Universal Hamiltonians for Exponentially Long Simulation

TL;DR

This paper constructs a universal, local, one-dimensional Hamiltonian capable of simulating any other Hamiltonian's dynamics for exponentially long times, advancing understanding of quantum complexity and holography.

Contribution

It introduces a universal Hamiltonian that can simulate all other Hamiltonians for exponentially long times, linking quantum simulation with complexity and holographic principles.

Findings

Hamiltonian simulates all others up to exponential times

Circuit complexity grows steadily with time

Supports conjecture relating complexity and holography

Abstract

We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a consequence, we show (under plausible computational complexity assumptions) that the circuit complexity of the unitary dynamics under this Hamiltonian grows steadily with time up to an exponential value in system size. This result makes progress on a recent conjecture by Susskind, in the context of the AdS/CFT correspondence, that the time evolution of the thermofield double state of two conformal fields theories with a holographic dual has a circuit complexity increasing linearly in time, up to exponential time.