QAQC · Quantum algorithms and the foundations of quantum computation

Quantum computing (and, more broadly, quantum information science) is a new area at the frontier of both computer science and physics. The laws of quantum mechanics are profoundly different from conventional physics. Quantum computing studies how to use them for the purposes of computer science and information processing. Quantum computing (and, more broadly, quantum infromation science) has seen tremendous progress in the last 15 years, both on its theoretical side (with Shor's quantum algorithm for factoring and Grover's quantum search algorithm) and experimental side (with small scale prototypes for quantum computers and commercially available systems for quantum cryptography). We plan to address the following questions: - What problems can we solve on a quantum computer (besides factoring and search)? More generally, can we isolate general principles for designing quantum algorithms? - What are the problems that {\em cannot} be solved by a quantum computer? Which of the conventionally hard problems remain hard, even if quantum computers are available? - What are the fundamental properties of quantum states and what insights do they provide for quantum computing? In particular, we plan to study randomness and pseudorandomness in the quantum world.