How to learn a quantum state

Abstract: In the area of quantum state learning, one is given a small number of "samples" of a quantum state, and the goal is use them to determine a feature of the state.  Examples include learning the entire state ("quantum state tomography"), determining whether it equals a target state ("quantum state certification"), or estimating its von Neumann entropy.  These are problems which are not only of theoretical interest, but are also commonly used in current-day implementation and verification of quantum technologies. In this talk, I will describe my work giving efficient algorithms for a variety of these problems, including the first optimal algorithms for tomography and state certification.  My results make use of a new connection between quantum state learning and longest increasing subsequences of random words, a famous topic in combinatorics dating back to a 1935 paper of Erdos and Szekeres.  Motivated by this connection, I will show new and optimal bounds on the length of the longest increasing subsequence of a random word.

Biography: John Wright received a B.Sc. from the University of Texas at Austin in 2010 and a Ph.D. from the CMU Computer Science Department in 2016. His Ph.D. advisor was Ryan O'Donnell. He is currently a postdoc at the MIT Center for Theoretical Physics in Eddie Farhi, Aram Harrow, and Peter Shor's group. His research areas include quantum information theory and quantum complexity theory.

 

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Media Contact: Sean Hallgren

 
 

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