An Introduction to Quantum Gates, Circuits and Algorithms Using Maple Interactive Texts

These Maple interactive texts were developed in order to introduce quantum computing into a capstone cybersecurity course. The target audience for this course is comprised of students that have already taken Calculus III (vector calculus) and/or AP Computer Science A. This course begins with an intensive study of cryptographic protocols, digital signatures, and public key cryptosystems, including all of the following: affine, Hill, Partitioned-Hill, DES, AES, Elgamal, RSA, elliptic curve, and cryptographic hash functions. After this cryptographic introduction, these encryption techniques are applied in order to achieve security for various network and internet protocols. Particularly interesting is the Transport Layer Security (TLS) protocol which in some cases may use several of these, e.g. TLS_ECDHE_RSA_AES_128_GCM_SHA256. Quantum computing is now an emergent technology as evidenced by the research and applications development of such companies as Google, IBM and D-Wave. Hence, quantum computing is both currently intrinsically interesting in itself, and specifically relevant to cybersecurity, as a possible threat to the TLS protocol through the theoretical ability of a large enough quantum computer to factor large integers. Furthermore, on the positive side, quantum cryptography promises secure encryption through quantum key distribution. All of which motivates the timely inclusion of quantum computing into the curriculum of a cybersecurity course. The introduction of quantum gates, circuits and algorithms in these Maple interactive texts follows the development in “Part I: Essential Algorithms” of the excellent book by Richard J. Lipton and Kenneth W. Regan, “Introduction to Quantum Algorithms via Linear Algebra”, (2nd Edition) MIT Press 2021. Since the students in our target audience are familiar with basic linear algebra and programming, but not with the ‘bra’ and ‘ket’ notation of quantum mechanics, this approach using vectors and matrices is especially clear and accessible. For more information, visit us at: http://www.maplesoft.com/products/?ref=youtube