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Explore the mathematical foundations of quantum computing through this comprehensive graduate summer school program featuring leading experts in quantum computation. Dive deeply into the mathematics relevant for building near-term quantum computers, analyzing their computational power, and understanding their practical applications. Master quantum learning theory fundamentals including strengths and weaknesses of learning functions from quantum examples, and discover how to learn various classes of quantum states. Understand the quantum Fourier transform beyond Shor's algorithm, exploring its broader applications in quantum algorithms. Study quantum information theory including distance measures between states, data processing for quantum relative entropy, and algorithmic aspects of optimal channel coding. Learn quantum and quantum-inspired linear algebra techniques, including quantum singular value transformation (QSVT) and sketching algorithms. Examine quantum query complexity through multiple methodologies including the hybrid method, recording method, and adversary method. Investigate quantum LDPC codes and their role in quantum error correction. Analyze quantum Hamiltonian complexity including stoquastic Hamiltonians and their computational implications. Explore the theory of near-term quantum advantage and understand what makes certain quantum experiments computationally superior to classical approaches. Study topological aspects of quantum codes including the quantum Singleton bound, homology connections, circuit complexity of code states, and transversal gates. Gain insights into verifiable quantum supremacy and quantum error correction principles from renowned researchers including Scott Aaronson and Barbara Terhal. Participate in structured problem sessions designed to develop practical facility with advanced quantum computing concepts across three intensive weeks of study.
