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Analysis of the efficiency of quantum computing simulation methods based on experimental data

S.M. Gushanskiy, A.Y. Mushaev

Published Jan 1, 2022• 0 citations
Publisher

Abstract

Nowadays the actual problem of creating a quantum computer that allows solving practical problems has not been fully resolved. One of the tasks on the way to creating quantum computers is called the development of quantum algorithms, which can be solved using existing computers. The basis for the development of quantum algorithms is the simulation of the operation of a quantum circuit. The results of that work are used to analyze the quantum computing algorithm providing information support in the development of the quantum computer architecture as well. This article analyzes the effectiveness of methods for modeling quantum computing using various tools, based on experimental data. As a result of the analysis, a conclusion was made about the most effective way to simulate quantum computing.

DOI
10.34219/2078-8320-2022-13-2-35-38

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Nowadays the actual problem of creating a quantum computer that allows solving practical problems has not been fully resolved. One of the tasks on the way to creating quantum computers is called the development of quantum algorithms, which can be solved using existing computers. The basis for the development of quantum algorithms is the simulation of the operation of a quantum circuit. The results of that work are used to analyze the quantum computing algorithm providing information support in the development of the quantum computer architecture as well. This article analyzes the effectiveness of methods for modeling quantum computing using various tools, based on experimental data. As a result of the analysis, a conclusion was made about the most effective way to simulate quantum computing.
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.
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.
Abstract Currently, there is an ongoing “race” to build the first practically useful quantum computer that provides substantial speed-ups for certain problems compared to conventional computers. In addition to the development of such devices, this also requires the development of automated tools and methods that provide assistance in the simulation and design of corresponding applications. Otherwise, a situation might be reached where we have powerful quantum computers but hardly any proper means to actually use them. This work provides an overview of corresponding solutions for the task of quantum circuit simulation, the task of quantum circuit design, as well as corresponding mapping tasks. The covered solutions utilise expertise on efficient data structures and algorithms gained in the design of conventional circuits and systems over the last decades. While the respective descriptions are kept brief and mainly convey the general ideas, references to further readings are provided for a more detailed treatment.
Recently, there has been a rapid increase in interest in quantum computers. Their work isbased on the use of quantum-mechanical phenomena such as superposition and entanglement forcomputing input data into output data that can actually provide effective performance 3 to 4 orders ofmagnitude higher than any modern computing devices, which will solve the above and others tasks ina natural and accelerated time scale. This article is devoted to solving the problem of research anddevelopment of corrective codes for correcting several types of quantum errors that appear duringcomputational processes in quantum algorithms and models of quantum computing devices. The aimof the work is to study existing methods for correcting various types and types of quantum errors andto create a 3-qubit corrective code for quantum error correction. The work touches upon the tasks ofresearch and development of the functioning methods of quantum circuits and models of quantumcomputing devices. The relevance of these studies lies in the mathematical and software modelingand implementation of corrective codes for correcting several types of quantum errors as part of thedevelopment and implementation of quantum algorithms for solving classes of classical problems.The scientific novelty of this area is expressed in the exclusion of one of the shortcomings of thequantum computing process. The scientific novelty of this area is primarily expressed in the constantupdating and addition of the field of quantum research in a number of areas, and computer simulation of quantum physical phenomena and features is poorly illuminated in the world. The aim of the work is computer simulation of a quantum computing process using the method of correctingphase types of errors, which allows one to evaluate the own phase of a unitary gate that hasgained access to the quantum state in proportion to its own vector.
The last two decades feature an ever-increasing interest in quantum information processing - generalization of the classical computational models in the view of quantum mechanics (QM). In theory, quantum computational devices are capable of solving in polynomial time problems for which only algorithms with exponential time complexity are known. Such enormous advantage explains the global scale of scientific efforts for creating the quantum computer - physical realization of such computational device. While the results of those efforts are still constrained inside the large experimental laboratories, an adequate tool for studying quantum algorithms will be of great help for educating the next generation of computer scientists - the engineers that will be responsible for operating these devices. The paper describes a quantum computer simulation model that exhibits a certain attractive property - the simulation slowdown does not depend directly on the size of the input data but rather on the complexity of the quantum state, meaning that transformations upon less-entangled data are performed faster. Based on this property the simulation can be spread between the nodes of a grid cluster in a way as to keep the entanglement in each job minimal
Recently, there has been a rapid increase interest in quantum computers. Their work is based on the use of quantum-mechanical phenomena such as superposition and entanglement for computing to transform input data into outputs, which can actually provide effective performance 3-4 orders of magnitude higher than any modern computing devices. In the past few decades, there has been an acute problem of creating a quantum computer that uses quantum mechanical effects for computations. Currently, there are prototypes of devices of this class, but it is not yet possible to achieve an effective solution to the planned tasks with their help due to a number of difficulties in implementation. However, there is a mathematical apparatus that describes the behavior of quantum particles using a wave function. Hence, it becomes possible to simulate quantum computations on the classical architecture and check the reliability of algorithms belonging to the NP class, which are theoretically executed on a quantum computer in polynomial time and which cannot be solved on classical computers within an acceptable time frame. Effectively simulate the operation of a quantum system on devices with classical architecture is impossible, it remains to propose methods for acceleration of quantum computing on classical systems.