Schedule

UNM Physics and Astronomy, Summer 2026 course

  1. [06/17] Overview of quantum learning theory and tomography.

    2. [Ariel Shlosberg]

    Summary. We will introduce and motivate the field of quantum learning theory. We will cover quantum state discrimination, the Holevo-Helstrom theorem, and Le Cam's two-point method.
    Reading.
    Slides. PDF

  2. [06/24] Pauli and pure-state tomography.

    3. [Andy Deneris and Ariq Haqq]

    Summary. We cover Pauli tomography for mixed states along with Hayashi's pure-state tomography scheme.
    Reading. Pg. 35-47 of Jacob Beckey's lecture notes.
    Slides. PDF

  3. [07/01] Optimal State Tomography.

    4. [Tristan Larkin and Omar Nazim]

    Summary. We will cover the recently introduced sample-optimal tomography scheme for mixed states through a reduction to pure state tomography.
    Reading. Mixed state tomography reduces to pure state tomography
    Slides. PDF

  4. [07/08] Lower Bound on State Tomography.

    5. [Nathaniel Hollingsworth]

    Summary. We will prove a lower bound for the sample complexity of state tomography using a communication protocol and epsilon-packing of Hilbert space.
    Reading.
    Slides. PDF

  5. [07/15] Classical Shadow Formalism.

    6. [Andrew Noe and Alex Gran]

    Summary. We will describe the classical shadow framework for observable estimation using single-copy measurements. Using two-copy measurements, we will see that there is an exponential improvement in sample complexity.
    Reading.
    Slides. PDF

  6. [07/22] Property Testing I.

    7. [Ethan Egger and Junho Kim]

    Summary. We introduce the topic of quantum property testing along with associated notions of completeness and soundness.
    Reading.
    Slides. PDF

  7. [07/29] Property Testing II.

    8. [Dayeon Yoo]

    Summary. We continue with property testing and describe lower bounds on purity testing and product testing.
    Reading.
    Slides. PDF

Bibliography