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EE671 Presentation Quantum Neural Networks

EE671 Presentation Quantum Neural Networks. Pratyush Pandey Y7315. Outline. Introduction Basic Quantum Concepts A Simple Quantum Neural Network (QNN) Quantum Search based Training Algorithms Advantages of a QNN Physical Limitations in Implementation Questions. Introduction.

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EE671 Presentation Quantum Neural Networks

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  1. EE671 PresentationQuantum Neural Networks PratyushPandey Y7315

  2. Outline • Introduction • Basic Quantum Concepts • A Simple Quantum Neural Network (QNN) • Quantum Search based Training Algorithms • Advantages of a QNN • Physical Limitations in Implementation • Questions

  3. Introduction

  4. Basic Quantum Concepts • Bra-Ket Notation • Linear Superposition of States • Quantum Measurement • Operators • Entanglement • Grover’s Search Algorithm

  5. A Simple QNN

  6. A Simple QNN • Each input node is |a>i • Weighted sum of inputs |y>ij • Threshold weight |y>i0 • Internal calculations represented by |b>k • Target outputs are |W>j • If output matches target, |f>j is set high • Performance of network stored in |r>

  7. Quantum Search Based Training Algorithms • We want |r> = n*m • Use generalised search algorithm with number of solutions unknown • Take |y> as the superposition of all possible weight vectors • Initialise all other states to |0> • Simultaneously obtain corresponding |r> entangled to each weight • Carry out a quantum search for |r>=n*m • Time required to find training set is O(sqrt(2b/t))

  8. Quantum Search Based Training Algorithms • We can use piecewise weight learning • Randomly select weights to update in same manner as before • Can use a percent error margin

  9. Advantages of a QNN • Exponential memory capacity • Higher performance for lower number of hidden neurons • Faster learning • Processing speed (1010 bits/s) • Small scale (1011 neurons/mm3)

  10. Physical Limitations in Implementation • NMR methods • Currently most mature • Large coherence times, hence slow • Take statistical averages • Bulky • Quantum Dots • Very short decoherence time • Fabrication at small scale • Need varying frequency or highly selective lasers

  11. Questions • What would be the time taken by a classical computer to simulate a quantum neural algorithm with O(n) • In the piecewise search algorithm, do we need to remove entanglement after every run? • Can we use a QNN to clone a quantum state without knowing what it is? • Can QNNs be a better model for brain function?

  12. References • “Quantum neural networks” Alexandr A. Ezhov and Dan Ventura • “Training a Quantum Neural Network” by Bob Ricks and Dan Ventura • Quantum Computation and Quantum Information, Nielsen and Chuang • From Schrodinger’s equation to the Search Algorithm, Luv Kr. Grover

  13. Thank You

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