Classical capacity of a qubit depolarizing channel with memory

The classical product state capacity of a noisy quantum channel with memory is investigated. A forgetful noise-memory channel is constructed by Markov switching between two depolarizing channels which introduces non-Markovian noise correlations between successive channel uses. The computation of the capacity is reduced to an entropy computation for a function of a Markov process. A reformulation in terms of algebraic measures then enables its calculation. The effects of the hidden-Markovian memory on the capacity are explored. An increase in noise-correlations is found to increase the capacity

The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry

Variational quantum algorithms are suitable for use on noisy quantum systems. One of the most important use-cases is the quantum simulation of materials, using the variational quantum eigensolver (VQE). To optimize VQE performance, a suitable parameterized quantum circuit (ansatz) must be selected. We investigate a class of ansatze that incorporates knowledge of the quantum hardware, namely the hardware efficient ansatze. The performance of hardware efficient ansatze is affected differently by noise, and our goal is to study the effect of noise on evaluating which ansatz gives more accurate results in practice. First, we study the effect of noise on the different hardware efficient ansatze by benchmarking and ranking the performance of each ansatz family (i) on a chemistry application using VQE and (ii) by the recently established metric of "expressibility". The results demonstrate the ranking of optimal circuits does not remain constant in the presence of noise. Second, we evaluate the suitability of the expressibility measure in this context by performing a correlation study between expressibility and the performance of the same circuits on a chemistry application using VQE. Our simulations reveal a weak correlation and therefore demonstrate that expressibility is not an adequate measure to quantify the effectiveness of parameterized quantum circuits for quantum chemistry. Third, we evaluate the effect of different quantum device noise models on the ordering of which ansatz family is best. Interestingly, we see that to decide which ansatz is optimal for use, one needs to consider the specific hardware used even within the same family of quantum hardware.Comment: 13 pages, 17 figures, 4 tables, conference paper, IEEE International Conference on Quantum Computing and Engineering (QCE21

Classical noise in quantum systems.

Ph. D. University of KwaZulu-Natal, Durban, 2013.Quantum mechanics contains a fresh and mysterious view of reality. Besides the philosophical intrigue, it has also produced and continues to inspire tantalizing new technological innovations. In any technological system, the designers must contend with the problem of noise. This thesis studies classical noise in two different quantum settings. The first is the classical capacity of a quantum channel with memory. Adding forgetful-memory, attempts to push the boundaries of our understanding of how best to transmit information in the presence of correlated noise. We study the noise within two different frameworks; Algebraic Measure theory and Monte Carlo simulations. Both tools are used to calculate the capacity of the channel as correlations in the noise are increased. The second classical-quantum system investigated is atomic clocks. Using power spectral density methods we study aliasing noise induced by periodic-correction which includes the Dick Effect. We propose a novel multi-window scheme that extends the standard method of noise correction and exhibits better anti-aliasing properties. A uniting thread that emerges is that correlations can be put to good use. In the classical capacity setting, correlations occur between uses of the quantum channel. We show that stronger correlations increase the classical capacity. The benefits of correlation are even seen at a meta-level within the framework of Monte Carlo simulations. Correlations are designed into the algorithm which have nothing to do with real-world correlations, but are abstract correlations created by a Markov chain employed in the algorithm to help efficiently sample from a distribution of exponential size. Finally, in the atomic clock setting, correlations in the measured noise are used to help predict and cancel noise on a short time-scale while trying to limit aliasing. Channel capacity and precise time-keeping are distinct topics and require very different approaches to study. However, common to both topics is their application to com- munication and other tasks, the need to overcome noise and the benefits of exploiting correlations in the noise