NLTS Hamiltonians from good quantum codes

TL;DR

This paper proves the NLTS conjecture by linking it to recent discoveries of quantum LDPC codes, demonstrating the existence of Hamiltonians with complex low-energy states.

Contribution

It establishes that certain quantum LDPC codes give rise to NLTS Hamiltonians, confirming the conjecture for these code families.

Findings

Quantum LDPC codes correspond to NLTS Hamiltonians

Confirmed the NLTS conjecture for specific code families

Low-energy states have high quantum circuit complexity

Abstract

The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). We prove this conjecture by showing that the recently discovered families of constant-rate and linear-distance QLDPC codes correspond to NLTS local Hamiltonians.