Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

Large-scale clustering measurements with photometric redshifts: comparing the dark matter haloes of X-ray AGN, star-forming and passive galaxies at z ≈ 1

We combine multi-wavelength data in the AEGIS-XD and C-COSMOS surveys to measure the typical dark matter halo mass of X-ray selected active galactic nuclei (AGN) [L_X(2–10 keV) > 10^42 erg s^− 1] in comparison with far-infrared selected star-forming galaxies detected in the Herschel/PEP survey (PACS Evolutionary Probe; L_IR > 10^11 L_⊙) and quiescent systems at z ≈ 1. We develop a novel method to measure the clustering of extragalactic populations that uses photometric redshift probability distribution functions in addition to any spectroscopy. This is advantageous in that all sources in the sample are used in the clustering analysis, not just the subset with secure spectroscopy. The method works best for large samples. The loss of accuracy because of the lack of spectroscopy is balanced by increasing the number of sources used to measure the clustering. We find that X-ray AGN, far-infrared selected star-forming galaxies and passive systems in the redshift interval 0.6 < z < 1.4 are found in haloes of similar mass, log M_DMH/(M_⊙ h^−1) ≈ 13.0. We argue that this is because the galaxies in all three samples (AGN, star-forming, passive) have similar stellar mass distributions, approximated by the J-band luminosity. Therefore, all galaxies that can potentially host X-ray AGN, because they have stellar masses in the appropriate range, live in dark matter haloes of log M_DMH/(M_⊙ h^−1) ≈ 13.0 independent of their star formation rates. This suggests that the stellar mass of X-ray AGN hosts is driving the observed clustering properties of this population. We also speculate that trends between AGN properties (e.g. luminosity, level of obscuration) and large-scale environment may be related to differences in the stellar mass of the host galaxies.

CB-norm estimates for maps between noncommutative Lp-spaces and quantum channel theory.

In the first part of this work, we show how certain techniques from quantum information theory can be used in order to obtain very sharp embeddings between noncommutative Lp-spaces. Then, we use these estimates to study the classical capacity with restricted assisted entanglement of the quantum erasure channel and the quantum depolarizing channel. In particular, we exactly compute the capacity of the first one and we show that certain nonmultiplicative results hold for the second one.