Mio Murao, University of Tokyo, Japan

Unitary operations are a fundamental components of quantum algorithms, but they seem to be far more useful if given with a "quantum control" as a controlled unitary operation. The set of possible quantum operations extend 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, of quantum combs. We propose a "neutralization" comb, 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 universal controllization algorithms for divisible unitary operations. (Reference: Q. Dong, S. Nakayama, A. Soeda, and M. Murao, arXiv:1911.01645).