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Towards Quantum Machine Learning
Stefano Carrazza 19th October 2020, QTI TH meeting, CERN.
Universit` a degli Studi di Milano, INFN Milan, CERN, TII
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Machine Learning • PDFs • QCD
N 3 PDF Machine Learning PDFs QCD Introduction NISQ era We are - - PowerPoint PPT Presentation
N 3 PDF Machine Learning PDFs QCD Introduction NISQ era We are - - PowerPoint PPT Presentation
Towards Quantum Machine Learning Stefano Carrazza 19th October 2020, QTI TH meeting, CERN. Universit` a degli Studi di Milano, INFN Milan, CERN, TII N 3 PDF Machine Learning PDFs QCD Introduction NISQ era We are in a Noisy
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NISQ era
⇒ We are in a Noisy Intermediate-Scale Quantum era ⇐ How can we contribute?
- Develop new algorithms
⇒ using classical simulation of quantum algorithms
- Adapt problems and strategies for current hardware
⇒ hybrid classical-quantum computation
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Quantum Algorithms
There are three families of algorithms: Gate Circuits
- Search (Grover)
- QFT (Shor)
- Deutsch
Variational (AI inspired)
- Autoencoders
- Eigensolvers
- Classifiers
Annealing
- Direct Annealing
- Adiabatic Evolution
- QAOA
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Variational Quantum Circuits
Getting inspiration from AI:
- Supervised Learning
⇒ Regression and classification
- Unsupervised Learning ⇒ Generative models, autoencoders
- Reinforcement Learning ⇒ Quantum RL / Q-learning
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Variational Quantum Circuits
Getting inspiration from AI:
- Supervised Learning
⇒ Regression and classification
- Unsupervised Learning ⇒ Generative models, autoencoders
- Reinforcement Learning ⇒ Quantum RL / Q-learning
Define new parametric model architectures for quantum hardware: ⇒ Variational Quantum Circuits
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Rational
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Rational for Variational Quantum Circuits
Rational: Deliver variational quantum states → explore a large Hilbert space. U( α) = Un . . . U2U1 U1 U3 U4 U2 Near optimal solution
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Rational for Variational Quantum Circuits
Rational: Deliver variational quantum states → explore a large Hilbert space. U( α) = Un . . . U2U1 U1 U3 U4 U2 Near optimal solution Idea: Quantum Computer is a machine that generates variational states. ⇒ Variational Quantum Computer!
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Solovay-Kitaev Theorem
Let {Ui} be a dense set of unitaries. Define a circuit approximation to V : |Uk . . . U2U1 − V | < δ Scaling to best approximation k ∼ O
- logc 1
δ
- where c < 4.
Optimal solution ⇒ The approximation is efficient and requires a finite number of gates.
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Many unexplored options
Add data in the course of computation?
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Example 1: VQE
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Variational Quantum Eigensolvers (VQE)
Aspuru-Guzik et al., IBM, Zapata, Blatt.
VQE is hybrid classical-quantum algorithm.
- 1. Define an optimization problem, e.g. energy, correlations, etc.
- 2. Apply ”machine learning“ on circuit design.
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Variational Quantum Eigensolvers (VQE)
First successful applications in quantum chemistry:
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Example 2: Quantum Classifier
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Data re-uploading strategy
P´ erez-Salinas et al. [arXiv:1907.02085]
Encode data directly “inside” circuit parameters:
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Data re-uploading strategy
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Data re-uploading strategy
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Example 3: ML to Quantum
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VQE with reinforcement learning
- A. Garcia-Saez, J. Riu [arXiv:1911.09682], Google [arXiv:2003:02989]
Strategies:
- Use Reinforcement Learning to tune VQE circuits.
- Use DL for variational circuit tune and data pre-post processing.
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Code tutorials
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Qibo applications and tutorial
- VQE-like examples:
- Scaling of VQE for condensed matter systems
- Variational Quantum Classifier
- Data reuploading for a universal quantum classifier
- Quantum autoencoder for data compression
- Measuring the tangle of three-qubit states
- Quantum autoencoders with enhanced data encoding (New!)
See: https://qibo.readthedocs.io/en/latest/applications.html
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Thank you for your attention.
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