# Quantum Complexity and Chaos in Young Black Holes

## TL;DR

This paper explores the complexity of calculating retention times in young black holes, linking it to the difficulty of decoding Hawking radiation and the exponential complexity of the required quantum operations.

## Contribution

It introduces a novel perspective connecting black hole retention times to relative state complexity and demonstrates the decoding challenge involves exponentially complex unitaries.

## Key findings

- Decoding Hawking radiation is computationally very difficult.
- Estimating black hole retention times requires exponentially complex quantum operations.
- The problem relates to the difficulty of implementing fine-tuned future precursor operators.

## Abstract

We argue the problem of calculating retention time scales in young black holes is a problem of relative state complexity. In particular, we suggest that Alice's ability to estimate the time scale for a perturbed black hole to release the extra $n$ qubits comes down to her decoding the Hilbert space of the Hawking radiation. We then demonstrate the decoding task Alice faces is very difficult, and in order to calculate the relative state complexity she would either need to act with an exponentially complex unitary operator or apply an extremely fine-tuned future precursor operator to the perturbed state in $SU(2^{K})$.