and distribution of quantum information. Reductions are achieved by avoiding replication and sparsity inherited from such operators. By using decompositions, applications may be divided into sub-steps to store only distinct values from Id-operators, instead of executing quantum transformations in a single step. Additional optimizations based on mixed partial processes provide control over increase in read/write memory states in quantum transformations, also contributing to increase the scalability regarding hardware-GPUs memory limit. Hadamard and Discret Quantum Fourier Transforms were simulated up to 28 qubits applications over a single GPU with drastic temporal complexity reduction and simulation time.
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 simulation of algorithms from quantum computing is currently the most affordable solution for development of new applications. Due to the high computational cost of such simulation, solutions towards novel features that increase the performance are always desired. This work proposes an extension for the D-GM's simulation framework, establishing the support for GPU-aware distributed quantum simulation. The project explores the concepts of heterogeneous computing, merging distributed and GPU computing in a single programming environment. Our results comprehend the distributed simulation of systems comprised by Hadamard transformations up to 21 qubits. Detailed analysis and a performance comparison between PyCUDA and JCUDA frameworks for our application are discussed. This work is a significant step towards the ultimate goal of our project, which is the hybrid simulation of quantum algorithms, i.e., exploring multi-core CPUs and GPUs distributed along a cluster, achieving scalability when larger systems are simulated.
Summary Because of 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 very relevant to develop and test new quantum algorithms. In order to overcome the increase in simulation complexity, 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 reached by decreasing replication and void elements inherited from quantum operators. In the evaluation of this proposal, Hadamard transformations from 21 to 28 qubits and Quantum Fourier Transforms from 26 to 28 qubits were simulated over CPU, sequentially and in parallel, and in graphics processing unit, showing reduced temporal complexity and, consequently, shorter simulation time. Moreover, evaluations of the Shor's algorithm considering 2n + 3 qubits in the order‐finding quantum algorithm were simulated up to 25 qubits. When comparing our implementations running on the same hardware with language‐integrated quantum operation, academic release version, our new simulator was faster and allowed for the simulation of more qubits. Copyright © 2016 John Wiley & Sons, Ltd.
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.