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The 2-local Hamiltonian problem encompasses NP

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Pawel Wocjan, Thomas Beth

Quantum Physics · Submitted 17 Jan 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We extend his result by showing that 2-locality is sufficient in order to encompass NP.

how it is stated · asserted 1.00 read the record →

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arXiv IDquant-ph/0301087 (version 1)
Pith IDTGFR52NY, Pith's permanent record of this paper and its review
CitationPawel Wocjan, Thomas Beth. "The 2-local Hamiltonian problem encompasses NP." arXiv:quant-ph/0301087 (2003). https://pith.science/paper/TGFR52NY
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,850 input tokens.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.61 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We show that the NP complete problems MAX CUT and INDEPENDENT SET can be formulated as the 2-local Hamiltonian problem as defined by Kitaev. He introduced the quantum complexity class BQNP as the quantum analog of NP, and showed that the 5-local Hamiltonian problem is BQNP-complete. It is not known whether the s-local Hamiltonian problem is BQNP-complete for s smaller than 5. Therefore it is interesting to determine what problems can be reduced to the s-local Hamiltonian problem. Kitaev showed that 3-SAT can be formulated as a 3-local Hamiltonian problem. We extend his result by showing that 2-locality is sufficient in order to encompass NP.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We show that the NP complete problems MAX CUT and INDEPENDENT SET can be formulated as the 2-local Hamiltonian problem as defined by Kitaev. result 0.51 0.94 0.51 asserted 1.00
s1 He introduced the quantum complexity class BQNP as the quantum analog of NP, and showed that the 5-local Hamiltonian problem is BQNP-complete. background 1.00 0.04 0.02 asserted 1.00
s2 It is not known whether the s-local Hamiltonian problem is BQNP-complete for s smaller than 5. gap 0.97 0.05 0.02 asserted 0.86
s3 Therefore it is interesting to determine what problems can be reduced to the s-local Hamiltonian problem. gap 0.42 0.05 0.03 asserted 0.65
s4 Kitaev showed that 3-SAT can be formulated as a 3-local Hamiltonian problem. background 1.00 0.03 0.03 asserted 1.00
s5 We extend his result by showing that 2-locality is sufficient in order to encompass NP. result 0.63 0.94 0.95 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We show that the NP complete problems MAX CUT and INDEPENDENT SET can be formulated as the 2-local Hamiltonian problem as defined by Kitaev. He introduced the quantum complexity class BQNP as the quantum analog of NP, and showed that the 5-local Hamiltonian problem is BQNP-complete. It is not known whether the s-local Hamiltonian problem is BQNP-complete for s smaller than 5. Therefore it is interesting to determine what problems can be reduced to the s-local Hamiltonian problem. Kitaev showed that 3-SAT can be formulated as a 3-local Hamiltonian problem. We extend his result by showing that 2-locality is sufficient in order to encompass NP.

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