Quantum information is shaping a new revolution in information processing. Indeed, a series of landmark findings over the last few decades have demonstrated that the unique behaviour of sub-atomic particles or qubits can be exploited to yield unparalleled advantages in security, computing, communication and control. In fact, security protocols such as QKD and the algorithms such as Shor’s factorization theorem accomplish tasks hitherto believed impossible. These suggest that we are at the cusp of a new age in information processing. The developed world is investing huge resources to get ahead in the quantum race. This has resulted in tremendous opportunities in research, birth of new new quantum computing divisions in established companies and spurt of new companies. All of this present a great opportunity to build successful research and technology-based careers in quantum information processing.
Going further from (the Fall25 half-semester course) QUANTIS, QUANTIP will further discuss a broad range of new topics that expose the audience to greater depth and wider applications.
color:blue">QUANTIP will be self-contained and will present all the required preliminaries. Even if you have not taken QUANTIS for credit you will still be able to follow everything presented in QUANTIP and you will have no problem doing and understanding well in QUANTIP even if you did not sit through QUANTIS.
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- Nielsen and Chuang, “Quantum Computing and Quantum Information”
- M. Wilde, “Quantum Information Theory” (https://arxiv.org/abs/1106.1445)
- A Holevo, “Quantum Systems, Channels and Information”
- Masahito Hayashi “Quantum Information Theory”
None. The course will be self-contained. Prior knowledge of QUANTIS NOT necessary.
Similar to QUANTIS, QUANTIP will be contain security protocols, computing algorithms and communication techniques and will therefore be useful for all students irrespective of their major. The course contents will be divided into four modules.
Module A (Basics): The first module will focus on the fundamentals. In QUANTIS, we presented the axioms in the pure state form. In this module, we will enhance our understanding by presenting the density operator formalism. The notions of purification, quantum evolutions will be presented. The next topic of interest will be distance measures which quantify the similarity/dissimilarity of quantum states.
Module B (Computing): The Shor’s integer factorization algorithm is considered as one of the cornerstone of quantum computing. Our goal here is present the Shor’s factorization algorithm. We first describe the quantum computation classes and connect them to the classical models of computation. Analogous to P, NP, NP complete classes, we present the QP, BQP and other computation classes. Towards presenting the Shor’s factorization algorithm, we shall first discuss the quantum Fourier Transform. Followed by this, we discuss both Shor’s factorization and the discrete Logarithm problem.
Module C (Security) : We will describe the main quantum security protocols based on BB84 protocol. Several variants of the BB84 protocol and a thorough analysis of the security It provides and bounds on information leakage will be discussed.
Module D (Communication): The notion of quantum evolution and density operators discussed in Module A will lead us to the ubiquitous problem of decoherence. Quantum states are “fragile” and continually decohere. This is analogous to noise on classical channels. Just as we design classical error correcting codes like Hamming, LDPC and Turbo codes, protecting qubits from decohering entails designing quantum error correction codes (Q-codes). We shall present the different Q-Codes such as stabilizer codes, CSS codes and such. Quantum codes are used in all fields – computing, communication and security. Our next topic will involve communicating classical and quantum information on quantum channels. We shall develop the necessary ideas to discuss ways to communicate classical and quantum information on quantum channels.
Evaluation :
HW and projects (60%), Exam (40%)
