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DESCRIPTION:Optimal spectrum estimation\nNorah Tan | MIT\nWe prove that the spectrum of an unknown d-dimensional quantum state can be estimated to error ε in total variation distance using O(d2min{1(εlogd)4\,1(εlogd)2}) copies. This matches the recent lower bound of Wang. When restricted to unentangled measurements\, we give an algorithm with an additional factor of d in copy complexity\, which we conjecture to be optimal. \n\nWe develop a framework for recovering the small eigenvalues of a quantum state by matching Chebyshev moments. We bound the variance of each Chebyshev moment estimate in terms of scalar derivatives of the corresponding polynomial\, using classical and quantum Efron--Stein decompositions. Different rescalings of the Chebyshev polynomials balance approximation error and variance\, yielding two regimes in our copy complexity bound.
X-ALT-DESC;FMTTYPE=text/html:Optimal spectrum estimation<br />Norah Tan | MIT<br />We prove that the spectrum of an unknown d-dimensional quantum state can be estimated to error ε in total variation distance using O(d2min{1(εlogd)4,1(εlogd)2}) copies. This matches the recent lower bound of Wang. When restricted to unentangled measurements, we give an algorithm with an additional factor of d in copy complexity, which we conjecture to be optimal. <br><br>We develop a framework for recovering the small eigenvalues of a quantum state by matching Chebyshev moments. We bound the variance of each Chebyshev moment estimate in terms of scalar derivatives of the corresponding polynomial, using classical and quantum Efron--Stein decompositions. Different rescalings of the Chebyshev polynomials balance approximation error and variance, yielding two regimes in our copy complexity bound.
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SUMMARY:IQC Math and CS seminar featuring Norah Tan
DTSTART;TZID=America/New_York:20261112T130000
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DTSTAMP:20261102T223505Z
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STATUS:CONFIRMED
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LOCATION:QNC 1201
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