Seminar "Universally superposing quantum operations toward quantum functional programming" by Prof. Mio Murao (Univ. of Tokyo)
Murao Mio (Professor, Department of Physics, Graduate School of Science, Universty of Tokyo)
Universally superposing quantum operations toward quantum functional programming
Unitary operations are fundamental components of quantum algorithms, but they seem to be far more useful if given with a "quantum control" as a controlled unitary operation, a coherent superposition of two different unitary operations depending on a control qubit. Quantum algorithms can be represented by quantum operations beyond unitary operations. Nevertheless, it is not a priori clear if a controlled form of these general quantum operations can be well-defined. To provide a novel tool in the toolbox for quantum programming, we propose a mathematically consistent definition of a controlled form of deterministic but non-unitary quantum operations and, more generally, quantum supermaps (quantum combs), higher-order transformations for quantum operations. We propose a higher-order transformations called "neutralization", which generates the identity operation to a particular set of input quantum operations, and study its controlled form based on our definition. We show that implementations of the controlled neutralization comb lead to new universal controllization algorithms for divisible unitary operations.
Reference: Q. Dong, S. Nakayama, A. Soeda, and M. Murao, arXiv:1911.01645