Unlocking the Power of Quantum Algorithms & Cryptography 🔐 | Part 1: Going Beyond Classical Computing

Welcome to 'Quantum Algorithms & Cryptography' course !

This lecture marks the beginning of exploring how to go beyond classical computation using quantum concepts. It starts by addressing questions regarding the EPR matrix and the usefulness of phase shifts in quantum computation. The lecture reviews the Toffoli gate and its ability to simulate classical logic gates and fanout. It poses a question about why this capability does not contradict the no-cloning theorem. The lecture then demonstrates the application of the Hadamard transform on the EPR state, resulting in a different entangled state. It highlights the importance of the Hadamard transform in quantum algorithms. The lecture formally defines what it means to implement a classical function using a quantum circuit, requiring the output state to reflect the evaluation of the classical function on the input. It emphasizes that any valid quantum computation must be reversible. The lecture then reiterates the universality of the NAND gate for classical computation and explains how the Toffoli gate can be used to simulate both the AND and NOT gates, demonstrating its universality for classical computation. It mentions the existence of a reversible variant of the NAND gate (the Toffoli gate) and the importance of reversible computation in quantum computing.
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