Invited Talks

An Analytic Theory for Quantum Neural Networks

  • Junyu Liu, the University of Chicago and IBM
  • Time: 2022-04-30 10:00
  • Host: Dr. Xiao Yuan
  • Venue: Online Talk


Parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.


Dr. Junyu Liu is a theoretical physicist currently working for the University of Chicago and IBM, associated with the Chicago Quantum Exchange with a maximally five-year position. He is primarily located in Uchicago in Prof. Liang Jiang's Group in the Pritzker School of Molecular Engineering, and also a Kadanoff fellow in Kadanoff Center for Theoretical Physics. Dr. Liu is interested in theoretical physics and its relation to computation, including random matrix theories, machine learning, optimization, quantum computing, and commercial value of modern computing technologies.


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