Lecture 1 - 25 September 2023- TURING MACHINE
Overview on the course content
Elements of classical information theory:
The Turing machine
example: addition of two numbers
The Universal Turing machine
Probabilistic Turing machine
Halting problem
Bibliography
Principles of quantum computation and information, volume 1, Paragraphs 1.1, 1.2, 1.6
Nielsen, and Chuang, Quantum Computation and Information, Paragraphs 3.1
Lecture 2 - 29 September 2023- COMPLEXITY CLASSES AND CIRCUITAL MODEL
Classical computation: set of universal logic gates
Computational complexity
Complexity classes: P, NP, NPC, BPP
Examples of NP problems: traveling salesman problem, factorization, determinant calculation, permanent calculation, simulation of a quantum system
Bibliography
Course notes
Principles of quantum computation and information, volume 1, Paragrafo 1.3,Nielsen, and Chuang, Quantum Computation and Information, Paragraph 3.2
Insight:
The Millennium Prize Problems | Clay Mathematics Institute
The circuital model
Set of universal logic gates (AND, OR, NOT, FANOUT)
Bibliography
Principles of quantum computation and information, volume 1, Paragraphs 1.1, 1.2, 1.6
Nielsen, and Chuang, Quantum Computation and Information, Paragraph 3.1
"Information is physical" (Landeauer)
Landaeur principle
Maxwell demons paradox
Reversible computation: Toffoli gate
Bibliography
Principles of quantum computation and information, volume 1, Paragrafo 1.5,
Nielsen, Chuang, Pagine 153 e 162, alla fine del capitolo storiografia sul "diavoletto di Maxwell"
"The Physics of forgetting: Landaeur's erasure principle and information theory", M.B. Plenio andV. Vitelli, arXiv:quant-ph/0103108
https://arxiv.org/pdf/quant-ph/0103108.pdf
Lecture 3 - 2 October 2023
Elements of classical information theory:
What is information? How is it quantified?
Shannon entropy
Classical information compression
Shannon noisless coding theorem (simplified proof: typical and atypical sequences)
References:
Course notes
Principles of quantum computation and information, volume 2, Paragraphs 5.7, 5.8
Nielsen, and Chuang, Quantum Computation and Information, Section 11.1
Lecture 4 - 6 Ottobre 2023 -Communication over noisy channels
Communication over noisy channels
Parity check coding: classical linear code
Generator matrix, parity check matrix, syndromes
Example: code [3,1,3], Hamming code [7,4,3]
The Shannon noisy channel coding theorem (proof)
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 7.6,
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 10.4
Introducation to classical cryptography
LETTURA CONSIGLIATA
PAGINE 1-9
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 5.11,
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 11.2
Elementi di crittografia classica
Introduzione storica
Lecture 5 - 9 Octobrer2023 (Dott. Nicolò Spagnolo)
Private key encryption
Public key encryption: RSA protocol
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 4.1
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 12.6.1
APPROFONDIMENTI
Libro: "Codici e segreti" (La storia affascinante dei messaggi cifrati dall'antico Egitto a Internet, Simon Singh, Biblioteca Universale Rizzoli
Protocollo RSA, descrizione tratta da articolo "Basic concepts in quantum computation" (pagine 24-28)
http://xxx.lanl.gov/PS_cache/quant-ph/pdf/0011/0011013v1.pdf
Calcolo delle combinazioni di enigma (file in inglese)
Lecture 6 - 14 October 2023
Pure states of a qubit and multiple qubits
The density operator
Density matrix of a single qubit
Examples two qubits: mixed states, Bell states
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.5
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 2.4
Pure states of a qubit and multiple qubits
The density operator
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 2.4
Lecture 7 - 16 October 2023 (dott. Valeria Cimini)
Measurement on mixed states
Purity of a state
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 2.4
The density operator
Density matrix of a single qubit
Representation by Bloch sphere
Reconstruction of an unknown density matrix - single qubit
Von Neumann equation for density matrices
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Lecture 8 - 20 October 2023
Equazione di Von Neumann per le matrici densità
Misura su stati misti
Purezza di uno stato
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Operatore densità per sistemi composti e matrice densità ridotta
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Matrice densità di un singolo qubit
Rappresentazione mediante sfera di Bloch
Ricostruzione di una matrice densità non nota - singolo qubit
Lecture 9 - 23 October 2023
Density operator for composite systems and reduced density matrix
Definition of entanglement also for mixed states
Examples on: entanglement, reduced density matrix and link between the two concepts
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Lecture 10 - 30 October 2023
Density operator for composite systems and reduced density matrix
Definition of entanglement also for mixed states
Examples on: entanglement, reduced density matrix and link between the two concepts
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Lecture 11 - 3 November 2023
Quantum Teleportation
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.2
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 2.4
Principles of quantum computation and information vol 1, Cap.4, par. 4.2, 4.5
Entanglement swapping
Principles of quantum computation and information, volume 2, Paragrafo 5.6
No-cloning theorem
Estimation of a quantum
Optimal quantum cloning
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 5.6
F. De Martini, F. Sciarrino, Non-linear parametric processes in quantum information, Prog. Quant. Electr. 29, 165 (2005).
Valerio Scarani, Sofyan Iblisdir, Nicolas Gisin, and Antonio Acín, Quantum Cloning, Rev. Mod. Phys. 77, 1225 (2005)
Quantum Cryptography
Protocollo BB84
Referenze
Principles of quantum computation and information vol 1, Cap.2, par.2.5
Principles of quantum computation and information vol 1, Cap.4, par.4.3
Lecture 12 - 6 November 2023
Quantum Cryptography
Protocollo BB84, Ekert 92
Referenze
Principles of quantum computation and information vol 1, Cap.2, par.2.5
Principles of quantum computation and information vol 1, Cap.4, par.4.3
Mutual entropy, conditioned entropy, mutual information
Principles of quantum computation and information, volume 2, Paragrafo 5.11,
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 11.2
Lecture 13 - 10 November 2023
FIRST TEST
Lecture 14 - 13 November 2023
Quantum operations - Kraus representations
Examples of single qubit maps: depolarizing channel, bit flip channel, phase-flip channel
The problem of quantum state decoherence: Schroedinger's cat
Referenze:
John Preskill: Lecture Notes
http://www.theory.caltech.edu/~preskill/ph219/index.html#lecture
Principles of quantum computation and information, volume 2, Paragrafo 5.4, 6.1
Lecture 15 - 17 November 2023
Axiomatic approach to quantum operations
Positive maps and maps that are not completely positive
Entanglement criterion based on partial transpose (Peres-Horodecki)
Application to Werner states
References:
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.2
Review paper on Quantum Entanglement:
Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki
Rev. Mod. Phys. 81, 865 – Published 17 June 2009
Lecture 16 - 20 November 2023
Generalized measures and POVM,
Neumark theorem with proof,
Holevo bound with intuitive proof and finally superdense coding
Principles of quantum computation and information vol 2, Cap.5, par.5.9, 5.10, 5.11.1
Principles of quantum computation and information vol 1, Cap.4, par. 4.4, 4.5
Principles of quantum computation and information vol 2, Cap.5, par. 5.11.1 e 5.11.2
Lecture 17 - 24 November 2023
Quantum cryptography
Protocol BB84, Ekert 91
References
Principles of quantum computation and information vol 1, Cap.2, par.2.5
Principles of quantum computation and information vol 1, Cap.4, par.4.3
Lecture 18- 27 November 202
Experimental implementation:
Single photon sources
Propagation in fibers/free space
Referenze:
Principles of quantum computation and information vol 1, Cap.2, par.2.5
Principles of quantum computation and information vol 1, Cap.4, par.4.3
Approfondimenti:
Nicolas Gisin, Gregoire Ribordy, and Hugo Zbinden, Quantum Cryptography, Rev. Mod. Phys. 74, 145–195 (2002)
Progetto europeo su quantum repeater:
- Quantum cryptography
Entanglement swapping
Quantum memory
-Experimental quantum optics:
Generation of single photon states
Detection of single photon states
Generation of photon pairs
Approfondimenti:
Nicolas Gisin, Gregoire Ribordy, and Hugo Zbinden, Quantum Cryptography, Rev. Mod. Phys. 74, 145–195 (2002)
Lecture 19 - 1 December 2023
Quantum Error Correction:
3 qubit error correcting code (bit flip e phase flip)
Quantum Error Correction:
9 qubit Shor error correcting code
General error correction
Quantum Hamming Bound
Fault-tolerant quantum computing
Principles of quantum computation and information vol 2, Cap.7, par.7.1, 7.2, 7.3, 7.4 (non nei dettagli), 7.4.1, 7.10 (solo 7.10.1 e 7.10.2)
Lecture 20 - 4 December 2023
Quantum parallelism, Deutsch and Deutsch-Jozsa Algorithms
References:
R. Portugal, "Basic Quantum Algorithms", arXiv:2201.10574, pages 28-42
Lecture 21 - 11 December 2023
Grover algorithms
References
Algoritmo di Shor: C. Lavor et al.m arxiv: quant-phys/0303175
-) Benenti, Casati, Strini, Vol. 1, cap. 3.10: 3.10.1, 3.10.2, 3.10.3, 3.11
Lezione 22 - 15 Dicember 2023
Algoritmo di Shor
Quantum Fourier Transform
Referenze:
Appunti del corso
Algoritmo di Shor: C. Lavor et al.m arxiv: quant-phys/0303175
Principles of quantum computation and information, vol 1, Cap.3, par.3.9.1, 3.11
Lecture 23 - 18 Dicembre 2023
SECOND TEST
Lecture 24 - 8 January 2024
Presentations
Lecture 25 - 12 January 2024
------------------------------------------------------------
Lecture 1 - 22 September 2021 - TURING MACHINE AND CIRCUITAL MODEL
Overview on the course content
Lecture 2 - 28 September 2021 - TURING MACHINE AND CIRCUITAL MODEL
Elements of classical information theory:
The Turing machine
example: addition of two numbers
The Universal Turing machine
Probabilistic Turing machine
Bibliography
Principles of quantum computation and information, volume 1, Paragraphs 1.1, 1.2, 1.6
Nielsen, and Chuang, Quantum Computation and Information, Paragraphs 3.1
Halting problem
Classical computation: set of universal logic gates
Computational complexity
Complexity classes: P, NP, NPC, BPP
Examples of NP problems: traveling salesman problem, factorization, determinant calculation, permanent calculation, simulation of a quantum system
Bibliography
Course notes
Principles of quantum computation and information, volume 1, Paragrafo 1.3,Nielsen, and Chuang, Quantum Computation and Information, Paragraph 3.2
Insight:
The Millennium Prize Problems | Clay Mathematics Institute
Lecture 3 - 29 September 2021 - TURING MACHINE AND CIRCUITAL MODEL
The circuital model
Set of universal logic gates (AND, OR, NOT, FANOUT)
Bibliography
Principles of quantum computation and information, volume 1, Paragraphs 1.1, 1.2, 1.6
Nielsen, and Chuang, Quantum Computation and Information, Paragraph 3.1
Lecture 4 - 30 September 2021
"Information is physical" (Landeauer)
Landaeur principle
Maxwell demons paradox
Reversible computation: Toffoli gate
Bibliography
Principles of quantum computation and information, volume 1, Paragrafo 1.5,
Nielsen, Chuang, Pagine 153 e 162, alla fine del capitolo storiografia sul "diavoletto di Maxwell"
"The Physics of forgetting: Landaeur's erasure principle and information theory", M.B. Plenio andV. Vitelli, arXiv:quant-ph/0103108
https://arxiv.org/pdf/quant-ph/0103108.pdf
Lezione 5 - 5 Ottobre 2021
Elementi di teoria dell'informazione classica:
Che cos'è l'informazione ? Come si quantifica?
Entropia Shannon
La compressione dell'informazione classica
Shannon noisless coding theorem (dimostrazione semplificata: sequenze tipiche ed atipiche)
Referenze:
Appunti del corso
Principles of quantum computation and information, volume 2, Paragrafi 5.7, 5.8
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 11.1
Lezione 6 - 6 Ottobre 2021 - Comunicazione su canali rumorosi
Spazi vettoriali discreti: Hamming space, Hamming distance, sottospazi di Hamming
Comunicazione su canali rumorosi
Codificata basata sulla ridondanza del messaggio (esempio del Codice Fiscale)
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 7.6
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 7.6
Lezione 7 - 7 Ottobre 2021 - Comunicazione su canali rumorosi
Comunicazione su canali rumorosi
Parity check coding: classical linear code
Generator matrix, parity check matrix, syndromes
Esempio: codice [3,1,3], codice di Hamming [7,4,3]
The Shannon noisy channel coding theorem (dimostrazione)
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 7.6,
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 10.4
LETTURA CONSIGLIATA
PAGINE 1-9
Entropia mutua, entropia condizionata, informazione mutua
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 5.11,
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 11.2
Elementi di crittografia classica
Introduzione storica
Crittografia con chiave privata
Crittografia con chiave pubblica: protocollo RSA
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 4.1
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 12.6.1
APPROFONDIMENTI
Libro: "Codici e segreti" (La storia affascinante dei messaggi cifrati dall'antico Egitto a Internet, Simon Singh, Biblioteca Universale Rizzoli
Protocollo RSA, descrizione tratta da articolo "Basic concepts in quantum computation" (pagine 24-28)
http://xxx.lanl.gov/PS_cache/quant-ph/pdf/0011/0011013v1.pdf
Calcolo delle combinazioni di enigma (file in inglese)
Lezione 8- 12 Ottobre 2021
Stati puri di un qubit e più qubit
L'operatore densità
Matrice densità di un singolo qubit
Esempi due qubit: stati misti, stati di Bell
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.5
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 2.4
Lezione 9- 14 Ottobre 2021
Stati puri di un qubit e più qubit
Matrice densità di un singolo qubit
Esempi due qubit: stati misti, stati di Bel
L'operatore densità
Matrice densità di un singolo qubit
Rappresentazione mediante sfera di Bloch
Ricostruzione di una matrice densità non nota - singolo qubit
Misura su stati misti
Purezza di uno stato
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 2.4
Lezione 10 - 20 Ottobre 2021
Misura su stati misti
Purezza di uno stato
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Operatore densità per sistemi composti e matrice densità ridotta
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Lezione 11 - 21 Ottobre 2011
Equazione di Von Neumann per le matrici densità
Misura su stati misti
Purezza di uno stato
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Operatore densità per sistemi composti e matrice densità ridotta
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Matrice densità di un singolo qubit
Rappresentazione mediante sfera di Bloch
Ricostruzione di una matrice densità non nota - singolo qubit
Operatore densità per sistemi composti e matrice densità ridotta
Definizione di entanglement anche per stati misti
Esempi su: entanglement, matrice densità ridotta e legame tra i due concetti
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Lezione 12 - 26 Ottobre 2021
Operatori ad un qubit
CNOT gate
Generazione e misura di stati di Bell
Referenze:
Principles of quantum computation and information, volume 1, Paragrafo 3.1, 3.2, 3.3
Principles of quantum computation and information vol 1, Cap.4, par. 4.4, 4.5
Teletrasporto quantistico
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.2
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 2.4
Principles of quantum computation and information vol 1, Cap.4, par. 4.2, 4.5
----
Lezione 13 - 27 Ottobre 2021
- Teletrasporto
- Entanglement swapping
- Definizione di fidelity
Lecture 14 - 28 Ottobre 2021
- Stato W a tre qubit: traccia parziale a uno e due qubit, entropia di Von Neumann, considerazioni sullo stato.
- Prodotto tensore tra operatori
- Esempi su matrici densità e traccia parziale
Referenze:
Benenti, Casati, Strini, Principles of Quantum Computation and Information, vol. 1 Cap. 2, pp. 74-76
Benenti, Casati, Strini, Principles of Quantum Computation and Information, vol. 1 Cap. 3, pp. 208-211
Lezione 15 - 2 Novembre 2021
- Stima di uno stato quantistico
- Optimal quantum cloning
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 5.6
F. De Martini, F. Sciarrino, Non-linear parametric processes in quantum information, Prog. Quant. Electr. 29, 165 (2005).
Valerio Scarani, Sofyan Iblisdir, Nicolas Gisin, and Antonio Acín, Quantum Cloning, Rev. Mod. Phys. 77, 1225 (2005)
(NOTA: Per scaricare gli articoli gratuitamente, é necessario collegarsi attraverso il portale della Sapienza)
Lezione 16 - 3 Novembre 2021
- Decomposizione di Schmidt
Lezione 17 - 4 Novembre 2021
Esonero
Lezione 18 - 9 Novembre 2021
Crittografia quantistica
Protocollo BB84, Ekert 91
Referenze
Principles of quantum computation and information vol 1, Cap.2, par.2.5
Principles of quantum computation and information vol 1, Cap.4, par.4.3
Lezione 19 - 10 Novembre 2021
Crittografia quantistica
Protocollo BB84, Ekert 91
Referenze
Principles of quantum computation and information vol 1, Cap.2, par.2.5
Principles of quantum computation and information vol 1, Cap.4, par.4.3
Lezione 20 - 11 Novembre 2021
Crittografia quantistica
Protocollo BB84, Ekert 91
Implementazione sperimentale:
Sorgenti a singolo fotone
Propagazione in fibre/free space
Referenze:
Principles of quantum computation and information vol 1, Cap.2, par.2.5
Principles of quantum computation and information vol 1, Cap.4, par.4.3
Approfondimenti:
Nicolas Gisin, Gregoire Ribordy, and Hugo Zbinden, Quantum Cryptography, Rev. Mod. Phys. 74, 145–195 (2002)
Progetto europeo su quantum repeater:
- Crittografia quantistica
Ceni al quantum decoy state protocol
Entanglement swapping
Quantum memory
-Ottica quantistica sperimentale:
Generazione di stati a singolo fotone
Rivelazione di stati a singolo fotone
Generazione di coppie di fotoni
Approfondimenti:
Nicolas Gisin, Gregoire Ribordy, and Hugo Zbinden, Quantum Cryptography, Rev. Mod. Phys. 74, 145–195 (2002)
Lezione 21 - 16 Novembre 2021
Operazioni quantistiche - rappresentazioni di Kraus
Esempi di mappa su singolo qubit: depolarizing channel, bit flip channel, phase-flip channel
Il problema della decoerenza di stati quantistica: gatto di Schroedinger
Referenze:
John Preskill: Lecture Notes
http://www.theory.caltech.edu/~preskill/ph219/index.html#lecture
Principles of quantum computation and information, volume 2, Paragrafo 5.4, 6.1
Lezione 22 - 17 Novembre 2021
Approccio assiomatico alle operazioni quantistiche
Mappe positive e mappe non completamente positive
Criterio di entanglement basato sulla trasposta parziale (Peres-Horodecki)
Applicazione agli stati di Werner
Referenze:
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.2
Review paper on Quantum Entanglement:
Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki
Rev. Mod. Phys. 81, 865 – Published 17 June 2009
Lezione 23 - 18 Novembre 2021
Parallelismo quantistico
Quantum Error Correction:
introduzione
Referenze:
Principles of quantum computation and information vol 2, Cap.7, par.7.1, 7.2
Lezione 24 - 23 Novembre 2021
Quantum Error Correction:
3 qubit error correcting code (bit flip e phase flip)
Referenze:
Quantum Error Correction:
9 qubit Shor error correcting code
Correzione errore generico
Quantum Hamming Bound
Fault-tolerant quantum computing
Principles of quantum computation and information vol 2, Cap.7, par.7.1, 7.2, 7.3, 7.4 (non nei dettagli), 7.4.1, 7.10 (solo 7.10.1 e 7.10.2)
Lezione 25 - 23 Novembre 2021
Algoritmo di Deutsch
Algoritmo di Deutsch-Jozsa
Referenze:
Algoritmo di Shor: C. Lavor et al.m arxiv: quant-phys/0303175
-) Benenti, Casati, Strini, Vol. 1, cap. 3.9
-) Benenti, Casati, Strini, Vol. 1, cap. 3.10: 3.10.1
Lezione 26 - 25 Novembre 2021
Algoritmo di Grover
Referenze:
Algoritmo di Shor: C. Lavor et al.m arxiv: quant-phys/0303175
-) Benenti, Casati, Strini, Vol. 1, cap. 3.10: 3.10.1, 3.10.2, 3.10.3, 3.11
Lezione 27 - 30 Novembre 2021
Completamento Algoritmo di Grover
Algoritmo di Shor
Quantum Fourier Transform
Referenze:
Appunti del corso
Algoritmo di Shor: C. Lavor et al.m arxiv: quant-phys/0303175
Principles of quantum computation and information, vol 1, Cap.3, par.3.9.1, 3.11
Algoritmo di Grover
Lezione 28 - 7 Dicembre 2021
Algoritmo di Shor
Quantum Fourier Transform
Referenze:
Appunti del corso
Algoritmo di Shor: C. Lavor et al.m arxiv: quant-phys/0303175
Principles of quantum computation and information, vol 1, Cap.3, par.3.9.1, 3.11
Algoritmo di Grover
Lezione 29 - 9 Dicembre 2021
Articolo EPR
Disuguaglianza di Bell (CHSH)
Referenze:
Appunti del corso
Articolo Einstein-Podolsky-Rosen
Principles of quantum computation and information vol 1, Cap.4, par.4.4, 4.5
Lezione 30 - 14 Dicembre 2021
Disuguaglianza di Bell: CHSH
Disuguaglianze di Bell: realizzazione sperimentali e loophole
detection loophole
locality loophole
Esercitazione su sistemi aperti
Referenze:
Appunti del corso
Articolo su esperimento di Aspect
Articolo su esperimento di Zeilinger
Articolo su esperimento senza fair sampling assumption
Lezione 30 - 15 Dicembre 2021
Implementazione sperimentale della Quantum Information
- Criteri di Di Vincenzo
-Ottica quantistica sperimentale:
Lezione 31 - 16 Dicembre 2021
- Esonero
Lecture 1 - 29 September 2020 - TURING MACHINE AND CIRCUITAL MODEL
Overview on the course content
Elements of classical information theory:
The Turing machine
example: addition of two numbers
The Universal Turing machine
Probabilistic Turing machine
Bibliography
Principles of quantum computation and information, volume 1, Paragraphs 1.1, 1.2, 1.6
Nielsen, and Chuang, Quantum Computation and Information, Paragraphs 3.1
Lecture 2 - 1 October 2020 - COMPUTATIONAL COMPLEXITY
Halting problem
Classical computation: set of universal logic gates
Computational complexity
Complexity classes: P, NP, NPC, BPP
Examples of NP problems: traveling salesman problem, factorization, determinant calculation, permanent calculation, simulation of a quantum system
Bibliography
Course notes
Principles of quantum computation and information, volume 1, Paragrafo 1.3,Nielsen, and Chuang, Quantum Computation and Information, Paragraph 3.2
Insight:
The Millennium Prize Problems | Clay Mathematics Institute
The circuital model
Set of universal logic gates (AND, OR, NOT, FANOUT)
Bibliography
Principles of quantum computation and information, volume 1, Paragraphs 1.1, 1.2, 1.6
Nielsen, and Chuang, Quantum Computation and Information, Paragraph 3.1
Lecture 3 - 6 October 2020 - COMPUTATIONAL COMPLEXITY
"Information is physical" (Landeauer)
Landaeur principle
Maxwell demons paradox
Reversible computation: Toffoli gate
Bibliography
Principles of quantum computation and information, volume 1, Paragrafo 1.5,
Nielsen, Chuang, Pagine 153 e 162, alla fine del capitolo storiografia sul "diavoletto di Maxwell"
"The Physics of forgetting: Landaeur's erasure principle and information theory", M.B. Plenio andV. Vitelli, arXiv:quant-ph/0103108
https://arxiv.org/pdf/quant-ph/0103108.pdf
Lecture 4 - 8 October 2020
What is information? How is it quantified?
Shannon Entropy
The compression of classical information
Shannon noisless coding theorem (simplified proof: typical and atypical sequences)
Bibliography:
Principles of quantum computation and information, volume 2, Paragrafi 5.7, 5.8
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 11.1
https://arxiv.org/pdf/quant-ph/0103108.pdf
Lecture 5 - 13 October 2020
Discrete vector spaces: Hamming space, Hamming distance, Hamming subspaces
Communication on noisy channels
Coded based on message redundancy (example of the Tax Code)
Bibliography
Principles of quantum computation and information, volume 2, Paragrafo 7.6
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 7.6
Wikipedia: Codice Fiscale
Communication on noisy channels
The Shannon noisy channel coding theorem (demonstration)
Parity check coding: classical linear code
Generator matrix, parity check matrix, syndromes
Example: code [3,1,3], Hamming code [7,4,3]
Bibliography
Principles of quantum computation and information, volume 2, Paragrafo 7.6,
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 10.4
Lecture 6 - 15 October 2020
Mutual entropy, conditioned entropy, mutual information
Bibliography
Principles of quantum computation and information, volume 2, Paragrafo 5.11,
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 11.2
Elements of classical cryptography
Historical introduction
Private key encryption
Public key encryption: RSA protocol
Bibliography
Principles of quantum computation and information, volume 1, Paragrafo 4.1
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 12.6.1
Additional references
Libro: "Codici e segreti" (La storia affascinante dei messaggi cifrati dall'antico Egitto a Internet, Simon Singh, Biblioteca Universale Rizzoli
Protocollo RSA, descrizione tratta da articolo "Basic concepts in quantum computation" (pages 24-28)
Lecture 7 - 20 October 2020
Pure states of one qubit and several qubits
Density matrix of a single qubit
Examples two qubits: Bell states
The density operator
Bibliography
Principles of quantum computation and information, volume 1, Paragrafo 3.1
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.5
Nielsen, and Chuang, Quantum Computation and Information, Paragrafo 2.4
Lecture 8 - 22 October 2020
Pure states of one qubit and multiple qubits
Density matrix of a single qubit
Examples two qubits: mixed states, Bell states
The density operator
Properties of the density operator
Density matrix of a single qubit
Mixed state measurement
Purity of a state
Bibliography
Principles of quantum computation and information, volume 1, Paragraph 3.1
Principles of quantum computation and information, volume 2, Paragraph 5.1, 5.1.1, 5.1.2, 5.5
Nielsen, and Chuang, Quantum Computation and Information, Paragraph 2.4
Lecture 9 - 27 October 2020
Von Neumann equation for the density operator.
Density matrix of composite systems
Composition of linear operators in compound Hilbert spaces
Exercises on compound systems
Bibliography
Principles of Quantum Computation and Information, Volume 2, Sez. 5.1, 5.1.1, 5.1.2
1 qubit density matrix tomography
N qubit density matrix tomography
Bibliography
Principles of Quantum Computation and Information, Volume 1, Sez. 3.1.2
Principles of Quantum Computation and Information, Volume 2, Sez. 5.5
Lecture 10 - 29 October 2020
Density matrix of a single qubit
Bloch sphere representation
Reconstruction of an unknown density matrix - single qubit
Density operator for composite systems and reduced density matrix
Definition of entanglement also for mixed states
Bibliography
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Lecture 11 - 3 November 2020
Examples on states, entropies and reduced density matrices
Entangled state of 3 qubits
Entropy of Von Neumann
Density matrix of a single qubit
Bloch sphere representation
Reconstruction of an unknown density matrix - single qubit
Density operator for composite systems and reduced density matrix
Definition of entanglement also for mixed states
Examples on: entanglement, reduced density matrix and link between the two concepts
Purity of a state
References:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Lecture 12 - 5 November 2020
Examples on states, entropies and reduced density matrices
Entangled state of 3 qubits
Entropy of Von Neumann
Density matrix of a single qubit
Bloch sphere representation
Reconstruction of an unknown density matrix - single qubit
Density operator for composite systems and reduced density matrix
Definition of entanglement also for mixed states
Examples on: entanglement, reduced density matrix and link between the two concepts
Purity of a state
References:
Principles of quantum computation and information, volume 1, Paragrafo 3.1.2
Principles of quantum computation and information, volume 2, Paragrafo 5.1, 5.1.1, 5.1.2, 5.5
Lecture 13 - 10 November 2020
Quantum teleportation
References:
Benenti, Casati, Strini, Principles of Quantum Computation and Information, vol. 1 Cap. 3, pp. 208-211
Entanglement swapping
References:
Principles of quantum computation and information, volume 2, Paragrafo 5.6
No-cloning theorem
Lecture 14 - 12 November 2020
One-qubit operators
CNOT gate
Generation and measurement of Bell states
Definition of fidelity
References:
Principles of quantum computation and information, volume 1, Paragraphs 3.1, 3.2, 3.3
Principles of quantum computation and information vol 1, Cap.4, par. 4.4, 4.5
Quantum teleportation: circuital model
References:
Benenti, Casati, Strini, Principles of Quantum Computation and Information, vol. 1 Cap. 3, pp. 208-211
Quantum operations - Kraus representations
Exercices
References:
John Preskill: Lecture Notes
http://www.theory.caltech.edu/~preskill/ph219/index.html#lecture
Principles of quantum computation and information, volume 2, Paragrafo 5.4, 6.1
Lecture 15 - 17 November 2020
Quantum operations - Kraus representations
Examples of map on single qubit: depolarizing channel, bit flip channel
Exercices
References:
John Preskill: Lecture Notes
http://www.theory.caltech.edu/~preskill/ph219/index.html#lecture
Principles of quantum computation and information, volume 2, Paragrafo 5.4, 6.1
Lecture 16 - 19 November 2020
Exercise: generation of W state
Exercise: CCNOT gate and its decomposition in elementary gates
Schmidt decomposition. Schmidt Number and entanglement criterion.
Example of Schmidt decomposition
References:
Principles of quantum computation and information, volume 1, Paragrafo 3.5
Principles of quantum computation and information, volume 2, Paragrafo 5.2