2-Local Hamiltonian with Low Complexity is QCMA

TL;DR

This paper establishes that the 2-Local Hamiltonian problem with low complexity constraints is QCMA-complete, bridging the gap between known QMA-complete and QCMA-complete problems through complexity reductions.

Contribution

It proves that 2-Local Hamiltonian with Low Complexity is QCMA-complete, combining existing results to identify a new complete problem in quantum complexity theory.

Findings

Proves 2-LH with Low Complexity is QCMA-complete.

Shows all QCMA problems reduce to 2-LH with Low Complexity.

Extends the understanding of complexity classes in quantum Hamiltonian problems.

Abstract

We prove that 2-Local Hamiltonian (2-LH) with Low Complexity problem is QCMA-complete by combining the results from the QMA-completeness[4] of 2-LH and QCMA-completeness of 3-LH with Low Complexity[6]. The idea is straightforward. It has been known that 2-LH is QMA-complete. By putting a low complexity constraint on the input state, we make the problem QCMA. Finally, we use similar arguments as in [4] to show that all QCMA problems can be reduced to our proposed problem.