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Programming and Computer Software

Simulation of quantum error correction by means of QuantumCircuit package

Vladimir P. Gerdt, Alexander N. Prokopenya

Published May 1, 2013• 8 citations
Publisher

Abstract

In the paper, the problem of simulation of quantum error correction by means of error correcting codes is discussed. Examples of error correction by means of quantum circuits constructed with the help of the QuantumCircuit package written in the language of the computer algebra system Mathematica are presented.
DOI
10.1134/s036176881303002x

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This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes. These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.
This study considers implementations of error correction in a simulation language on a classical computer. Error correction will be necessarily in quantum computing and quantum information. We will give some examples of the implementations of some error correction codes. These implementations will be made in a more general quantum simulation language on a classical computer in the language Mathematica. The intention of this research is to develop a programming language that is able to make simulations of all quantum algorithms and error corrections in the same framework. The program code implemented on a classical computer will provide a connection between the mathematical formulation of quantum mechanics and computational methods. This gives us a clear uncomplicated language for the implementations of algorithms.
In Chapter 4 we introduced different quantum gates and quantum circuits and in Chapter 5 we described several quantum algorithms. So far the analysis of the algorithms and the circuits has been made with the assumption that the required unitary operations can be implemented exactly without any error. This is an abstraction. In an actual physical system that implements a quantum algorithm or a quantum circuit there are several sources of errors. The situation is similar in classical computation and to circumvent this problem error correcting codes are used in classical digital computing. Since qubits are more delicate and more susceptible to errors we need to introduce quantum error correcting codes. It is very important, as without such codes it will not be possible to build a scalable quantum computer. Such quantum error correcting codes are introduced in this chapter. However, we will not limit ourselves to the discussion of error correcting codes alone. We will also discuss more general aspects of errors and error correction, like decoherence, decoherence free subspace and fault-tolerance.
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and correct corresponding errors. However, most of the research on quantum error correction is theoretical or has been evaluated for specific hardware models only. Moreover, the development of corresponding codes and the evaluation of whether they indeed solve the problem for a particular hardware model, still often rests on tedious trial-and-error thus far. In this work, we propose an open-source framework that supports engineers and researchers in these tasks by automatically applying error-correcting codes for a given application followed by an automatic noise-aware quantum circuit simulation. Case studies showcase that this allows for a substantially more efficient implementation and evaluation of error-correcting codes.
Quantum Error Correction (QEC) is an important technique for protecting quantum information against decoherence and errors. This involves the design and implementation of algorithms and techniques to minimize error rates and increase the stability of quantum circuits. One of the key parameters in QEC is the distance of the error- correcting code, which determines the number of errors that can be corrected. Another important parameter is the error probability, which quantifies the likelihood of errors occurring in the quantum system. In this context, the goal of a simulation sweeps like the one performed in the code is to study the performance of the QEC code for different values of the distance and error probability, and to optimize the code for maximum accuracy. By varying these parameters and observing the performance of the code, researchers can gain insights into how to design better codes and improve the reliability of quantum computing systems. We also discuss the challenges that need to be addressed for quantum computing to realize its potential in solving practical Error-correction problems.