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1NIT DelhiQuantum Computing in machine learningPresented By :MOH KHALIDRoll No. 192211009M.Tech-CSE (NIT DELHI)MAY - 2021

Content• Introduction• History• Quantum superposition and qubits• Architecture of quantum computer• Why quantum machine learning• Classical computer vs quantum computer• Quantum k-mean, quantum k-median and quantum KNN• Future work• Conclusion• Reference2NIT Delhi

Introduction• Quantum machine learning is the integration of quantumalgorithms within machine learning program.• The quantum machine is a human-made device that follow thelaw of quantum mechanics (Qubits, interference ,superpositionand entanglement) to information processing.• Qubit can be one state, zero state or a combination of two statesat same time known as linear superposition.• Mathematically to represent qubit state we use ket-notation,qubit in state zero is |0>=transpose([1 0]) and qubit in state oneis |1>=transpose([0 1]).• A qubit is represented as a linear superposition of both basisstate simultaneously.3NIT Delhi

History• 1982- Feynman proposed the idea of creating machines based on thelaw of quantum mechanics.• 1985- David Deutsch developed the quantum turing machine,showing that quantum circuits are universal.• 1994- Peter Shor came up with a quantum algorithm to factor verylarge numbers in polynomial time.• 1997- Lov Grover develops a quantum search algorithm with O(√𝑛)complexity.• 2001- A 7 qubit machine was built and programmed to run Shor’salgorithm.• 2015- D-Wave System unveiled their 1152- qubit D-Wave 2xquantum computer.• 2019- Researchers at google that quantum computer had solved aproblem that would overwhelm the supercomputers.

Quantum superposition and Qubits• Superposition is essentially the ability of a quantumsystem to be in multiple state at same time.• Qubits is a quantum generalization of classical bits thetwo basic state of qubits are |0> and |1> whichcorrespondence with the state 0 and 1 respectively ofclassical bits.• If |y>=a|0>+b|1> where a and b are complex coefficientthen the probability of |0> is |a|^2 and probability of |1> is|b|^2 hence |a|^+|b|^2 =1.

Quantum superposition and Qubits…..Fig: Classical vs Quantum bits [3]

Quantum entanglement• Entanglement is the ability of a quantum system toexhibit correlations• In sort quantum entanglement means that multipleparticles are linked together in a way such that themeasurement of one particle’s quantum state determinesthe possible state of other particles.• When this happens, the state of the particles is said to beentangled.• If probability of 1 is p than probability of then for 0 itwill be 1-p.

Architecture of quantum computer8NIT DelhiFig: Architecture of Quantum computer [7]

Classical computer vs quantum computer9NIT DelhiClassical computers use bits. Having twostate 0 and 1.Quantum computers use Qbits.Qubits is a linear combination of basisstates like |0> and |1>Classical computers use logic gates to processbits.Logic gate may not be reversible.Quantum computers use quantum gate toprocess Qbits.Quantum gate operation are reversible.Classical computer slow in compare to quantumcomputer.According to professor Catherine a quantumcomputer is faster then classical computer.

Why Quantum machine learning• There are many problems that need exponential rise incompute processing power and many take very long oralmost impossible to solve with classical computer. e.g.1) finding prime factors of a very very large numbers2) ground state energies of molecules,3) simulating flow dynamics and so on4) Clustering and classification problem for very largerdata pointWE NEED QUANTUM COMPUTING !

Quantum k-meanAlgorithm Quantum K-mean clustering:1. Require: Initial K point and data point2. Ensure: Clusters and their mean3. Output: k cluster4. Repeat5. For all xi do6. Attach to closest one7. End for8. For all K cluster do9. Calculate mean for cluster using Grover’s algorithms10 End for11 Until cluster stabilize11NIT Delhi

Quantum k-medianAlgorithm k-median clustering:1. Input: k value and data point(DP)2. Ensure: median and cluster3. Output: k cluster4. Repeat5. For each data point in DP do6. Attach it to its closest centre7. End for8. For each cluster do9. Compute the median of the cluster and make it its new centre using Grover’salgorithm10. End for11. Until stabilization of clusters12 . Return cluster12NIT Delhi

Quantum-KNNAlgorithm k-median clustering:1. Input: k value and data point(DP)2. Ensure: class and distance3. Output: k-class4. Repeat5. For each data point in DP do6. select k nearest neighbor7. End for8. For each cluster do9. Compute the hamming distance using Lloyd quantum algorithm10. End for11. Until stabilization of clusters12 . Return cluster

Analysis of QML AlgorithmsAlgorithm Time in classicalversionTime in QuantumversionwhyK-mean O(𝑁2) O(NlogN) We apply quantumalgorithm to computemean of differentcluster(Grover’salgorithm)K-median O(𝑁2) O(𝑁3/2) To find median weuse quantumalgorithmKNN O(NlogN) O(√NlogN)

Future workThere are some other quantum machine algorithmwhich provide speedup over classical algorithms. Wewill try to analyse them. Like support vector machineand regression algorithms.15NIT Delhi

Conclusion• Quantum machine learning is not going to solve allthe problems of machine learning but some.• Quantum version of k-means provide exponentialspeedup over classical version and k- medianprovide factor of √N over classical version. AndQuantum KNN is √N speedup.• In quantum machine learning we use quantumalgorithms with machine learning.• It is very advance technology.• Implementation is difficult.

References[1]. T. M. Khan and A. Robles-Kelly, "Machine Learning: Quantum vs Classical," in IEEEAccess, vol. 8, pp. 219275-219294, 2020, doi: 10.1109/ACCESS.2020.3041719.[2] W. O'Quinn and S. Mao, "Quantum Machine Learning: Recent Advances andOutlook," in IEEE Wireless Communications, vol. 27, no. 3, pp. 126-131, June 2020,doi: 10.1109/MWC.001.1900341.[3]https://in.images.search.yahoo.com/yhs/search;_ylt=Awrx5Za_1TxgwMQAKQfnHgx.;_y8lu=Y29sbwMEcG9zAzEEdnRpZAMEc2VjA3BpdnM[4] E. P. DeBenedictis, "A Future with Quantum Machine Learning," in Computer, vol. 51, no. 2,pp. 68-71, February 2018, doi: 10.1109/MC.2018.1451646.17NIT Delhi

[5] D. Zubov, F. Volponi and M. Khosravy, "D-wave quantum computing Ising model: A casestudy for the forecasting of heat waves," 2015 International Conference on Control,Automation and Information Sciences (ICCAIS), Changshu, China, 2015, pp. 149-152, doi:10.1109/ICCAIS.2015.7338651.[6] P. W. Shor, "Algorithms for quantum computation: discrete logarithms and factoring,"Proceedings 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM,USA, 1994, pp. 124-134, doi: 10.1109/SFCS.1994.365700.[7] A. Narayanan, "Quantum computing for beginners," Proceedings of the 1999 Congress onEvolutionary Computation-CEC99 (Cat. No. 99TH8406), Washington, DC, USA, 1999, pp.2231-2238 Vol. 3, doi: 10.1109/CEC.1999.785552.[8] K. Svore, "Keynote addresses: Quantum computing: Revolutionizing computation throughquantum mechanics," 2017 IEEE/ACM International Conference on Computer-Aided Design(ICCAD), Irvine, CA, USA, 2017, pp. 1-2, doi: 10.1109/ICCAD.2017.8203750.

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