Il corso introduce i concetti alla base della computazione quantistica attraverso lo studio dei fenomeni fisici che caratterizzano questo paradigma rispetto a quello classico.
Si articola in tre parti principali: lo studio del modello circuitale quantistico e della sua universalità, lo studio delle più importanti tecniche quantistiche per la progettazione di algoritmi e la loro analisi,
e l'introduzione di alcuni linguaggi di programmazione quantistica e di alcune piattaforme software per la specifica di computazioni quantistiche.
Si articola in tre parti principali: lo studio del modello circuitale quantistico e della sua universalità, lo studio delle più importanti tecniche quantistiche per la progettazione di algoritmi e la loro analisi,
e l'introduzione di alcuni linguaggi di programmazione quantistica e di alcune piattaforme software per la specifica di computazioni quantistiche.
Curriculum
scheda docente
materiale didattico
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.
Programma
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.
Testi Adottati
Richard J. Lipton, Kenneth W. Regan Introduction to Quantum Algorithms via Linear Algebra, Second Edition, ISBN 9780262045254, (2021), MIT Press;Bibliografia Di Riferimento
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).Modalità Erogazione
Lezione Frontale.Modalità Frequenza
Facoltativa.Modalità Valutazione
L'esame consiste consiste di due parti: [-] di un esame scritto, sostituibile con attività seminariali di presentazione degli argomenti studiati. [-] Una prova orale è a completamento del voto ottenuto allo scritto.
scheda docente
materiale didattico
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.
Mutuazione: 20410773 IN570 – QUANTUM COMPUTING in Scienze Computazionali LM-40 PEDICINI MARCO
Programma
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.
Testi Adottati
Richard J. Lipton, Kenneth W. Regan Introduction to Quantum Algorithms via Linear Algebra, Second Edition, ISBN 9780262045254, (2021), MIT Press;Bibliografia Di Riferimento
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).Modalità Erogazione
Lezione Frontale.Modalità Frequenza
Facoltativa.Modalità Valutazione
L'esame consiste consiste di due parti: [-] di un esame scritto, sostituibile con attività seminariali di presentazione degli argomenti studiati. [-] Una prova orale è a completamento del voto ottenuto allo scritto.
scheda docente
materiale didattico
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.
Programma
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.
Testi Adottati
Richard J. Lipton, Kenneth W. Regan Introduction to Quantum Algorithms via Linear Algebra, Second Edition, ISBN 9780262045254, (2021), MIT Press;Bibliografia Di Riferimento
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).Modalità Erogazione
Lezione Frontale.Modalità Frequenza
Facoltativa.Modalità Valutazione
L'esame consiste consiste di due parti: [-] di un esame scritto, sostituibile con attività seminariali di presentazione degli argomenti studiati. [-] Una prova orale è a completamento del voto ottenuto allo scritto.