Normally autocorrelation functions refer to noise in the system, so an important question will be how to turn a noise autocorrelation function into an error autocorrelation function.Ĭurrent QECCs can be built from pairs of classical error correcting codes, as can current independent sigma-x and sigma-z errors with different error rates. It will be very important to include autocorrelation functions in the error model, and hopefully ask the question of how to deal with an arbitrary (parametrized) autocorrelation function. Based on these abstract error parameters, the main goal will be to create parameterized families of quantum error correcting codes and tie the code parameters to error parameters. The first order of business should be to create general abstract parameterized error models with a clear understanding of what all the parameters are and their interrelations, if any. It is important to deal with abstract parameterized error models in this project, rather than tie the error models to specific quantum computing architectures or specific types of qubits. The goal here is to develop a theory of quantum error correction that takes into account correlated coherent errors and, in particular to deal with errors that are temporally correlated, such as those that might arise in a non-white noise environment. However, the underlying error model for most QECCs has been that of independent identically distributed (IID) errors, and that model is known to inaccurately represent the errors that arise in the true noise environment of a quantum computer. Research Topic Description, including Problem Statement:įrom a theoretical perspective, the development of quantum error correcting codes (QECCs) has been a resounding success, much of which has been built on the underlying theory of classical error correcting codes.
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