The parallel evolution of entangled quantum states is at the heart of quantum computation theory; the most renowned results are the exponentially improved efficiencies for finding hidden stabilizer subgroups (the RSA cryptosystem belongs to this class of problems).\u00a0 The potential power of quantum algorithms is largely unknown, however.\u00a0 It is thus of particular interest to find new regimes for quantum algorithms that provide computationally simple problems (since quantum computers are very much in their infancy) with non-trivial solutions.<\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0 A number of classical dynamic maps (e.g. the baker\u2019s transformation, kicked rotator), which are simple in mathematical form, are in fact chaotic systems.\u00a0 Such systems (which are often intractable classically) exhibit precisely the combination desired for new quantum algorithms.\u00a0 We will be seeking classically chaotic mappings which lend themselves to 1) quantum operator representations, 2) simple quantum algorithms to describe the map, with a minimal number of qubits, and 3) exponentially more efficient implementations.\u00a0 Establishing correspondences between the quantized and classical dynamics is also likely.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":" Anthony Hall with Robert BrownStudies in Quantum Computing and Chaos<\/p>\n The parallel evolution of entangled quantum states is at the heart of quantum computation theory; the most renowned results are the exponentially improved efficiencies for finding hidden stabilizer subgroups (the RSA cryptosystem belongs to this class of problems).\u00a0 The potential power of quantum algorithms is largely unknown, however.\u00a0 It is thus of particular interest to find new regimes for quantum algorithms that provide computationally simple problems (since quantum computers are very much in their infancy) with non-trivial solutions.<\/p>\n \u00a0\u00a0\u00a0\u00a0 A number of classical dynamic maps (e.g. the baker\u2019s transformation,<\/p>\n