“The question posed by the ‘Hodge conjecture’ is a very natural one… Unfortunately, despite the word ‘conjecture’, as far as I know there is not the slightest reason to believe it; one would be doing geometers a service if the question could be settled by means of a counterexample.” — André Weil
Jiahao Cao
Research Interests
Quantum Information
Quantum Many-Body Physics
Machine Learning
Complexity Theory
Miscellanea
Some informal notes on physics, mathematics, and machine learning.
Research Notes
Some research ideas and notes to be continued
The main result is: for an R × C Bacon–Shor code, after fixing t independent commuting gauge constraints and optimizing over all possible gauge-fixing choices, the exact worst-case tradeoff is ΔE*_t = ⌈t / max(R − 1, C − 1)⌉. The result covers all gauge fixings, including mixed non-CSS choices. Moreover, there exists a protocol that adds gauge constraints one by one and remains globally optimal for every t. At complete fixing, the result reaches d_dressed − 1.