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International Conference on Quantum, Nano and Micro Technologies (ICQNM)

Symbolic and numeric quantum circuit simulation

Alexandre de A. Barbosa, Bernardo Lula, Aércio Ferreira de Lima

Published Jan 1, 2007• 0 citations
Publisher

Abstract

Simulation fulfills an important mechanism for the study and the development of many areas. Quantum computation simulation tools have become essential, because no effective quantum hardware has been implemented yet. However, the currently available simulators have serious deficiencies, which makes the description of this new computational paradigm incomplete. This article presents a universal quantum circuit simulator, called Zeno, and the symbolic extension that is being developed to it. The extension will allow a symbolic description of the system's state allied to the graphical representation of the circuit to be visualized together. Users will be able to work in a faster and more efficient way than making this calculations by hand. The extension will make possible a faithful description of the system computation like the descriptions observed in related literature.

DOI
10.1109/icqnm.2007.20

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Simulation fulfills an important mechanism for the study and the development of many areas. Quantum computation simulation tools have become essential, because no effective quantum hardware has been implemented yet. However, the currently available simulators have serious deficiencies, which makes the description of this new computational paradigm incomplete. This article presents a universal quantum circuit simulator, called Zeno, and the symbolic extension that is being developed to it. The extension will allow a symbolic description of the system's state allied to the graphical representation of the circuit to be visualized together. Users will be able to work in a faster and more efficient way than making this calculations by hand. The extension will make possible a faithful description of the system computation like the descriptions observed in related literature.
Current technology for building digital computers is predicted to reach its limit within the next 10 years due to the increasing miniaturization of digital components. By reaching sizes of a few nanometers, electrons stop behaving as particles and start behaving as waves, obeying essentially the principles of Quantum Mechanics, and effects such as interference, superposition and entanglement become dominant. The utilization of those effects allows more that just an evolution of the miniaturization process. It allows for a computational parallelism impossible to be obtained efficiently through classical computational methods or devices. Several algorithms utilizing such effects have been proposed and indicated that Quantum Computation is significantly more efficient at solving certain class of problems than classical computation. Actually, there is not yet any hardware (a quantum computer) able to compute a useful algorithm outside of research labs. A turn-around to that problem is to simulate the behavior of a quantum computer by a classical computer. There are, to this day, a number of quantum computer simulators available which, in general, use the quantum circuit model defined by Deutsch. Just a few of them are universal. We have developed a novel universal quantum circuit simulator, called Zeno, to the design and test of quantum algorithms. Zeno offers a set of features that engulfs most of the features presented by the other existing universal quantum circuit simulators and that also allows it to be used in the design and simulation of quantum channels.
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.
Work is in progress throughout the globe to efficiently use the potential of the quantum theory of computation over their classical counterpart and hence there is a need of building quantum computing hardware. The target of building quantum computers can be achieved if we have better tools for the design of quantum hardware. Quantum circuit simulators are tools for the logic verification of quantum circuits and they can be an essential component of quantum CAD tools in the future. This work is the extension of the previous work by the authors, in order to increase the efficiency of the simulator and to incorporate more components in the gate library. In this paper we have proposed an efficient simulator which can simulate a quantum circuit specified using the proposed quantum hardware descriptive language (QHDL).
Abstract The simulation of quantum circuits on classical computers is an important problem in quantum computing. Such simulation requires representations of distributions over very large sets of basis vectors, and recent work has used symbolic data-structures such as Binary Decision Diagrams (BDDs) for this purpose. In this tool paper, we present Quasimodo, an extensible, open-source Python library for symbolic simulation of quantum circuits. Quasimodo is specifically designed for easy extensibility to other backends. Quasimodo allows simulations of quantum circuits, checking properties of the outputs of quantum circuits, and debugging quantum circuits. It also allows the user to choose from among several symbolic data-structures—both unweighted and weighted BDDs, and a recent structure called Context-Free-Language Ordered Binary Decision Diagrams (CFLOBDDs)—and can be easily extended to support other symbolic data-structures.
The quantum computing represents a new field, which is still being researched, that may have numerous applications in the computer arithmetic, in the encryption - decryption systems, rapid search algorithms and physical systems' emulations. The hardware device that can make this type of calculations is still expensive nowadays and the number of the manufacturers is reduced. On the other hand, the simulation of a quantum computer using the devices currently available on the market - like the FPGA digital circuits - helps in getting an overview of the possibilities that the quantum calculations can provide and it can also be used when simulating physical processes in general. The aim of this article is to present our own solution of an emulator for the quantum calculations using the digital modules implemented in FPGA.
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.