Controlled quantum operations and combs, and their applications to universal controllization of divisible unitary operations
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Abstract
Unitary operations are a fundamental component of quantum algorithms, but they seem to be far more useful if given with a "quantum control" as a controlled unitary operation. However, quantum operations are not limited to unitary operations. Nevertheless, it is not a priori clear if a controlled form of these general deterministic quantum operations can be well-defined. This paper proposes a mathematically consistent definition of a controlled form of general deterministic quantum operations and, more generally, of quantum combs for utilizing controlled quantum operations and combs in quantum computation. We propose a "neutralization" comb, which transforms a set of input quantum operations to the identity operation, and study its controlled form based on our definition. We propose two new quantum algorithms for universal controllization of divisible unitary operations utilizing the most coherently controlled neutralization combs.