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High-precision operation of quantum computing systems must be robust to uncertainties and noises in the quantum hardware. We show that through a game played between the uncertainties (or noises) and the controls, adversarial uncertainty samples can be generated to find highly robust controls through the search for Nash equilibria. We propose a broad family of adversarial learning algorithms, namely a-GRAPE algorithms, which includes two effective learning schemes referred to as the best-response approach and the better-response approach within game-theoretic terminology, providing options for learning highly robust controls. Numerical experiments demonstrate that the balance between fidelity and robustness depends on the details of the chosen adversarial learning algorithm, which can effectively lead to a significant enhancement of control robustness while attaining high fidelity.
The learning curves of a-GRAPE for robust controls of the two-qubit system. The red (upper) line corresponds to the worst-case infidelity, while the blue (lower) one corresponds to the minimized average infidelity over selected adversarial samples in cases (a) the best-response approach with memory size s=10 and (b) the better-response approach with M=100 and r=0.1.
The relationship between sample size and number of risk loci detected varies between traits, but all show a sharp increase at a critical sample size. To date, there has been no trait with evidence of a plateau of the number of risk loci discovered with increasing sample size. For some traits, such as height, schizophrenia, and IBD, discovery samples in the next 5 years are likely to continue to increase, perhaps at a lower rate per additional sample. A diminishing rate of discovery of new loci will provide a more complete picture of genetic architecture and will best satisfy the understanding of contributing biological pathways. According to the knowledge of Mendelian disease, the expectation is that multiple risk variants will be detected within loci that have already been identified. Hence, as sample sizes increase, the new discoveries of associated pathways will be saturated first, followed by genes and lastly variants.
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