{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T12:03:11Z","timestamp":1754481791748},"reference-count":0,"publisher":"Rinton Press","issue":"13&14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"published-print":{"date-parts":[[2015,10]]},"abstract":"<jats:p>Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum $k$-local Hamiltonian up to an absolute error $\\epsilon$. Typically, gadget constructions involve terms with large interaction strengths of order $\\text{poly}(\\epsilon^{-1})$. Here we present a 2-body gadget construction and prove that it approximates a Hamiltonian of interaction strength $\\gamma = O(1)$ up to absolute error $\\epsilon\\ll\\gamma$ using interactions of strength $O(\\epsilon)$ instead of the usual inverse polynomial in $\\epsilon$. A key component in our proof is a new condition for the convergence of the perturbation series, allowing our gadget construction to be applied in parallel on multiple many-body terms. We also discuss how to apply this gadget construction for approximating 3- and $k$-local Hamiltonians. The price we pay for using much weaker interactions is a large overhead in the number of ancillary qubits, and the number of interaction terms per particle, both of which scale as $O(\\text{poly}(\\epsilon^{-1}))$. Our strong-from-weak gadgets have their primary application in complexity theory (QMA hardness of restricted Hamiltonians, a generalized area law counterexample, gap amplification), but could also motivate practical implementations with several weak interactions simulating a much stronger quantum many-body interaction.<\/jats:p>","DOI":"10.26421\/qic15.13-14-7","type":"journal-article","created":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T01:52:57Z","timestamp":1614477177000},"page":"1197-1222","source":"Crossref","is-referenced-by-count":4,"title":["Perturbative gadgets without strong interactions"],"prefix":"10.26421","volume":"15","author":[{"given":"Yudong","family":"Cao","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Nagaj","sequence":"additional","affiliation":[]}],"member":"10955","published-online":{"date-parts":[[2015,10]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T01:53:02Z","timestamp":1614477182000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rintonpress.com\/journals\/doi\/QIC15.13-14-7.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10]]},"references-count":0,"journal-issue":{"issue":"13&14","published-online":{"date-parts":[[2015,10]]},"published-print":{"date-parts":[[2015,10]]}},"URL":"https:\/\/doi.org\/10.26421\/qic15.13-14-7","relation":{},"ISSN":["1533-7146","1533-7146"],"issn-type":[{"value":"1533-7146","type":"print"},{"value":"1533-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10]]}}}