Reading Group: Quantum Learning and Testing

Next Date/Time: 15 July 2025 at 2:30 pm - 4:00 pm

Location: MB2.23

Notes: Overleaf

The quickly growing field of quantum learning and testing lies at the intersection of quantum physics and computer science. It revolves around questions like "How can quantum data access help with classical learning and testing tasks?" or "How can we efficiently learn and test properties of quantum systems?". In this reading group, we will explore different aspects of quantum learning and testing, guided by recent research papers on the topic.

Everyone is welcome to attend the reading group. If you'd like to join us, please send an email to matthias.caro@warwick.ac.uk.

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Reading group sessions:

1. June 10, 2025 / 2:30 pm - 4:00 pm: Introduction and overview
   • Reading: A survey of quantum property testing, A Survey of Quantum Learning Theory, A survey on the complexity of learning quantum states, The randomized measurement toolbox
2. June 30, 2025/ 2:30 pm - 4:00 pm: Lower bounds via information-theoretic quantities (see this excerpt from Matthias's LSIT 2023 slides for a zoomed-out perspective):
   • Primary references:
     • Sections 1.2.1 and 3 in Optimal Quantum Sample Complexity of Learning Algorithms
     • Section 6 in

       Shadow Tomography of Quantum States

     • Section VI in

       Sample-optimal tomography of quantum states

     • Supplementary Information 7 and 8 in

       Predicting Many Properties of a Quantum System from Very Few Measurements

   • Secondary references:

     • Optimal lower bounds for Quantum Learning via Information Theory

       for an improvement
     • Section 6.1 in Quantum Learning Boolean Linear Functions w.r.t. Product Distributions
     • Section 7 in Classical Verification of Quantum Learning
     • Appendix E in Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix
     • Appendices B.2 and C.3 in Learning quantum states and unitaries of bounded gate complexity
     • Appendix C.1 in Information-theoretic bounds on quantum advantage in machine learning

3. July 15, 2025 / 2:30 pm - 4:00 pm: Lower bounds via LeCam's method and the tree representation:

   • Primary references:
     • Exponential separations between learning with and without quantum memory
     • Assouad, Fano and Le Cam (classical) and Minimax and Bayesian risk lower bound techniques (supplementary to the first short note)
   • Secondary references:
     • The Complexity of NISQ
     • Optimal tradeoffs for estimating Pauli observables
     • Exponential learning advantages with conjugate states and minimal quantum memory
     • Quantum Channel Certification with Incoherent Strategies

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Possible topics for future sessions:

• Randomized measurement framework and classical shadow formalism
• Representation-theoretic foundations of state tomography
• Testing properties of quantum states, unitaries, Hamiltonians, and channels
• Learning structured classes of states such as matrix product states, stabilizer states, t-doped stabilizer states, or Gaussian states
• PAC learning and property testing from quantum examples or quantum queries
• Quantum learning vs quantum cryptography