CS6846 - Quantum Algorithms and Quantum Complexity (Reading)

Meetings  

• Theme 1 : The Quantum Computing Model - 4 meetings

  • Meeting 01 : Thu, Jan 22, 01:00 pm-02:30 pm - Jayalal

  Introduction. History. Church-Turing Thesis. Quantum vs Probabilistic Algorithms. Qubits, Basic Qubit operations. Single Qubit Gates. X Gate. Matrix formulation. Unitary Property. Reversibility.

  References
  Exercises
  Reading

  Introduction. History. Church-Turing Thesis. Quantum vs Probabilistic Algorithms. Qubits, Basic Qubit operations. Single Qubit Gates. X Gate. Matrix formulation. Unitary Property. Reversibility.
  

  References

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  None

  • Meeting 02 : Thu, Jan 29, 01:00 pm-02:30 pm - Jayalal, Sajin

  Mutiple Qubit Gates. CNOT Gate. No-cloning theorem (statement) and a proof why the obvious would not work. Swap trick. <br> Simulating the classical gates with Quantum gates. Troofili gate. Toffoli gate. <br An example of Quantum Parallelism. <p><br> (TA session by Sajin Koroth) Basic Linear Algebra : Vector spaces, Matrices, Eigen Values.

  References
  Exercises
  Reading

  Mutiple Qubit Gates. CNOT Gate. No-cloning theorem (statement) and a proof why the obvious would not work. Swap trick.
  Simulating the classical gates with Quantum gates. Troofili gate. Toffoli gate.
  
  (TA session by Sajin Koroth) Basic Linear Algebra : Vector spaces, Matrices, Eigen Values.
  

  References

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  None

  • Meeting 03 : Tue, Feb 10, 05:15 pm-06:00 pm - Students

  Linear Algebra Background (Continued).

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  Exercises
  Reading

  Linear Algebra Background (Continued).
  

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  None

  • Meeting 04 : Tue, Feb 17, 06:00 pm-07:30 pm - Students

  Universal Quantum Gates.<br> Leads : Nikhilesh, Pranav, Dikesh.

  References
  Exercises
  Reading

  Universal Quantum Gates.
  Leads : Nikhilesh, Pranav, Dikesh.
  

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• Theme 2 : Quantum Algorithms Toolkit - 7 meetings

  • Meeting 05 : Sat, Feb 21, 10:00 am-11:30 am - Students

  Deutsch's Algorithm. Deutsch-Jozsa Algorithm, Simon's Algorithm.<br> Leads : Kaushik, Parshuram, Vamsi.

  References	Reading Target : Chapter 1.4.1 and 1.4.2 from [NC] and Chapter 6.3,6.4,6.5 from [KLM]
  Exercises
  Reading	Additional References: Chapter 1.4.3 and 1.4.4 from "Quantum Computation and Quantum Information" by Michael A. Nielsen & Isaac L. Chuang. <br> Simon's Algorithm: https://cs.uwaterloo.ca/~watrous/CPSC519/LectureNotes/06.pdf

  Deutsch's Algorithm. Deutsch-Jozsa Algorithm, Simon's Algorithm.
  Leads : Kaushik, Parshuram, Vamsi.
  

  References	:	Reading Target : Chapter 1.4.1 and 1.4.2 from [NC] and Chapter 6.3,6.4,6.5 from [KLM]
  Reading	:	Additional References: Chapter 1.4.3 and 1.4.4 from "Quantum Computation and Quantum Information" by Michael A. Nielsen & Isaac L. Chuang. Simon's Algorithm: https://cs.uwaterloo.ca/~watrous/CPSC519/LectureNotes/06.pdf

  • Meeting 06 : Sat, Feb 28, 09:30 am-11:30 am - Students

  Phase Estimation and Quantum Fourier Transform.<br> Leads : Manoj, Punit, Sagar

  References	<br>Leads : Sagar JP, Punit Khanna, Manoj Kumar<br> Reading plans for this week:<br> Sections specified below are from text book "An Introduction to Quantum Computing" , Kaye, Laflamme, Mosca.<br><br> Topic Division: Topic 1: Section 7.1 - Quantum Phase Estimation and Quantum Fourier Transform : Estimated effort - 1 hour Topic 2: Section 7.1.1 - Error analysis for estimating arbitrary phases : Estimated effort - 2 hours Topic 3: Section 7.1.2 ,7.1.3 - Periodic states and GCD, LCM, Extended Euclidean Algorithm : Estimated effort - 2 hours Overview:<br> In this discussion, we study the problem of quantum phase estimation which leads us naturally to Quantum Fourier Transform. To introduce the idea of phase estimation, we begin by noting how the final hadamard gate in the Deutsch algorithm, Deutsch-jozsa algorithm was used to get the information encoded in the relative phases of a state.<br> Then we show that with high probability , the estimated phase will be a good estimate for the actual phase. We then look at using Quantum Fourier Transform to find the period of periodic states and introduce some elementary number theory and Extended Euclidean algorithm which will be useful for some of the classical reductions that will be discussed later in the course.<br><br> Additional References: Chapters 5.1 and 5.2 of "Quantum Computation and Quantum Complexity" - Nielsen, Chuang<br>
  Exercises
  Reading

  Phase Estimation and Quantum Fourier Transform.
  Leads : Manoj, Punit, Sagar
  

  References

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  Leads : Sagar JP, Punit Khanna, Manoj Kumar Reading plans for this week: Sections specified below are from text book "An Introduction to Quantum Computing" , Kaye, Laflamme, Mosca. Topic Division: Topic 1: Section 7.1 - Quantum Phase Estimation and Quantum Fourier Transform : Estimated effort - 1 hour Topic 2: Section 7.1.1 - Error analysis for estimating arbitrary phases : Estimated effort - 2 hours Topic 3: Section 7.1.2 ,7.1.3 - Periodic states and GCD, LCM, Extended Euclidean Algorithm : Estimated effort - 2 hours Overview: In this discussion, we study the problem of quantum phase estimation which leads us naturally to Quantum Fourier Transform. To introduce the idea of phase estimation, we begin by noting how the final hadamard gate in the Deutsch algorithm, Deutsch-jozsa algorithm was used to get the information encoded in the relative phases of a state. Then we show that with high probability , the estimated phase will be a good estimate for the actual phase. We then look at using Quantum Fourier Transform to find the period of periodic states and introduce some elementary number theory and Extended Euclidean algorithm which will be useful for some of the classical reductions that will be discussed later in the course. Additional References: Chapters 5.1 and 5.2 of "Quantum Computation and Quantum Complexity" - Nielsen, Chuang

  • Meeting 07 : Tue, Mar 03, 06:00 pm-07:30 pm - Students

  Eigenvalue estimation, Order Finding, Factoring. <br> Leads : Pratik, Akshay, Deekshit

  References
  Exercises
  Reading

  Eigenvalue estimation, Order Finding, Factoring.
  Leads : Pratik, Akshay, Deekshit
  

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  None

  • Meeting 08 : Tue, Mar 10, 06:00 pm-07:30 pm - Students

  Period Finding, Discrete Logarithms, The Hidden Subgroup Problem. <br> Leads : Rohit, Hemant, Naga.

  References
  Exercises
  Reading

  Period Finding, Discrete Logarithms, The Hidden Subgroup Problem.
  Leads : Rohit, Hemant, Naga.
  

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  • Meeting 09 : Tue, Mar 24, 06:00 pm-07:30 pm - Students

  Quantum Search Algorithm - The Procedure and Geometric Visualizations.<br> Leads : Pankaj, Krishnachaitanya, Rejeesh.

  References
  Exercises
  Reading

  Quantum Search Algorithm - The Procedure and Geometric Visualizations.
  Leads : Pankaj, Krishnachaitanya, Rejeesh.
  

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  • Meeting 10 : Tue, Apr 07, 06:00 pm-07:30 pm - Students

  Quantum Counting, Searching an Unstructured Database. Optimality of the Search Algorithm<br> Leads : Pramod, Jitendra, Ajay.

  References
  Exercises
  Reading

  Quantum Counting, Searching an Unstructured Database. Optimality of the Search Algorithm
  Leads : Pramod, Jitendra, Ajay.
  

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  • Meeting 11 : Tue, Apr 14, 06:00 pm-07:30 pm - Students

  <a href="http://homepages.cwi.nl/~rdewolf/qcnotes.pdf">Quantum Walks</a><br> Leads : Ameya, Samir, Aditi

  References
  Exercises
  Reading

  Quantum Walks
  Leads : Ameya, Samir, Aditi
  

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• Theme 3 : Quantum Complexity Theory & Lower Bounds - 2 meetings

  • Meeting 12 : Tue, Apr 21, 06:00 pm-07:30 pm - Students

  <a href="http://homepages.cwi.nl/~rdewolf/qcnotes.pdf">Query Lower Bounds</a><br><br> Leads : Mitali, Kartik, Tejaswini

  References
  Exercises
  Reading

  Query Lower Bounds
  
  Leads : Mitali, Kartik, Tejaswini
  

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  • Meeting 13 : Tue, Apr 28, 06:00 pm-07:30 pm - Students

  <a href="http://homepages.cwi.nl/~rdewolf/qcnotes.pdf">Quantum Complexity Classes</a>. <br> Discussion Leads : Deekshit Reddy, Ramya T.R., Swetha T.

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  Exercises
  Reading

  Quantum Complexity Classes.
  Discussion Leads : Deekshit Reddy, Ramya T.R., Swetha T.
  

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