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Accelerating Quantum Computer Simulation via Parallel Eigenvector Computation

Karl Stathakis

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Quantum-dot cellular automata (QDCA) hold great potential to produce the next generation of computer hardware, but their development is hindered by computationally intensive simulations. Our research therefore focuses on rewriting one such simulation to run parallel calculations on a graphics processing unit (GPU). We have decreased execution time from 33 hours 11 minutes to 1 hour 39 minutes, but current progress has shown that further gains are possible. The calculation of eigenvectors holds particular promise for acceleration. Our research has two components: testing MATLAB’s algorithm for these calculations and creating a C-based algorithm to improve on MATLAB’s execution time. MATLAB requires 0.2352 +/- 0.0074 seconds to execute this function, while our function requires 0.0674 +/- 0.0143 seconds. Further, our function’s iterative and many-threaded nature makes it ideal for parallel implementation in the CUDA language, which is expected to further increase execution speed. At the time of this writing, implementation is ongoing. Our presentation shall focus on our functions’ efficiency increases over their MATLAB counterparts, and the application of GPUs’ immense computational power to QDCA device simulation.

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Quantum-dot cellular automata (QDCA) hold great potential to produce the next generation of computer hardware, but their development is hindered by computationally intensive simulations. Our research therefore focuses on rewriting one such simulation to run parallel calculations on a graphics processing unit (GPU). We have decreased execution time from 33 hours 11 minutes to 1 hour 39 minutes, but current progress has shown that further gains are possible. The calculation of eigenvectors holds particular promise for acceleration. Our research has two components: testing MATLAB’s algorithm for these calculations and creating a C-based algorithm to improve on MATLAB’s execution time. MATLAB requires 0.2352 +/- 0.0074 seconds to execute this function, while our function requires 0.0674 +/- 0.0143 seconds. Further, our function’s iterative and many-threaded nature makes it ideal for parallel implementation in the CUDA language, which is expected to further increase execution speed. At the time of this writing, implementation is ongoing. Our presentation shall focus on our functions’ efficiency increases over their MATLAB counterparts, and the application of GPUs’ immense computational power to QDCA device simulation.
Due to the increasing computing power of the graphics processing units (GPU), they are becoming more and more popular when solving general purpose algorithms. As the simulation of quantum computers results on a problem with exponential complexity, it is advisable to perform a parallel computation, such as the one provided by the SIMD multiprocessors present in recent GPUs. In this paper, we focus on an important quantum algorithm, the quantum Fourier transform (QTF), in order to evaluate different parallelization strategies on a novel GPU architecture. Our implementation makes use of the new CUDA software/hardware architecture developed recently by NVIDIA.
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.
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.
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.
Among the many computational models for quantum computing, the Quantum Circuit Model is the most well-known and used model for interacting with current quantum hardware. The practical implementation of quantum computers is a very active research field. Despite this progress, access to physical quantum computers remains relatively limited. Furthermore, the existing machines are susceptible to random errors due to quantum decoherence, as well as being limited in number of qubits, connectivity and built-in error correction. Simulation on classical hardware is therefore essential to allow quantum algorithm researchers to test and validate new algorithms in a simulated-error environment. Computing systems are becoming increasingly heterogeneous, using a variety of hardware accelerators to speed up computational tasks. One such type of accelerators, Field Programmable Gate Arrays (FPGAs), are reconfigurable circuits that can be programmed using standardized high-level programming models such as OpenCL and SYCL. FPGAs allow to create specialized highly-parallel circuits capable of mimicking the quantum parallelism properties of quantum gates, in particular for the class of quantum algorithms where many different computations can be performed concurrently or as part of a deep pipeline. They also benefit from very high internal memory bandwidth. This paper focuses on the analysis of quantum algorithms for applications in computational fluid dynamics. In this work we introduce novel quantum-circuit implementations of model lattice-based formulations for fluid dynamics, specifically the D1Q3 model using quantum computational basis encoding, as well as, efficient simulation of the circuits using FPGAs. This work forms a step toward quantum circuit formulation of the Lattice Boltzmann Method (LBM). For the quantum circuits implementing the nonlinear equilibrium distribution function in the D1Q3 lattice model, it is shown how circuit transformations can be introduced that facilitate the efficient simulation of the circuits on FPGAs, exploiting their fine-grained parallelism. We show that these transformations allow us to exploit more parallelism on the FPGA and improve memory locality. Preliminary results show that for this class of circuits the introduced transformations improve circuit execution time. We show that FPGA simulation of the reduced circuits results in more than 3× improvement in performance per Watt compared to the CPU simulation. We also present results from evaluating the same kernels on a GPU.