The Complexity of Single-Interaction Hamiltonians

arXiv:2609.39592 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Verifier — 33× in this paper · explained in 2 episodes
• Single-Interaction Hamiltonian — 25× in this paper
• Hypergraph — 21× in this paper · explained in 2 episodes
• BQP — 20× in this paper · explained in 2 episodes
• Spectral Gap — 16× in this paper · explained in 5 episodes
• Verification — 16× in this paper · explained in 2 episodes
• Frustration — 13× in this paper · explained in 2 episodes
• Accuracy — 8× in this paper · explained in 1 episode
• Hilbert Space — 7× in this paper · explained in 2 episodes
• BQP-complete — 5× in this paper · explained in 2 episodes
• Degeneracy — 4× in this paper · explained in 3 episodes
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Ancilla Qubits — 2× in this paper · explained in 1 episode
• Consistency — 2× in this paper · explained in 3 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Arbitrary Superpositions — 1× in this paper · explained in 1 episode
• Homogeneity — 1× in this paper · explained in 2 episodes

Sources

• StoqMA vs. MA: the power of error reduction
• The Complexity of Translationally-Invariant Spin Chains with Low Local Dimension
• Efficient Universal Quantum Compilation: An Inverse-free Solovay-Kitaev Algorithm
• Efficient algorithm for a quantum analogue of 2-SAT
• Complexity of the XY antiferromagnet at fixed magnetization
• Quantum Merlin Arthur with Exponentially Small Gap
• The Quantum and Classical Complexity of Translationally Invariant Tiling and Hamiltonian Problems
• Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture
• QMA-complete problems for stoquastic Hamiltonians and Markov matrices
• BQP-complete Problems Concerning Mixing Properties of Classical Random Walks on Sparse Graphs
• The Complexity of the Local Hamiltonian Problem
• Quantum Information Processing with Adversarial Devices
• On the power quantum computation over real Hilbert spaces
• Pinned QMA: The power of fixing a few qubits in proofs
• The complexity of quantum spin systems on a two-dimensional square lattice
• Quantum Max-Cut is NP hard to approximate
• The complexity of antiferromagnetic interactions and 2D lattices
• A 2 rebit gate universal for quantum computing
• The Complexity of Local Stoquastic Hamiltonians on 2D Lattices

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