qtml2024.pptx presentation bmw group airbus

qtml 2024

1. Classification of the Fashion-MNIST Dataset on a Quantum Computer - with a focus on data encoding Kevin Shen , Bernhard Jobst , Elvira Shishenina , Frank Pollmann | QTML 2024, Melbourne

2. Data Encoding What ? - Loading classical data ( stored on classical computer) into quantum states 1 . 1 When yes ? - P rocess classical data by quantum algorithms - Q uantum algorithm encoding + processing   When no? - When data are given as quantum states - For some generative modelling algorithms - …

3. Data Encoding 2 1. Vojtěch Havlíček et al. Supervised learning with quantum-enhanced feature spaces 2. Schuld et al. Quantum machine learning in feature hilbert spaces 3. Sofiene Jerbi et al. Quantum machine learning beyond kernel methods aaaaaaa Consider . How?   Decision to be made: Do we look for quantum advantage from encoding or processing ? If processing : Encoding should be resource efficient and keep sufficient information If encoding : “Quantum feature maps”: kernel methods variational circuits 1 2 3  

4. Data Encoding 3 Suppose we look for quantum advantage from processing . Consider . How? 1 - Amplitude encoding :   Efficiency? - encoding gate count is exponential in the number of qubits 2 3 1. Alessandro Luongo https:// quantumalgorithms.org / 2. Ville Bergholm et al. ‚Quantum circuits with uniformly controlled one-qubit gates‘ 3 . Xiaoming Sun et al. ‚ Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis‘ Consequences? - challenges provable quantum advantage from processing - challenges empirical studies now / in near future

5. Our motivation : To make amplitude encoding more practical for quantum machine learning experiments - Use data compression ( efficient but approximate encoding ) - If processing is robust against (or benefit from ) noises in data 4 Data Encoding Data Compression   How to evaluate data compression? - Fidelity - Performance of the processing task

6. Data Compression by Matrix Product States (MPS) 5 What is MPS? - One way to classically store 1D quantum state (Amplitude encoding goes here )   Image source: https:// tensornetwork.org / - Can compress data by lowering bond dimension - If low entanglement in state low bond dimension ( low memory ) & l ow approximation errors  

7. Data Compression by Matrix Product States (MPS) 6 How to use MPS- compressed amplitude encoding for QML? 1. Classically optimize . 2. Make MPS in right-canonical form. 3. Map MPS to sequential quantum circuit .   Rohit Dilip et al. ‚Data Compression for Quantum Machine Learning‘ Circuit gate count : - compared to from exact encoding where and is bond dimension   Key Question: - How big is ? Better not be  

8. Question 1: Why can we assume low ?   Amplitude encoding and Flexibile Representation of Quantum Images (FRQI) of real-life images have low entanglement -> low bond dimension   7 1. Phuc Q. Le et al. A flexible representation of quantum images for polynomial preparation , image compression , and processing operations (Our work #1) Bernhard Jobst et al. Efficient MPS representations and quantum circuits from Fourier modes of classical image data FRQI 1 : FRQI preserves global color scaling, Amplitude encoding d oes not.

9. 8 Exact Encoding Compressed by   (Our work #1) Bernhard Jobst et al. Efficient MPS representations and quantum circuits from Fourier modes of classical image data

10. We derived an error bound : R egardless of image resolution ( which determines how many qubits are needed ), MPS of gives approximation error ( infidelity ), if data have algebraically-decaying Fourier c oefficients which is satisified by most natural images ( see figure )   1. Phuc Q. Le et al. A flexible representation of quantum images for polynomial preparation , image compression , and processing operations (Our work #1) Bernhard Jobst et al. Efficient MPS representations and quantum circuits from Fourier modes of classical image data Remaining question: How to compute the MPS? - SVD, stochastic methods, interpolation methods, …

11. Question 2: Can we make it more experiment- friendly ? We consider MPS- inspired sequetial circuits with 1. Repeating layers of general two qubit gates 10 2. Repeating layers of hardware native gates qubit gates   (Our work #2) Kevin Shen et al. Classification of the Fashion-MNIST dataset on a Quantum Computer Rohit Dilip et al. ‚Data Compression for Quantum Machine Learning‘ L   L  

12. 11 (Our work #2) Kevin Shen et al. Classification of the Fashion-MNIST dataset on a Quantum Computer We want to observe the tradeoff between efficiency and accuracy in experiments More expressive More accurate   Simpler circuit Fewer hardware errors  

13. 12 - We compressed the full Fashion-MNIST dataset ( 10.5281/zenodo.10680772 ) - We classically simulated the training of a 10-class variational quantum classifier - We deployed the variational classifier on an IBMQ 27 qubit chip. (Not available anymore) Experiment setup (Our work #2) Kevin Shen et al. Classification of the Fashion-MNIST dataset on a Quantum Computer

14. 13 Red: simpler Ansatz Blue: more complex Ansatz Solid: On simulator Dotted: On IBMQ Dash: Exact FRQI encoding (Our work #2) Kevin Shen et al. Classification of the Fashion-MNIST dataset on a Quantum Computer

15. What can we do together? Think more about data encoding Encoding for different data structure and different applications Resource efficiency Experimental implementation … 14

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