Anthony Hall with Robert Brown

Studies in Quantum Computing and Chaos

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).  The potential power of quantum algorithms is largely unknown, however.  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.

     A number of classical dynamic maps (e.g. the baker’s transformation, kicked rotator), which are simple in mathematical form, are in fact chaotic systems.  Such systems (which are often intractable classically) exhibit precisely the combination desired for new quantum algorithms.  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.  Establishing correspondences between the quantized and classical dynamics is also likely.