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Taking the Quantum Leap with Machine Learning

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Taking the Quantum Leap with Machine Learning Introduction Quantum Algorithms Current Research Conclusion Taking the Quantum Leap with Machine Learning Zack Barnes University of Washington Bellevue College Mathematics and Physics Colloquium Series [email protected] January 15, 2019 Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion Overview 1 Introduction What is Quantum Computing? What is Machine Learning? Quantum Power in Theory 2 Quantum Algorithms HHL Quantum Recommendation 3 Current Research Quantum Supremacy(?) 4 Conclusion Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion What is Quantum Computing? \Quantum computing focuses on studying the problem of storing, processing and transferring information encoded in quantum mechanical systems.\ [Ciliberto, Carlo et al., 2018] Unit of quantum information is the qubit, or quantum binary integer. Zack Barnes University of Washington UW Quantum Machine Learning Supervised Uses labeled examples to predict future events Unsupervised Not classified or labeled Introduction Quantum Algorithms Current Research Conclusion What is Machine Learning? \Machine learning is the scientific study of algorithms and statistical models that computer systems use to progressively improve their performance on a specific task.\ (Wikipedia) Zack Barnes University of Washington UW Quantum Machine Learning Uses labeled examples to predict future events Unsupervised Not classified or labeled Introduction Quantum Algorithms Current Research Conclusion What is Machine Learning? \Machine learning is the scientific study of algorithms and statistical models that computer systems use to progressively improve their performance on a specific task.\ (Wikipedia) Supervised Zack Barnes University of Washington UW Quantum Machine Learning Unsupervised Not classified or labeled Introduction Quantum Algorithms Current Research Conclusion What is Machine Learning? \Machine learning is the scientific study of algorithms and statistical models that computer systems use to progressively improve their performance on a specific task.\ (Wikipedia) Supervised Uses labeled examples to predict future events Zack Barnes University of Washington UW Quantum Machine Learning Not classified or labeled Introduction Quantum Algorithms Current Research Conclusion What is Machine Learning? \Machine learning is the scientific study of algorithms and statistical models that computer systems use to progressively improve their performance on a specific task.\ (Wikipedia) Supervised Uses labeled examples to predict future events Unsupervised Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion What is Machine Learning? \Machine learning is the scientific study of algorithms and statistical models that computer systems use to progressively improve their performance on a specific task.\ (Wikipedia) Supervised Uses labeled examples to predict future events Unsupervised Not classified or labeled Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion What is Machine Learning? Image Source: MathWorks Zack Barnes University of Washington UW Quantum Machine Learning Q.C. can quickly solve what a C.C. also solves quickly BQP * P There are things Q.C. can do quickly that C.C. can't BQP ⊆ EXP EXP * BQP NP? Introduction Quantum Algorithms Current Research Conclusion Quantum Power in Theory Polynomial Time Hierarchy EXP P ⊆ BQP BQP P Zack Barnes University of Washington UW Quantum Machine Learning BQP * P There are things Q.C. can do quickly that C.C. can't BQP ⊆ EXP EXP * BQP NP? Introduction Quantum Algorithms Current Research Conclusion Quantum Power in Theory Polynomial Time Hierarchy EXP P ⊆ BQP Q.C. can quickly solve what a C.C. also solves BQP quickly P Zack Barnes University of Washington UW Quantum Machine Learning There are things Q.C. can do quickly that C.C. can't BQP ⊆ EXP EXP * BQP NP? Introduction Quantum Algorithms Current Research Conclusion Quantum Power in Theory Polynomial Time Hierarchy EXP P ⊆ BQP Q.C. can quickly solve what a C.C. also solves BQP quickly P BQP * P Zack Barnes University of Washington UW Quantum Machine Learning BQP ⊆ EXP EXP * BQP NP? Introduction Quantum Algorithms Current Research Conclusion Quantum Power in Theory Polynomial Time Hierarchy EXP P ⊆ BQP Q.C. can quickly solve what a C.C. also solves BQP quickly P BQP * P There are things Q.C. can do quickly that C.C. can't Zack Barnes University of Washington UW Quantum Machine Learning EXP * BQP NP? Introduction Quantum Algorithms Current Research Conclusion Quantum Power in Theory Polynomial Time Hierarchy EXP P ⊆ BQP Q.C. can quickly solve what a C.C. also solves BQP quickly P BQP * P There are things Q.C. can do quickly that C.C. can't BQP ⊆ EXP Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion Quantum Power in Theory Polynomial Time Hierarchy EXP P ⊆ BQP Q.C. can quickly solve what a C.C. also solves BQP quickly P BQP * P There are things Q.C. can do quickly that C.C. can't BQP ⊆ EXP EXP * BQP NP? Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion HHL Harrow, Hassidim, Lloyd Algorithm (2008) Given an n × n matrix A and a vector ~b; we must find (or approximately find) the vector ~x such that A~x = ~b: On a classical computer this takes O(nc ); for a constantc: HHL algorithm takes O((log n)2): A common optimization subroutine technique is to minimize (A~x − ~b)2: HHL algorithm gave birth to quantum machine learning. Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion HHL Important Caveats 1 QRAM 2 Apply unitary transformation 3 Matrix must be invertible and well conditioned 4 Solution is given in quantum superposition jxi i \To summarize, HHL is not exactly an algorithm for solving a system of linear equations in logarithmic time... its an algorithm for approximately preparing a quantum superposition of the form ~ jxi i, where ~x is the solution to a linear system A~x = b...\ [Aaronson, 2015]. Zack Barnes University of Washington UW Quantum Machine Learning If the preference matrix is known prior, the solution would be simply to recommend the highest value entry for that user. We must use matrix reconstruction by using samples of the preference matrix to find a good low-rank approximation [Tang, 2018]. Introduction Quantum Algorithms Current Research Conclusion Quantum Recommendation Netflix & Complex Given past purchases or ratings of n products and m users. This data is then given as an m × n preference matrix. Zack Barnes University of Washington UW Quantum Machine Learning We must use matrix reconstruction by using samples of the preference matrix to find a good low-rank approximation [Tang, 2018]. Introduction Quantum Algorithms Current Research Conclusion Quantum Recommendation Netflix & Complex Given past purchases or ratings of n products and m users. This data is then given as an m × n preference matrix. If the preference matrix is known prior, the solution would be simply to recommend the highest value entry for that user. Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion Quantum Recommendation Netflix & Complex Given past purchases or ratings of n products and m users. This data is then given as an m × n preference matrix. If the preference matrix is known prior, the solution would be simply to recommend the highest value entry for that user. We must use matrix reconstruction by using samples of the preference matrix to find a good low-rank approximation [Tang, 2018]. Zack Barnes University of Washington UW Quantum Machine Learning Last year, UW1 Ph.D. candidate, Ewin Tang, developed a classical algorithm inspired by its quantum counterpart that also runs in O(poly(k)polylog(mn))! Introduction Quantum Algorithms Current Research Conclusion Quantum Supremacy(?) Current Research When the quantum recommendation system was given in 2016, the best known classical algorithm was O(poly(mn)); and the quantum algorithm does in O(poly(k)polylog(mn)): 1Go Dawgs Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion Quantum Supremacy(?) Current Research When the quantum recommendation system was given in 2016, the best known classical algorithm was O(poly(mn)); and the quantum algorithm does in O(poly(k)polylog(mn)): Last year, UW1 Ph.D. candidate, Ewin Tang, developed a classical algorithm inspired by its quantum counterpart that also runs in O(poly(k)polylog(mn))! 1Go Dawgs Zack Barnes University of Washington UW Quantum Machine Learning Tang was able to replicate this implicit representation with sampling from a probability distribution and take sub-samples of larger pieces of data. Introduction Quantum Algorithms Current Research Conclusion Quantum Supremacy(?) How? One way is that the algorithm gives a sample of good recommendations instead of complete list. Another source of the quantum speed up was from uses of quantum mechanics (superposition) to represent data implicitly. Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion Quantum Supremacy(?) How? One way is that the algorithm gives a
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