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Paper 1
Improved error thresholds for measurement-free error correction
Daniel Crow, Robert Joynt, Mark Saffman
- Year
- 2015
- Journal
- arXiv preprint
- DOI
- arXiv:1510.08359
- arXiv
- 1510.08359
Motivated by limitations and capabilities of neutral atom qubits, we examine whether measurement-free error correction can produce practical error thresholds. We show that this can be achieved by extracting redundant syndrome information, giving our procedure extra fault tolerance and eliminating the need for ancilla verification. The procedure is particularly favorable when multi-qubit gates are available for the correction step. Simulations of the bit-flip, Bacon-Shor, and Steane codes indicate that coherent error correction can produce threshold error rates that are on the order of $10^{-3}$ to $10^{-4}$---comparable with or better than measurement-based values, and much better than previous results for other coherent error correction schemes. This indicates that coherent error correction is worthy of serious consideration for achieving protected logical qubits.
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Entanglement renormalization and integral geometry
Xing Huang, Feng-Li Lin
- Year
- 2015
- Journal
- arXiv preprint
- DOI
- arXiv:1507.04633
- arXiv
- 1507.04633
We revisit the applications of integral geometry in AdS$_3$ and argue that the metric of the kinematic space can be realized as the entanglement contour, which is defined as the additive entanglement density. From the renormalization of the entanglement contour, we can holographically understand the operations of disentangler and isometry in multi-scale entanglement renormalization ansatz. Furthermore, a renormalization group equation of the long-distance entanglement contour is then derived. We then generalize this integral geometric construction to higher dimensions and in particular demonstrate how it works in bulk space of homogeneity and isotropy.
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