The Interlink Between Quantum Theory and Machine Learning - Phdassistance

1. The Interlink Between Quantum Theory and MachineLearning An Academic presentationby Dr. Nancy Agnes, Head, Technical Operations,Phdassistance Group www.phdassistance.com Email:info@phdassistance.com

2. TODAY'SDISCUSSION Outline Introduction Quantum neural networks representation Quantum-based machinelearning Futurescope

3. INTRODUCTION Machine learningis a branch of computerscience that aims to create programs that can find useful knowledge and make assumptions aboutdata. It's at the heart of artificial intelligence (AI), and it's powering anything from facial recognitionto natural language processing to automatic self- drivingvehicles. Dimensionality is the most challenging machine learning problem; in general, the numberof training data sets needed for the machine to learn the desired information is exponential in dimensiond. Contd...

4. If a data set is located in a high-dimensional space, it becomes computationallyuncontrollable. This level of sophistication is comparable to quantum mechanics, where an infinite number of data is needed to explain a quantum many-body statecompletely. This article will explain the scientific interlink between quantum theory and machine learning.

5. QUANTUM NEURAL NETWORKS REPRESENTATION Artificial neural networks (ANNs) are models used in grouping, regression, compression, generative modelling, and statisticalinference. The alternation of linear operations with nonlinear transformations (e.g. sigmoid functions) in a theoretically hierarchical manner is their unifyingfeature. In Quantum Machine Learning (QLM), NNs have been extensivelystudied Contd...

6. The main research directionshave been to speed up classical models' training and build networks with all constituent components, from single neurons to training algorithms, running on a quantum computer (a so-called quantum neuralnetwork). Along with the rapid development of machine-learning algorithms for determining phases of matter, artificial neural networks have made significant progress in describing quantum states and solving important quantum many-bodyproblems. Completely defining an arbitrary many-body state in quantum mechanics necessitates an exponential number ofdata. Contd...

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8. For computational simulations of quantum many-body structures on a classical machine, the exponential difficulty presents a huge challenge—describing even a few qubits necessitates a massive amount ofmemory. Moreover, only a small part of all Hilbert's Quantum space, such as the ground states of many-body Hamiltonians, can enter physical states of concern and be depicted with fewerdetails. Compact models of quantum many-body states must be constructed while maintaining their basic physical properties to solve quantum many-body problems using classicalcomputers. Contd...

9. The tensor-network representation [2], in which each qubit is given a tensor, and these tensors together characterise the many-body quantum state, is a well-known explanation for suchstates. Since the volume of data required is only polynomial instead of exponential, the system's size is the most accurate description of the physicalcondition.

10. QUANTUM-BASED MACHINELEARNING Most quantum machine learningalgorithms necessitate fault-tolerant quantum computing, which necessitates the aggregation of millions of qubits on a wide scale, which is currently unavailable. Quantum machine learning (QML),however, includes applied the first breakthrough algorithms on commercially viable noisy (NISQ) intermediate-scale quantum computers. Contd...

11. Many interesting breakthroughs were made at the crossroads of quantum mechanics and machinelearning. Machine learning has been successfully used in many-body quantum mechanics to speed up calculations, simulate phases of matter, and find vibrational analysis for many-body quantum states, forexample. In quantum computing, machine learning has recently shown performance in quantum control and errorcorrection. Finding the system's ground state or the dynamics of the system's time evolution is typically the first step in solving quantum many-bodyproblems. Contd...

12. Carleo and Troyer proposed the RBM representation, used an RBM-based variational learning algorithm to dothis. They applied the technique to two prototypical quantum spin models: the Ising model in a transverse magnetic field and the antiferromagnetic Heisenbergmodel. They discovered that it accurately captured the ground state and time evolution forboth. Contd...

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14. A series of new recent algorithms covering core areas of machine learning (supervised, unsupervised, and reinforcement learning), as well as other quantum-classicaldata and algorithms (QQ, QC, CQ models), is still to bedone. Scaling up the algorithms to the limits of actual hardware while doing an effective scaling study of performances and corresponding errors isimportant. Finally, one should determine if a quantum speedup using quantum machine learning models operating on NISQ machines is technically and experimentally feasible.

15. FUTURESCOPE In the case of quantum algorithms for linear algebra, where robust guarantees are already possible, data access issues and limitations on the types of problems that can be solved can impede their success inpractice. Indeed, developments in quantum hardware growth in the coming future would be critical for empirically assessing the true potential of these techniques. It's worth noting that the bulk of the QML literature has come from within the quantumculture. Contd...

16. Further advancements in the area are expected to arrive only after major contacts between the twocultures. The interdisciplinary field of mixing machine learning and quantum physics is increasingly expanding, with promisingresults. The points raised above are just the tip of theiceberg.

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