20410773 - IN570 – Quantum Computing

This course introduces basic concepts of quantum computation through the study of those physical phenomena that characterize this paradigm by comparing to the classical one.
The course is divided into three main parts: the study of the quantum circuit model and its universality, the study of the most important quantum techniques for the design of algorithms and their analysis,
and the introduction of quantum programming languages ​​and software platforms for the specification of quantum computations.

Curriculum

teacher profile | teaching materials

Programme

Basic Linear Algebra:
Hilbert Spaces, Products and Tensor Products, Matrices, Complex Spaces and Inner Products, Matrices, Graphs, and Sums Over Paths.
Boolean Functions, Quantum Bits, and Feasibility:
Feasible Boolean Functions, Quantum Representation of Boolean Arguments Quantum Feasibility.
Special Matrices:
Hadamard Matrices, Fourier Matrices, Reversible Computation and Permutation Matrices, Feasible Diagonal Matrices, Reflections. Tricks: Start Vectors, Controlling and Copying Base States, The Copy-Uncompute Trick, Superposition Tricks, Flipping a Switch, Measurement Tricks, Partial Transforms.
Algorithms:
Phil’s Algorithm: Phil Measures Up, Quantum Mazes versus Circuits versus Matrices.
Deutsch’s Algorithm: Superdense Coding and Teleportation.
The Deutsch-Jozsa Algorithm. Simon’s Algorithm. Shor’s Algorithm, Quantum Part of the Algorithm, Analysis of the Quantum Part, Continued Fractions.
FactoringIntegers: Basic Number Theory, Periods Give the Order, Factoring.
Grover’s Algorithm: The binary case, the general case, with k Unknowns, Grover Approximate Counting.
QuantumWalks:
Classical Random Walks, Random Walks and Matrices, Defining Quantum Walks, Interference and Diffusion.

Core Documentation

Richard J. Lipton, Kenneth W. Regan Introduction to Quantum Algorithms via Linear Algebra, Second Edition, ISBN 9780262045254, (2021), MIT Press;

Reference Bibliography

Mika Hirvensalo Quantum Computing ISBN: 978-3-540-40704-1, 2nd edition, Springer-Verlag, (2004). Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information ISBN: 9781107002173, Cambridge University Press (2010). Eleanor G. Rieffel, Wolfgang H. Polak Quantum Computing: A Gentle Introduction (10th Anniversary Edition) ISBN: 9780262526678, MIT Press, (2014). Zdzislaw Meglicki Quantum Computing Without Magic: Devices ISBN:9780262288187, MIT Press (2008). Song Y. Yan, Quantum Computational Number Theory ISBN:978-3-319-25821-8, Springer-Verlag (2015).

Type of delivery of the course

Lectures

Attendance

Optional.

Type of evaluation

The exam consists of two parts: [-] a written exam, which can be replaced with seminar activities presenting some of the studied topics. [-] an oral exam completes the exam.

teacher profile | teaching materials

Mutuazione: 20410773 IN570 – QUANTUM COMPUTING in Scienze Computazionali LM-40 PEDICINI MARCO

Programme

Basic Linear Algebra:
Hilbert Spaces, Products and Tensor Products, Matrices, Complex Spaces and Inner Products, Matrices, Graphs, and Sums Over Paths.
Boolean Functions, Quantum Bits, and Feasibility:
Feasible Boolean Functions, Quantum Representation of Boolean Arguments Quantum Feasibility.
Special Matrices:
Hadamard Matrices, Fourier Matrices, Reversible Computation and Permutation Matrices, Feasible Diagonal Matrices, Reflections. Tricks: Start Vectors, Controlling and Copying Base States, The Copy-Uncompute Trick, Superposition Tricks, Flipping a Switch, Measurement Tricks, Partial Transforms.
Algorithms:
Phil’s Algorithm: Phil Measures Up, Quantum Mazes versus Circuits versus Matrices.
Deutsch’s Algorithm: Superdense Coding and Teleportation.
The Deutsch-Jozsa Algorithm. Simon’s Algorithm. Shor’s Algorithm, Quantum Part of the Algorithm, Analysis of the Quantum Part, Continued Fractions.
FactoringIntegers: Basic Number Theory, Periods Give the Order, Factoring.
Grover’s Algorithm: The binary case, the general case, with k Unknowns, Grover Approximate Counting.
QuantumWalks:
Classical Random Walks, Random Walks and Matrices, Defining Quantum Walks, Interference and Diffusion.

Core Documentation

Richard J. Lipton, Kenneth W. Regan Introduction to Quantum Algorithms via Linear Algebra, Second Edition, ISBN 9780262045254, (2021), MIT Press;

Reference Bibliography

Mika Hirvensalo Quantum Computing ISBN: 978-3-540-40704-1, 2nd edition, Springer-Verlag, (2004). Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information ISBN: 9781107002173, Cambridge University Press (2010). Eleanor G. Rieffel, Wolfgang H. Polak Quantum Computing: A Gentle Introduction (10th Anniversary Edition) ISBN: 9780262526678, MIT Press, (2014). Zdzislaw Meglicki Quantum Computing Without Magic: Devices ISBN:9780262288187, MIT Press (2008). Song Y. Yan, Quantum Computational Number Theory ISBN:978-3-319-25821-8, Springer-Verlag (2015).

Type of delivery of the course

Lectures

Attendance

Optional.

Type of evaluation

The exam consists of two parts: [-] a written exam, which can be replaced with seminar activities presenting some of the studied topics. [-] an oral exam completes the exam.

teacher profile | teaching materials

Programme

Basic Linear Algebra:
Hilbert Spaces, Products and Tensor Products, Matrices, Complex Spaces and Inner Products, Matrices, Graphs, and Sums Over Paths.
Boolean Functions, Quantum Bits, and Feasibility:
Feasible Boolean Functions, Quantum Representation of Boolean Arguments Quantum Feasibility.
Special Matrices:
Hadamard Matrices, Fourier Matrices, Reversible Computation and Permutation Matrices, Feasible Diagonal Matrices, Reflections. Tricks: Start Vectors, Controlling and Copying Base States, The Copy-Uncompute Trick, Superposition Tricks, Flipping a Switch, Measurement Tricks, Partial Transforms.
Algorithms:
Phil’s Algorithm: Phil Measures Up, Quantum Mazes versus Circuits versus Matrices.
Deutsch’s Algorithm: Superdense Coding and Teleportation.
The Deutsch-Jozsa Algorithm. Simon’s Algorithm. Shor’s Algorithm, Quantum Part of the Algorithm, Analysis of the Quantum Part, Continued Fractions.
FactoringIntegers: Basic Number Theory, Periods Give the Order, Factoring.
Grover’s Algorithm: The binary case, the general case, with k Unknowns, Grover Approximate Counting.
QuantumWalks:
Classical Random Walks, Random Walks and Matrices, Defining Quantum Walks, Interference and Diffusion.

Core Documentation

Richard J. Lipton, Kenneth W. Regan Introduction to Quantum Algorithms via Linear Algebra, Second Edition, ISBN 9780262045254, (2021), MIT Press;

Reference Bibliography

Mika Hirvensalo Quantum Computing ISBN: 978-3-540-40704-1, 2nd edition, Springer-Verlag, (2004). Michael A. Nielsen, Isaac L. Chuang, Quantum Computation and Quantum Information ISBN: 9781107002173, Cambridge University Press (2010). Eleanor G. Rieffel, Wolfgang H. Polak Quantum Computing: A Gentle Introduction (10th Anniversary Edition) ISBN: 9780262526678, MIT Press, (2014). Zdzislaw Meglicki Quantum Computing Without Magic: Devices ISBN:9780262288187, MIT Press (2008). Song Y. Yan, Quantum Computational Number Theory ISBN:978-3-319-25821-8, Springer-Verlag (2015).

Type of delivery of the course

Lectures

Attendance

Optional.

Type of evaluation

The exam consists of two parts: [-] a written exam, which can be replaced with seminar activities presenting some of the studied topics. [-] an oral exam completes the exam.