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IEEE International Symposium on Applied Computational Intelligence and Informatics (SACI)

QC | pp >: A Behavioral Quantum Computing Simulation Library

Sebastian Mihai Ardelean, Mihai Udrescu

Published May 1, 2018• 0 citations
Publisher

Abstract

In this paper we describe a quantum computing simulation library named QC|pp). In the state-of-the-art most of the available libraries and simulators make use of the structural modeling of quantum circuits which requires a high memory consumption and huge runtime. Indeed, under the structural modeling framework, the simulation of quantum computers for n qubits entails multiplication of sparse 2n. x 2nsize matrices with vectors of dimension 2n, thus making this a memory-bound application. Through QC|pp) we propose a behavioral modeling framework of quantum circuits to reduce memory consumption, increase performance and allow for testing our simulator on more qubits. We will also present the results obtained by testing our library on simulating Grover's algorithm.

DOI
10.1109/saci.2018.8440993

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In this paper we describe a quantum computing simulation library named QC|pp). In the state-of-the-art most of the available libraries and simulators make use of the structural modeling of quantum circuits which requires a high memory consumption and huge runtime. Indeed, under the structural modeling framework, the simulation of quantum computers for n qubits entails multiplication of sparse 2n. x 2nsize matrices with vectors of dimension 2n, thus making this a memory-bound application. Through QC|pp) we propose a behavioral modeling framework of quantum circuits to reduce memory consumption, increase performance and allow for testing our simulator on more qubits. We will also present the results obtained by testing our library on simulating Grover's algorithm.
As quantum computers of non-trivial size become available in the near future, it is imperative to develop tools to emulate small quantum computers. This allows for validation and debugging of algorithms as well as exploring hardware-software co-design to guide the development of quantum hardware and architectures. The simulation of quantum computers entails multiplications of sparse matrices with very large dense vectors of dimension 2n, where n denotes the number of qubits, making this a memory-bound and network bandwidth-limited application. We introduce the concept of a quantum computer emulator as a component of a software framework for quantum computing, enabling a significant performance advantage over simulators by emulating quantum algorithms at a high level rather than simulating individual gate operations. We describe various optimization approaches and present benchmarking results, establishing the superiority of quantum computer emulators in terms of performance.
Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a new data structure called the Quantum Information Decision Diagram (QuIDD) that exploits the structure of quantum operators, many of these matrices and vectors can be represented in a form that grows polynomially. Using QuIDDs, we implemented a general-purpose quantum computing simulator in C++ called QuIDDPro and tested it on Grover's algorithm. Our QuIDD technique asymptotically outperforms other known simulation techniques.
Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and vectors modeling qubit states grow exponentially with the number of qubits. It has been shown experimentally that the QuIDD (Quantum Information Decision Diagram) datastructure greatly facilitates simulations using memory and runtime that are polynomial in the number of qubits. In this paper, we present a complexity analysis which formally describes this class of matrices and vectors. We also present an improved implementation of QuIDDs which can simulate Grover's algorithm for quantum search with the asymptotic runtime complexity of an ideal quantum computer up to negligible overhead.
Simulating quantum computation on a classical com-puter is a difficult problem. The matrices representing quantum gates, and vectors modeling qubit states grow ex-ponentially with the number of qubits. It has been shown ex-perimentally that the QuIDD (Quantum Information Deci-sion Diagram) datastructure greatly facilitates simulations using memory and runtime that are polynomial in the num-ber of qubits. In this paper, we present a complexity analysis which formally describes this class of matrices and vectors. We also present an improved implementation of QuIDDs which can simulate Grover’s algorithm for quantum search with the asymptotic runtime complexity of an ideal quantum computer up to negligible overhead. 1.
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.
Quantum-mechanical phenomena are playing an increasing role in information processing as transistor sizes approach the nanometer level, while the securest forms of communication rely on quantum data encoding. When they involve a finite number of basis states, these phenomena can be modeled as quantum circuits, the quantum analogue of conventional or classical logic circuits. Simulation of quantum circuits can therefore be used as a tool to evaluate issues in the design of quantum information processors. Unfortunately, simulating such phenomena efficiently is exceedingly difficult. The matrices representing quantum operators (gates) and vectors modeling quantum states grow exponentially with the number of quantum bits. The information represented by quantum states and operators often exhibits structure that can be exploited when simulating certain classes of quantum circuits. We study the development of simulation methods that run on classical computers and take advantage of such repetitions and redundancies. In particular, we define a new data structure for simulating quantum circuits called the quantum information decision diagram (QuIDD). A QuIDD is a compressed graph representation of a vector or matrix and permits computations to be performed directly on the compressed data. We develop a comprehensive set of algorithms for operating on QuIDDs in both the state-vector and density-matrix formats, and evaluate their complexity. These algorithms have been implemented in a general-purpose simulator program for quantum-mechanical applications called QuIDDPro. Through extensive experiments conducted on representative quantum simulation applications, including Grover's search algorithm, error characterization, and reversible circuits, we demonstrate that QuIDDPro is faster than other existing quantum-mechanical simulators such as the National Institute of Standards and Technology's QCSim program, and is far more memory-efficient. Using QuIDDPro, we explore the advantages of quantum computation over classical computation, simulate quantum errors and error correction, and study the impact of numerical precision on the fidelity of simulations. We also develop several novel algorithms for testing quantum circuit equivalence and compare them empirically. The QuIDDPro software is equipped with a user-friendly interface and is distributed with numerous example scripts. It has been used as a laboratory supplement for quantum computing courses at several universities.