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Paper 1

Phase analysis on the error scaling of entangled qubits in a 53-qubit system.

Huang WJ, Chien WC, Cho CH, Huang CC, Huang TW, Tan SG, Cao C, Zeng B, Chang CR.

Year

2021

Journal

Sci Rep

DOI

10.1038/s41598-021-93856-8

arXiv

-

No abstract.

Open paper

Paper 2

A constrained gentlest ascent dynamics and its applications to finding excited states of Bose-Einstein condensates

Wei Liu, Ziqing Xie, Yongjun Yuan

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.04684

arXiv

2209.04684

In this paper, the gentlest ascent dynamics (GAD) developed in [W. E and X. Zhou, Nonlinearity, 24 (2011), pp. 1831--1842] is extended to a constrained gentlest ascent dynamics (CGAD) to find constrained saddle points with any specified Morse indices. It is proved that the linearly stable steady state of the proposed CGAD is exactly a nondegenerate constrained saddle point with a corresponding Morse index. Meanwhile, the locally exponential convergence of an idealized CGAD near nondegenerate constrained saddle points with corresponding indices is also verified. The CGAD is then applied to find excited states of single-component Bose--Einstein condensates (BECs) in the order of their Morse indices via computing constrained saddle points of the corresponding Gross--Pitaevskii energy functional under the normalization constraint. In addition, properties of the excited states of BECs in the linear/nonlinear cases are mathematically/numerically studied. Extensive numerical results are reported to show the effectiveness and robustness of our method and demonstrate some interesting physics.

Open paper