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SUMMARY:Quantum state tomography via non-convex Riemannian gradient descen
 t - Wei-Hsuan Yu (俞韋亘)\, National Central University
DTSTART:20230613T130000Z
DTEND:20230613T141500Z
UID:TALK202438@talks.cam.ac.uk
CONTACT:Sergii Strelchuk
DESCRIPTION:The recovery of an unknown density matrix of large size requir
 es huge computational resources. \nState-of-the-art performance has recent
 ly been achieved with the Factored Gradient Descent (FGD) algorithm and it
 s variants since they are able to mitigate the dimensionality barrier by u
 tilizing some of the underlying structures of the density matrix. \nDespit
 e the theoretical guarantee of a linear convergence rate\, convergence in 
 practical scenarios is still slow because the contracting factor of the FG
 D algorithms depends on the condition number $\\kappa$ of the ground truth
  state.\nConsequently\, the total number of iterations needed to achieve t
 he estimation error $\\varepsilon$ can be as large as $O(\\sqrt{\\kappa}\\
 ln(\\frac{1}{\\varepsilon}))$. \nIn this work\, we derive a quantum state 
 tomography scheme that improves the dependence on $\\kappa$ to the logarit
 hmic scale. Thus\, our algorithm can achieve the approximation error $\\va
 repsilon$ in $O(\\ln(\\frac{1}{\\kappa\\varepsilon}))$ steps. The improvem
 ent comes from the application of non-convex Riemannian gradient descent (
 RGD). The contracting factor in our approach is thus a universal constant 
 that is independent of the given state. \nOur theoretical results of extre
 mely fast convergence and nearly optimal error bounds are corroborated by 
 the numerical results. 
LOCATION:MR4
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