The Quantum Computing Course covers a topic from foundational concepts to specific implementations and protocols. This allows for structuring a course from basic to advanced levels.
Here is a 60-day course outline including these topics
Week 1 & 2: Foundations of Quantum Computing (Days 1-14)
Day 1-3: Introduction to Quantum Computing
Why Quantum Computing? Potential to solve problems intractable for classical computers and Brief history of quantum computing and also discuss the Quantum computing vs Classical Computing.
- Quantum Computing
- History
- Architecture
- Quantum Computing comparison with classical computing
- Why We need Quantum Computing
- Reversible Computing
Day 4-7: Basics of Quantum Mechanics for QC
Quantum bits (qubits) and their representation using Dirac notation (|0〉 and |1〉). Superposition of basis states. Amplitudes and their significance. Basic suggestions of quantum mechanics. Introduction to Hilbert spaces as the mathematical framework for quantum mechanics. Linear algebra reviews relevant to quantum computing.
- Qubits
- Mathematical Representation
- Physical Implimentations
- Dirac notation
- Quantum Mechanics
- Linear Algebra use in Quantum Computing
- HilbertSpace in Quantum Computing
- Hamiltonian in quantum mechanics
- Bloch Sphere
Day 8-10: Quantum Gates
Introduction to quantum gates as elementary quantum operations. Basic quantum gates: Hadamard, Pauli-X (NOT), Pauli-Y, Pauli-Z, Phase gate. Two-qubit gates: Controlled-NOT (CNOT) gate. Universality of gate sets. Almost any two-input/output quantum gate is universal with single-input rotation gates.
Day 11-12: Quantum Circuits
Construction of quantum circuits using qubits and quantum gates. The process of quantum computation: initialization, applying gates, and measurement. Quantum measurement: Projective measurements. Measurement outcomes and probabilities.
Day 13: Quantum Measurement
Day 14: Quantum Register
Week 3 & 4: Core Quantum Concepts (Days 15-28)
Day 15-16: Superposition and Interference
Day 17-20: Quantum Entanglement
Day 21: Quantum Turing machine
Day 22: No-Cloning Theorem
Day 23: Heisenberg Uncertainty Principle
Day 24-25: Automata
Week 5 & 6: Quantum Algorithms (Days 26-42)
Day 26-42: Introduction to Quantum Algorithms
Deutsch’s algorithm . Introduction to Grover’s database search algorithm. Introduction to Shor’s algorithm for factorization.
- Quantum Algorithms
- The Quantum Fourier Transform (QFT)
- Deutsch-Jozsa Algorithm
- Grover’s Algorithm
- Shor’s Algorithm
- Quantum Walks Algorithm
- HHL Algorithm
- Simon Algorithms
- Quantum Amplitude Amplification (QAA)
- Quantum Amplitude Estimation (QAE)
- Variational Quantum Algorithms (VQAs)
- Variational Quantum Eigensolvers (VQEs) Algorithm
- Variational Quantum Simulation (VQS)
- Quantum Approximate Optimization Algorithm (QAOA)
Week 7 & 8: Quantum Communication, Quantum Error Correction and Cryptography (Days 43-56)
Day 43-45 Quantum Communication
- Quantum Computational Complexity Theory
- Quantum communication complexity in Brief Explanation
- Difference Between Quantum Computational and Communication complexity
Day 46-55: Quantum Cryptography
Introduction to Quantum Cryptography, Quantum Key Distribution (QKD). Potential impact of Shor’s algorithm on modern cryptographic systems. Quantum-safe cryptography.
- Quantum Cryptography
- Quantum Key Distribution (QKD)
- BB84 Protocol
- B92 Protocol
- E91 Protocol
- Superdense Coding protocol
- BBM92 Protocol
- Quantum Secret Sharing
- Quantum Secure Direct Communication (QSDC)
- Quantum Bit Commitment (QBC)
- Quantum Coin Flipping
- Deterministic Secure Quantum Communication (DSQC)
- Quantum Oblivious Transfer (QOT)
- Post Quantum Cryptography
- Heisenberg Uncertainty Principle
Day 53-58: Quantum Error Correction
Week 9: Quantum Hardware and Implementations Day (59-60):
Types of Qubits:
- Superconducting qubits.
- Trapped-ion qubits.
- Photonic qubits.
- Spin qubits.
- Quantum dots.
- Neutral atom quantum computing.
- Nuclear Magnetic Resonance (NMR) in quantum computing.
Week 10: Advanced Topics
- Quantum Simulator
- How Quantum Processors Work
- Fault Tolerant Quantum Computation
- Quantum Threshold Theorem
- Quantum Machine Learning (QML): Introduction to Quantum Machine Learning (QML). Combining quantum computing with machine learning. Quantum algorithms for optimization and learning, Quantum Neural Networks (QNN).
- Quantum Programming Languages
Reference Books
Here is a list of reference books and their authors
- ‘Feynman and Computation’ edited by Anthony J.G. Hey
- ‘The Quantum Universe’ by A.J.G. Hey and P. Walters (CUP, Cambridge 1987)
- Combinatory Logic I by H. B. Curry and R. Feys (North-Holland Publishing, 1958)
- Algebraic Topology by A. Hatcher (Cambridge University Press, 2002)
- Basic Simple Type Theory by R.J. Hindley (Cambridge University Press, 1997)
- Categories for the Working Mathematician (2nd Ed.) by S. Mac Lane (Springer-Verlag, 1997)
- Proofs and Types by J.-Y. Girard, Y. Lafont, and P. Taylor (Cambridge University Press, 1989)
- Quantum computation and quantum information by Michael A. Nielsen and Isaac Chuang
- Integer programming by Michele Conforti, Gérard Cornuéjols, and Giacomo Zambelli (Springer International Publishing, 2014)
- Mathematical methods in quantum mechanics by Gerald Teschl (Graduate Studies in Mathematics, 2009)
- Quantum Computing by J. Gruska (McGraw Hill, 1999)
- Quantum Computation and Quantum Information by M. A. Nielsen and I. L. Chuang (Cambridge University Press, 2000)
- The Haskell 98 Report by S. L. Peyton Jones and J. Hughes (1999)
- Numerical Recipes in C: The Art of Scientific Computing (2nd edn.) by W. H. Press, S. A. Teukolsky, W. T. Vetterling & B. P. Flannery (Cambridge University Press, Cambridge, 1992)
- Quantum Theory: Concepts and Methods by A. Peres (Kluwer Academic Publishers, Dordrecht, 1995)
- Statistical Mechanics by R. P. Feynman (Westview Press, 1998)
- Introduction to Superconductivity by M. Tinkham (Dover Publications, Inc., Mineola, 2004)
- Density matrix renormalization by S. Rommer & S. Östlund (Springer, Berlin, 1999)
- Linear Logic by J.-Y. Girard (Theoretical Computer Science, 50(1), 1987)
- Quantum Computing by J. Gruska (1999)
- Understanding machine learning: From theory to algorithms by S. Shalev-Shwartz and S. Ben-David (Cambridge University Press, 2014)
- Machine Learning with Quantum Computers by M. Schuld and F. Petruccione (Springer, second edition, 2021)
- Quantum Computing: An Applied Approach (1st ed. 2019 ed.) by J. D. Hidary (Springer, 2019)
- Quantum computation and quantum information by Isaac Chuang and Michael A Nielsen (2002)
- Quantum Computation and Quantum Information by M. A. Nielsen and I. L. Chuang (Cambridge Univ. Press, 2000)
- Introduction to Superconductivity (Dover Publications, Inc., Mineola, 2004) by M. Tinkham
- Statistical Mechanics (Westview Press, 1998) by R. P. Feynman
- Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, Dordrecht, 1995) by A. Peres
- Density matrix renormalization (Springer, Berlin, 1999) by S. Rommer & S. Östlund
- Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1992), 2nd edn. by W. H. Press, S. A. Teukolsky, W. T. Vetterling & B. P. Flannery
- Quantum Computation and Quantum Information by M. A. Nielsen and I. L. Chuang
- Numerical Methods for Nonlinear Partial Differential Equations (Springer) by S. Bartels (2015)
- Computational Fluid Dynamics (Cambridge University Press) by T J Chung (2002)
- Mesh Free Methods: Moving Beyond the Finite Element Method (CRC Press) by G R Liu (2003)
- Smoothed particle hydrodynamics (Rep. Prog. Phys.) by J J Monaghan (2005)
- Smoothed particle hydrodynamics and its diverse applications (Annu. Rev. Fluid Mech.) by J J Monaghan (2012)
- Quantum Computation and Quantum Information by Michael A. Nielsen, Isaac L. Chuang (2000)
- Quantum Programming in QCL by Bernhard Ömer (2000)
- The Design and Analysis of Computer Algorithms by Alfred V. Aho, John E. Hopcroft, and Jeffrey D. Ullman (Addison-Wesley, Reading, MA, 1974)
- Quantum Computer Algorithms by Michele Mosca (D.Phil. Dissertation, Wolfson College, University of Oxford, 1999)
- Codes and Cryptography by Dominic Welsh (Oxford University Press, Oxford, 1998)
- Quantum Computing by Philip Kaye, Micale Moza (This source mentions the book but the full title and year might be incomplete based on the context.)
- Linear Logic by J.-Y. Girard (Theoretical Computer Science, 50:1–102, 1987)
- Quantum Computing by J. Gruska (1999)
- Mathematical Methods for Physics and Engineering by K. F. Riley, M. P. Hobson, and S. J. Bence (Cambridge University Press, 1st edition, 1998)
- Quantum computing, Citeseer by J. Gruska (1999)
- Quantum cryptography and secret-key distillation by G. Van Assche (Cambridge University Press, 2006)
- The Codebreakers by David Kahn (Simon and Schuster, 1997)
- The Code Book by Simon Singh (Fourth Estate, 1999)
- Alice in Quantumland: An Allegory of Quantum Physics by Robert Gilmore (Copernicus Books, 1995)
- Introducing Quantum Theory by J. P. McEvoy & Oscar Zarate (Icon Books, 1999)
- Quantum Computation and Quantum Information by M.A. Nielsen and I. L. Chuang (Cambridge University Press, 2000)
- Mathematical methods in quantum mechanics by Gerald Teschl (Graduate Studies in Mathematics, 99, 2009)
- Quantum Theory by A. Peres (1995)
- Introduction to Quantum Computing for Non-Physicists by Eleanor Rieffel, Wolfgang Polak (2000)
- Quantum Information & Computation by S. Beauregard (2003) (This appears to be a journal or conference proceeding but listed here for completeness as the source is slightly ambiguous.)
- Quantum Theory: Concepts and Methods by A. Peres (1995)
- The Principles of Quantum Mechanics by P. A. M. Dirac (Clarendon, Oxford, 1984)
- Synthesis and Optimization of Digital Circuits by G. De Micheli (McGraw-Hill, 1994)
- A Textbook of Quantum Mechanics by P.M. Mathews and K. Venkatesan (Tata McGraw-Hill, 1976)
- The Theory of Groups and Quantum Mechanics by H. Weyl (Dover Publications, 1932)
- Quantum computation and quantum information by Michael A Nielsen (This is likely a reference to the book by Nielsen and Chuang.)
- Solid State Physics by Ashcroft NW, Mermin D (New York: Holt, Rinehardt and Winston, 1976)
- Quantum liquids by Leggett AJ (Oxford: Oxford University Press, 2006)
- Superconductivity by Ginzburg VL, Andryushin EA (Singapore: World Scientific Publishing, 2004)
- Textbook of Drug Design and Discovery by Madsen U, Krogsgaard-Larsen P, Liljefors T (Washington DC: Taylor and Francis, 2002)
- Guidebook on Molecular Modeling in Drug Design by Cohen NC (Boston: Academic Press, 1996)
- The computer as a Physical System: A Microscopic Quantum Mechanical Hamiltonian Model of Computers as Represented by Turing Machines by P. Benioff (Journal of Statistical Physics, 1980)
- Quantum Computation and Quantum Information by M. A. Nielsen and I. L. Chuang (2000)
- An Introduction to Quantum Computing by Philip Kaye, Micale Moza