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Paper 1
Robustness of QMA against witness noise
Friederike Anna Dziemba
- Year
- 2016
- Journal
- arXiv preprint
- DOI
- arXiv:1611.07332
- arXiv
- 1611.07332
Using the tool of concatenated stabilizer coding, we prove that the complexity class QMA remains unchanged even if every witness qubit is disturbed by constant noise. This result may not only be relevant for physical implementations of verifying protocols but also attacking the relationship between the complexity classes QMA, QCMA and BQP, which can be reformulated in this unified framework of a verifying protocol receiving a disturbed witness. While QCMA and BQP are described by fully dephasing and depolarizing channels on the witness qubits, respectively, our result proves QMA to be robust against 27% dephasing and 18% depolarizing noise.
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Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates
Yongyao Li, Zhihuan Luo, Yan Liu, Zhaopin Chen, Chunqing Huang, Shenhe Fu, Haishu Tan, Boris A. Malomed
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1706.06725
- arXiv
- 1706.06725
We study two-dimensional (2D) matter-wave solitons in spinor Bose-Einstein condensates (BECs) under the action of the spin-orbit coupling (SOC) and opposite signs of the self- and cross-interactions. Stable 2D two-component solitons of the mixed-mode (MM) type are found if the cross-interaction between the components is attractive, while the self-interaction is repulsive in each component. Stable solitons of the semi-vortex type are formed in the opposite case, under the action of competing self-attraction and cross-repulsion. The solitons exist with the total norm taking values below a collapse threshold. Further, in the case of the repulsive self-interaction and inter-component attraction, stable 2D self-trapped modes, which may be considered as quantum droplets (QDs), are created if the beyond-mean-field Lee-Huang-Yang (LHY) terms are added to the self-repulsion in the underlying system of coupled Gross-Pitaevskii equations. Stable QDs of the MM type, of a large size with an anisotropic density profile, exist with arbitrarily large values of the norm, as the LHY terms eliminate the collapse. The effect of the SOC term on characteristics of the QDs is systematically studied. We also address the existence and stability of QDs in the case of SOC with mixed Rashba and Dresselhaus terms, which makes the density profile of the QD more isotropic. Thus, QDs in the spin-orbit-coupled binary BEC are for the first time studied in the present work.
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