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Dates Chiseled into an ancient tombstone have more in common with the data in your phone or laptop than you may realize. They both involve conventional, classical information, carried by hard-ware that is relatively immune to errors. The situation inside a quantum computer is far different: The information itself has its own idiosyncratic properties, and compared with standard digital microelectronics, state-of-the-art quantum-computer hardware is more than a billion trillion times as likely to suffer a fault. This tremendous susceptibility to errors is the single biggest problem holding back quantum computing from realizing its great promise. [ABSTRACT FROM AUTHOR]

We study the performance of composite pulses in the presence of time-varying control noise on a single qubit. These protocols, originally devised only to correct for static, systematic errors, are shown to be robust to time-dependent non-Markovian noise in the control field up to frequencies as high as ~10% of the Rabi frequency. Our study combines a generalized filter-function approach with asymptotic dc-limit calculations to give a simple analytic framework for error analysis applied to a number of composite-pulse sequences relevant to nuclear magnetic resonance as well as quantum information experiments. Results include examination of recently introduced concatenated composite pulses and dynamically corrected gates, demonstrating equivalent first-order suppression of time-dependent fluctuations in amplitude and/or detuning, as appropriate for the sequence in question. Our analytic results agree well with numerical simulations for realistic 1/ƒ noise spectra with a roll-off to 1/ƒ², providing independent validation of our theoretical insights. [ABSTRACT FROM AUTHOR]

We study dynamical error suppression from the perspective of reducing sequencing complexity, with an eye toward facilitating the development of efficient semiautonomous quantum-coherent systems. To this end, we focus on digital sequences where all interpulse time periods are integer multiples of a minimum clock period and compatibility with digital classical control circuitry is intrinsic. We use so-called Walsh functions as a unifying mathematical framework; the Walsh functions are an orthonormal set of basis functions which may be associated directly with the control propagator for a digital modulation scheme. Using this insight, we characterize the suite of resulting Walsh dynamical decoupling sequences-including both familiar and novel control sequences-and identify the number of periodic square-wave (Rademacher) functions required to generate the associated Walsh function as the key determinant of the error-suppressing features. We also show how Walsh modulation may be employed for the protection of certain nontrivial logic gates. Based on these insights, we identify Walsh modulation as a digital-efficient approach for physical-layer error suppression. [ABSTRACT FROM AUTHOR]

Among the most popular and well-studied quantum characterization, verification, and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in "Pauli space." Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a Γ distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes--consistent with existing experimental data--highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation. [ABSTRACT FROM AUTHOR]