Uncomplexity

Uncomplexity is a concept in quantum information theory and computational complexity that denotes the amount of computational resource remaining in a system. It is defined as the difference between the maximum possible circuit complexity for the system and its current circuit complexity. Intuitively, it measures how much further complexity a state or unitary can be driven before reaching a maximal, typical level.

For n qubits, the maximum circuit complexity grows rapidly with n, so the uncomplexity is a large, potentially enormous quantity for a new system and shrinks as the system is evolved by gates or interactions. If a state has not been prepared, its uncomplexity is near the maximum; as gates accumulate and the state becomes more complex, uncomplexity decreases. The concept can be formalized by C_max − C, where C is the current circuit complexity and C_max is an upper bound on the complexity of states or unitaries on n qubits.

Origin and usage: the term was popularized by Scott Aaronson in discussions of quantum complexity and holography. It is used as a resource-theoretic way to think about how much computation remains possible within a given system, and to compare physical processes in quantum computers, scramblers, or black holes.

Applications: in quantum information, uncomplexity provides intuition about the limits of quantum computation and information processing. In theoretical physics, it has been used to discuss the interior structure of black holes and the growth of complexity under chaotic dynamics, framing how computational work can be carried out within a system that has attracted interest in holographic duality.

See also: complexity, quantum complexity, holography, black hole information paradox.