Simple approach to approximate quantum error correction based on the transpose channel

We demonstrate that there exists a universal, near-optimal recovery map—the transpose channel—for approximate quantum error-correcting codes, where optimality is defined using the worst-case fidelity. Using the transpose channel, we provide an alternative interpretation of the standard quantum error correction (QEC) conditions and generalize them to a set of conditions for approximate QEC (AQEC) codes. This forms the basis of a simple algorithm for finding AQEC codes. Our analytical approach is a departure from earlier work relying on exhaustive numerical search for the optimal recovery map, with optimality defined based on entanglement fidelity. For the practically useful case of codes encoding a single qubit of information, our algorithm is particularly easy to implement

Optimisation of the Wax and Oil Phases in a Conventional Lipstick Using Mixture Design

Lipstick is essentially a mixture of oils, waxes and pastes. The type and ratio of ingredients in the lipstick base determine the type and intensity of interactions, which directly affect the quality of lipstick. Fundamentally, a lipstick must have sufficient stick strength to withstand the force during application, but it should also have appropriate ‘pay off’ characteristics. The traditional empirical approach may be inefficient in the development of lipsticks, because of the number of formulation variables and the two competing requirements. The results of this study have revealed the quantitative relationship between the hardness of a lipstick (expressed as its breaking and softening point) and its ‘glide’ performance. The use of the Mixture Design approach has made it possible to effectively select the samples with the best overall characteristics, on the basis of limited but focused experimental work

Implementing a neutral-atom controlled-phase gate with a single Rydberg pulse

One can implement fast two-qubit entangling gates by exploiting the Rydberg blockade. Although various theoretical schemes have been proposed, experimenters have not yet been able to demonstrate two-atom gates of high fidelity due to experimental constraints. We propose a novel scheme, which only uses a single Rydberg pulse illuminating both atoms, for the construction of neutral-atom controlled-phase gates. In contrast to the existing schemes, our approach is simpler to implement and requires neither individual addressing of atoms nor adiabatic procedures. With parameters estimated based on actual experimental scenarios, a gate fidelity higher than 0.99 is achievable.Comment: 6 pages, 5 figure

Combining dynamical decoupling with fault-tolerant quantum computation

We study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. We prove upper bounds on the accuracy of DD-protected quantum gates and derive sufficient conditions for DD-protected gates to outperform unprotected gates. Under suitable conditions, fault-tolerant quantum circuits constructed from DD-protected gates can tolerate stronger noise and have a lower overhead cost than fault-tolerant circuits constructed from unprotected gates. Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer and can be expressed either in terms of the operator norm of the bath’s Hamiltonian or in terms of the power spectrum of bath correlations; we explain in particular how the performance of recursively generated concatenated pulse sequences can be analyzed from either viewpoint. Our results apply to Hamiltonian noise models with limited spatial correlations