Lecture 19, Thurs March 30: RSA and Shor’s Algorithm Today we’ll see Shor’s algorithm. Given a positive integer ​N​, which we’ll assume for simplicity is a product of two primes |​and , this algorithm lets

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• Cryptography
• Mathematics
• Algebra
• Finite fields
• Computational hardness assumptions
• Integer factorization algorithms
• Emerging technologies
• Quantum computing
• RSA
• Euclidean algorithm
• Quantum algorithm
• XTR

Lecture 22, Tues April 11: Grover The next quantum algorithm we’ll cover is… Grover’s Algorithm which was discovered in 1995, shortly after Shor’s algorithm. Both Grover and Shor were working at Bell Labs at the

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• Theoretical computer science
• Computational complexity theory
• Mathematics
• Emerging technologies
• Quantum computing
• Quantum algorithms
• Quantum information science
• Quantum algorithm
• Algorithm
• P versus NP problem
• NP
• PP

Lecture 23, Thurs April 13: BBBV, Applications of Grover It’s great that we can get a quadratic speedup with Grover’s algorithm, but we were able to get an exponential​ speedup with Shor’s algorithm… So why can

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• Theoretical computer science
• Emerging technologies
• Quantum computing
• Computational complexity theory
• Quantum information science
• Computer science
• Quantum algorithm
• Time complexity
• Asymptotically optimal algorithm
• Grover's algorithm
• Quantum algorithm for linear systems of equations

Lecture 21, Thurs April 6: Continued Fractions, Shor Wrap-Up Today we’ll finish Shor’s algorithm and then discuss some of its implications. Last we saw our protagonists, they were in a superposition of the form |​r

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• Cryptography
• Mathematics
• Theoretical computer science
• Computational complexity theory
• Quantum computing
• Group theory
• Emerging technologies
• Quantum algorithm
• Elliptic curve
• Time complexity
• Real number
• NP

Lecture 20, Tues April 4: Shor, Quantum Fourier Transform Last time we started in on Shor’s algorithm, a quantum algorithm that can factor ​N​ into ​p​×​q​ in polynomial time by reducing the problem to per

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• Mathematical analysis
• Mathematics
• Mathematical logic
• Set theory
• Operator theory
• Code
• Inner model theory
• Partial differential equations
• Complex analysis
• Omega-regular language
• Differential forms on a Riemann surface

CSE 599d - Quantum Computing Grover’s Algorithm Dave Bacon Department of Computer Science & Engineering, University of Washington After Peter Shor demonstrated that quantum computers could efficiently factor, great in

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Quantum algorithms (CO 781, WinterProf. Andrew Childs, University of Waterloo LECTURE 3: Quantum attacks on elliptic curve cryptography In the last lecture we discussed Shor’s algorithm, which can calculate disc

Source URL: www.math.uwaterloo.ca

Quantum algorithms (CO 781, WinterProf. Andrew Childs, University of Waterloo LECTURE 2: The HSP and Shor’s algorithm for discrete log In this lecture we will discuss the discrete logarithm problem and its relev

Source URL: www.math.uwaterloo.ca