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Simulating and executing circuits employing the quantum computing paradigm

Daniel Abellán, Antonio Valdivia, Alberto Antonio Del Barrio, Guillermo Botella, Ginés Carrascal

Published Jul 22, 2019• 2 citations
OpenAlex

Abstract

Although Quantum Computing was introduced several decades ago, today is a hot-topic under research and development. Due to the technological difficulties to fabricate this type of computers, the employment of simulators become critical in order to allow researchers developing algorithms that can leverage the unique features of quantum computers, such as the case of Shor's or Grover's algorithms. Then, it is essential for these simulations to be as close as possible to the real results. In this paper we present a comparison between simulations and real executions of a 2-qubit adder. As the experiments show, the backends provided by IBM are able to obtain comparable simulated results to those obtained in real quantum computers.

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Although Quantum Computing was introduced several decades ago, today is a hot-topic under research and development. Due to the technological difficulties to fabricate this type of computers, the employment of simulators become critical in order to allow researchers developing algorithms that can leverage the unique features of quantum computers, such as the case of Shor's or Grover's algorithms. Then, it is essential for these simulations to be as close as possible to the real results. In this paper we present a comparison between simulations and real executions of a 2-qubit adder. As the experiments show, the backends provided by IBM are able to obtain comparable simulated results to those obtained in real quantum computers.
Quantum computing and quantum algorithms have been said to be able to provide significant speed-up over classical computation with classical algorithms by exploiting the nature of quantum mechanical systems. In this work, we will study the qubit architecture of quantum systems available at IBM Quantum (IBM-Q) such as the properties of the qubit system, the qubit layout and connectivity as well as the transpilation process of circuits and its effects to the circuits. We investigate the correspondence between limited and sparse connectivity and connected physical qubits to Grover's algorithm implementation of 2 and 3 qubits. We will also test Grover's algorithm on the different connectivity available on four IBM-Q systems for 2, 3, 4 and 5 qubits using optimization level of 0, 1, 2 and 3 to compare the circuit depth of the transpiled circuits as well as their execution times. This work will provide guidance for researchers on the important factors to consider before implementing a quantum algorithm on a real quantum system.
Quantum computing has gained a lot of interest recently because of its claims of solving some problems that are almost impossible solving in classical computing.Prime factorization of big numbers using Shor's algorithm and Grover database search algorithm are two of them.Furthermore, quantum algorithms are developed to make it more realistic in real world.In classical computing the basic unit of computation is a bit which is in 0 or 1 state at a time, whereas in quantum computing it is called a qbit which can be 0 and 1 at the same time and we call it superposition.This paper proposes an implementation of quantum full adder using IBM quantum experience.Quantum circuits are drawn using Qiskit and run on Qiskit simulators, IBM quantum simulators and real IBM quantum machines.Proposed circuit will help in future for drawing more complex circuits and algorithms.
With the growth of quantum computing hardware technology, more developers are becoming involved in the design and development of quantum algorithms, leading to the creation of practical applications that align with real-world needs through the combination of quantum hardware and software. Among quantum algorithms, the most well-known include Grover’s algorithm and Shor’s algorithm. Grover’s algorithm can quickly provide search results, making it highly valuable for search-related applications. In light of this, this study primarily examines the theoretical usability of Grover’s algorithm and explores its limitations. Additionally, on the practical side, this research implements Grover’s algorithm using IBM Quantum Computing and the IBM Qiskit package. By comparing simulation results with those obtained from execution on real quantum computers, the study discusses the current limitations of quantum computing hardware technology.
Quantum computation is becoming an increasingly interesting field, especially with the rise of real quantum computers. However, current quantum processors contain a few tens of error-prone qubits and the realization of large-scale quantum computers is still very challenging. Therefore, quantum computer simulators are particularly suitable for testing and analysing quantum algorithms without having a real quantum computer at one's disposal. In this thesis, different quantum algorithms such as Grover's and Shor's algorithm as well as key quantum routines such as the Quantum Fourier Transform (QFT) and a quantum adder/subtractor are described and analysed (optimal number of iterations, time complexity). Some of them have been implemented for an arbitrary number of qubits and have been simulated using two different quantum simulators, the QX simulator developed at QuTech and the Liquid simulator from Microsoft. In addition, how errors affect the success rate of the algorithms has been investigated.
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 computers are able to efficiently solve certain problems that are very computationally demanding or even intractable on classical computers. With recent advances in quantum computing hardware, we are entering an exciting era where it is becoming possible to execute ‘useful’ quantum algorithms. However, quantum computers will continue to be noisy for the foreseeable future. In this paper, quantum adder circuits are used to evaluate three simple error mitigation methods: (1) error correction through the use of replicated circuits and a voter circuit, (2) error detection by encoding, which involves expanding the qubit space and partitioning it into orthogonal subspaces consisting of correct and incorrect code words, and (3) error mitigation by reducing circuit depth at the expense of increasing the number of qubits. These three mitigation methods are what we dub replication, encoding, and simplification, respectively. We find simplification to be most effective for implementing the simple quantum adders on the IBM Quantum Experience, while replication increases the gate count and the error count on current quantum devices. The encoding methods used in this study proved to be not effective for even the simple adder circuits that were implemented, suggesting the need to study and evaluate more sophisticated error correcting schemes.