Quantum Computation vs. Firewalls

TL;DR

This paper reframes the AMPS firewall paradox through the lens of quantum computational complexity, arguing that decoding the Hawking radiation required to realize the AMPS experiment is generically exponentially hard in the black hole's entropy. By analyzing quantum circuit models, error-correcting codes, and various black-hole geometries (including AdS throats), the authors show that the decoding task is unlikely to be feasible within the black hole's lifetime, undermining the operational viability of firewalls as a necessary fix. They connect these computational limits to a broader nonlocality criterion for effective field theory and explore how interior physics might be consistently described without firewalls under a single, possibly nonlocal Hilbert space, e.g., via A=R_B mappings and bulk operator constructions. The work suggests that complexity-theoretic barriers, rather than fundamental conflicts in unitarity, may prevent the AMPS scenario from being realized, with implications for black hole information, EFT validity, and holographic interpretations.

Abstract

In this paper we discuss quantum computational restrictions on the types of thought experiments recently used by Almheiri, Marolf, Polchinski, and Sully to argue against the smoothness of black hole horizons. We argue that the quantum computations required to do these experiments take a time which is exponential in the entropy of the black hole under study, and we show that for a wide variety of black holes this prevents the experiments from being done. We interpret our results as motivating a broader type of non-locality than is usually considered in the context of black hole thought experiments, and claim that once this type of non-locality is allowed there may be no need for firewalls. Our results do not threaten the unitarity of of black hole evaporation or the ability of advanced civilizations to test it.

Figures (6)

• Figure 1: Alice's quantum mechanics, compared to Charlie's. The world inside her horizon is drawn in blue and the time slice she quantizes on is in red. For reference Charlie's world is in yellow, and the overlap is green. We've chosen Charlie's black slice to coincide closely with Alice's near $B$ and $R$.
• Figure 2: What the computer does. The connecting lines at the top and bottom indicate entanglement, and time goes up. The subsystem $H$ goes along for the ride, and after the computation its purification is split between $R$ and $C$ in some complicated way.
• Figure 3: The standard representations of the three gates described in the text, as well as a simple circuit that maps the product basis $|b_1,b_2\rangle$ to a basis each element of which has the two qubits maximally entangled. In the CNOT gate the addition is done at the hollow circle.
• Figure 4: The black hole dynamics for a 7-bit black hole. With each step the subfactor we interpret as the radiation gets larger.
• Figure 5: Quantum error correction. Here $S$ is the system whose state we want to restore, $E$ is the environment it becomes entangled with via the interaction $U_{noise}$, and $A$ is the ancilla it interacts with via $U_{correct}$. At the end the environment is entangled with the ancilla and the system $S$ is in the same quantum state it started in.