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量子計算のシミュレーション

Hachiro Ijuin, Sin-ichi KATO

Published Mar 1, 2001• 0 citations
OpenAlex

Abstract

When it is quite difficult to implement quantum computing as hardware in spite of increase of proposed calculation models, simulation of quantum computing as software has been examined. By preparing of the routines that process the peculiar matrices for the quantum computing and designing of the graphical user interface (GUI), a simulator for the quantum computing has been developed on which characteristics of the quantum gates and circuits can be easily inspected.

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When it is quite difficult to implement quantum computing as hardware in spite of increase of proposed calculation models, simulation of quantum computing as software has been examined. By preparing of the routines that process the peculiar matrices for the quantum computing and designing of the graphical user interface (GUI), a simulator for the quantum computing has been developed on which characteristics of the quantum gates and circuits can be easily inspected.
A quantum computer simulator is presented. This simulator is an engineering work and no deep understanding of quantum mechanics is required from the user. The simulator is based on the circuit model of quantum computation in which quantum gates act on quantum registers which comprise a number of quantum bits (qubits). The inputs to the simulator are the initial states of the qubits that form a quantum register and the quantum gates applied at each computation step. The inputs are entered through a graphical user interface. The outputs of the simulator are the matrices that represent the quantum register state at each quantum computation step and graphical outputs that show the probability of measuring each one of the possible quantum register base states and the phase of each state at each computation step. The well-known Deutsch's algorithm and the quantum Fourier transform, which is the base of many quantum algorithms, are presented using this simulator. Furthermore, the generation and variation of entanglement during quantum computations can be calculated using this simulator. The quantum computer simulator is a useful tool for the study of quantum computer circuits, quantum computing, and the development of new quantum algorithms.
During the study, software techniques for optimizing the quantum computer model were considered. The main goal of techniques that increase the efficiency of modeling is to reduce the amount of data that must be processed when modeling quantum gates. The most suitable algorithm for implementing a hardware accelerator was considered and modeled in the experimental part. Algorithms of graph theory or decision diagrams are not very suitable for this task, since their implementation will require the implementation of tensor matrix products, which is more convenient to do on a software simulator. It is also worth noting the increasingly growing interest in modeling quantum computing on special hardware, such as video cards or supercomputers. Therefore, the technique presented in the work is relevant, because it combines software solutions in the field of optimization over the past few years and recently studied methods for modeling quantum computing.
The rapid development of the quantum computing field has created the need for effective study tools.Although the physical implementation of quantum systems is still at an early stage, the simulation of quantum circuits using classical computational resources offers a feasible and practical way for experimentation and evaluation.This work focuses on creating functions that enable the implementation of basic quantum gates and circuits on graphics cards (GPUs).Functions were developed that include fundamental operations for the representation and execution of quantum gates and circuits.Through examples and tests, their performance is evaluated, while a simple command-line interface is also provided so that it can be easily used by individuals without prior experience in the field.
The theory of quantum computing is being actively developed. Despite the fact that quantum computing device has some peculiarities, any task designed for a classical computer can be reproduced on a quantum system. The aim of the research is to develop a methodology for constructing models of quantum systems simulators using hardware simulators. The subject of this research is methods for constructing quantum computing devices and systems. In the course of the research, the system analysis methods and computer modeling, methods of object-oriented design were used. Modern high-level languages were used to solve the problems of constructing a modular quantum system with an open architecture. The work of a quantum microarchitecture using an algorithm for optimizing a quantum computational process has been developed and modeled. A universal methodology for modeling algorithms of a quantum nature using the hardware core and requirements for the mutual operation of software and hardware components for the efficient operation of a quantum system is derived.
Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.
Quantum computing (QC) research has gained a lot of momentum recently due to several theoretical analyses that indicate that QC is significantly more efficient at solving certain classes of problems than classical computing. While experimental validation will ultimately be required, the primitive nature of current QC hardware leaves practical testing limited to trivial examples. Thus, a robust simulator is needed to study complex QC issues. Most QC simulators model ideal operations, and thus cannot predict the actual time required to execute an algorithm or quantify the effects of errors in the calculation. We have developed a novel QC simulator that models physical hardware implementations. This simulator not only allows the accurate simulation of quantum algorithms on various hardware implementations, but also takes an important step towards providing a framework to determine their true performance and vulnerability to errors.