Circuit lower bounds for low-energy states of quantum code Hamiltonians

💡 Research Summary

The paper addresses a central challenge in quantum complexity theory: proving that low‑energy states of certain local Hamiltonians cannot be generated by shallow quantum circuits. This problem is encapsulated in the No Low‑energy Trivial States (NLTS) conjecture, which, if true, would imply the quantum PCP conjecture by ruling out classical witnesses for QMA‑complete Hamiltonian problems. The authors focus on Hamiltonians derived from quantum error‑correcting codes, specifically stabilizer LDPC (low‑density parity‑check) codes, and establish strong circuit‑depth lower bounds for all states whose energy is at most a constant fraction of the system size.

Main Result (Theorem 1).
For any