{"corpus_id":41550628,"paper_sha":"587fc938a22f9169a18827fc3d88f092d224a691","doi":"10.1103/PhysRevA.88.062314","arxiv_id":"1310.0529","pmid":null,"pmcid":null,"mag_id":1965719193,"dblp_id":null,"acl_id":null,"title":"Adiabatic quantum optimization with the wrong Hamiltonian","year":2013,"publication_date":"2013-10-02","venue":"","journal":{"name":"Physical Review A","pages":"062314","volume":"88"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Physics"],"reference_count":23,"citation_count":58,"influential_citation_count":3,"is_open_access":true,"arxiv_categories":["quant-ph"],"arxiv_license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","arxiv_journal_ref":"Phys. Rev. A 88, 062314 (2013)","mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"https://arxiv.org/pdf/1310.0529","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/587fc938a22f9169a18827fc3d88f092d224a691","s2_open_access_license":null,"s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement these Hamiltonians will be imperfect and limited in its precision. Even small perturbations and imprecisions can have profound effects on the nature of the ground state. Here we consider an imperfect implementation of adiabatic quantum optimization and show that, for a widely applicable random control noise model, quantum stabilizer encodings are able to reduce the effective noise magnitude and thus improve the likelihood of a successful computation or simulation. This reduction builds upon two design principles: summation of equivalent logical operators to increase the energy scale of the encoded optimization problem, and the inclusion of a penalty term comprising the sum of the code stabilizer elements. We illustrate our findings with an Ising ladder and show that classical repetition coding drastically increases the probability that the ground state of a perturbed model is decodable to that of the unperturbed model, while using only realistic two-body interaction. Finally, we note that the repetition encoding is a special case of quantum stabilizer encodings, and show that this in principle allows us to generalize our results to many types of analog quantum information processing, albeit at the expense of many-body interactions.","claims":[{"public_id":"cl_5431cb7ce5c573a9a0948aec435a4955","status":"active","text":"Classical repetition coding drastically increases the probability that the ground state of a perturbed Ising ladder model is decodable to that of the unperturbed model using only realistic two-body interactions.","confidence":0.9,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_5431cb7ce5c573a9a0948aec435a4955"},{"public_id":"cl_3a074b473372bb5c9560dd7943cd89c2","status":"active","text":"Quantum stabilizer encodings reduce effective noise magnitude in imperfect adiabatic quantum optimization under a random control noise model.","confidence":0.85,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_3a074b473372bb5c9560dd7943cd89c2"},{"public_id":"cl_db36b474b5c5a35cf4674913b0adba0d","status":"active","text":"Repetition encoding is a special case of quantum stabilizer encodings, allowing generalization to many types of analog quantum information processing at the expense of many-body interactions.","confidence":0.75,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_db36b474b5c5a35cf4674913b0adba0d"},{"public_id":"cl_1ef8c3769a8584805ff866f5a4154343","status":"active","text":"Summation of equivalent logical operators increases the energy scale of the encoded optimization problem, and inclusion of a penalty term comprising the sum of code stabilizer elements improves noise reduction.","confidence":0.8,"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_1ef8c3769a8584805ff866f5a4154343"}],"concepts":[{"public_id":"co_0f8aeec4a05168766c156abe9f54c4ac","status":"active","name":"quantum stabilizer encodings","description":"Error-correcting codes based on stabilizer formalism used to protect quantum information against noise.","types":["method","encoding"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_0f8aeec4a05168766c156abe9f54c4ac"},{"public_id":"co_2529dda5c200a5498eb62cd1ba5550a0","status":"active","name":"repetition encoding","description":"An encoding that repeats logical information to increase robustness, here a special case of quantum stabilizer encodings.","types":["encoding","special case"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_2529dda5c200a5498eb62cd1ba5550a0"},{"public_id":"co_37bc23a16750b733f5b38b2c88e1dfee","status":"active","name":"classical repetition coding","description":"A classical error-correcting code that repeats each bit multiple times to protect against noise.","types":["encoding","method"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_37bc23a16750b733f5b38b2c88e1dfee"},{"public_id":"co_40b206ec3086ffa0482862eb4fbf1877","status":"active","name":"penalty term","description":"An additional Hamiltonian term composed of the sum of code stabilizer elements to penalize errors.","types":["component","technique"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_40b206ec3086ffa0482862eb4fbf1877"},{"public_id":"co_565627ac2c8a01afb12fadc4b575f6ee","status":"active","name":"Ising ladder model","description":"A spin model on a ladder lattice used as an example to illustrate the noise reduction effect.","types":["model","system"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_565627ac2c8a01afb12fadc4b575f6ee"},{"public_id":"co_75ee332d3814191a6cee47c5a7bbe8ba","status":"active","name":"code stabilizer elements","description":"The set of stabilizer operators of a quantum error-correcting code used to detect errors.","types":["element","operator"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_75ee332d3814191a6cee47c5a7bbe8ba"},{"public_id":"co_800e08cb935d361a4b4b17526d1d9845","status":"active","name":"analog quantum information processing","description":"Quantum information processing using continuous Hamiltonian evolution, including adiabatic quantum computation and analog quantum simulation.","types":["paradigm","class"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_800e08cb935d361a4b4b17526d1d9845"},{"public_id":"co_9323713f525a4e1b9520f0ae010d3e6b","status":"active","name":"two-body interactions","description":"Interactions involving only two particles, realistic for experimental implementation.","types":["interaction","property"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_9323713f525a4e1b9520f0ae010d3e6b"},{"public_id":"co_ea6a36facfdbcb9d1fe7ec7abda4d7de","status":"active","name":"random control noise model","description":"A noise model where Hamiltonian perturbations are random and imprecise, representing hardware imperfections.","types":["model","noise model"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_ea6a36facfdbcb9d1fe7ec7abda4d7de"},{"public_id":"co_f17bd97011c3a6bb6821d812158ac0c2","status":"active","name":"summation of equivalent logical operators","description":"Adding together logical operators that produce the same effect to amplify the energy scale of the encoded problem.","types":["design principle","technique"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_f17bd97011c3a6bb6821d812158ac0c2"},{"public_id":"co_f545cd15ed630c51a15084aa26e40c7a","status":"active","name":"adiabatic quantum optimization","description":"A quantum computation approach that slowly evolves a Hamiltonian to find the ground state encoding an optimization problem.","types":["method","paradigm"],"aliases":[],"contributors":[{"id":32,"public_id":"7c402c1b98","public_label":"뀨 (7c402c1b98)","roles":["extraction"],"url":"https://sah.borca.ai/u/7c402c1b98"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_f545cd15ed630c51a15084aa26e40c7a"}],"external_ids":{"DOI":"10.1103/PhysRevA.88.062314","ArXiv":"1310.0529","PubMed":null,"PubMedCentral":null,"MAG":1965719193,"DBLP":null,"ACL":null},"open_access":{"is_open_access":true,"pdf_url":"https://arxiv.org/pdf/1310.0529","landing_url":"https://www.semanticscholar.org/paper/587fc938a22f9169a18827fc3d88f092d224a691","source":"semantic_scholar","pdf_url_source":"semantic_scholar_open_access_pdf","license":null,"status":"GREEN","reason":null},"reference_availability":{"status":"available","references_indexed":true,"full_text_available":true,"full_text_source":"arxiv","count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":1},"paper_id":635908,"paper_uid":"aba345c0-51de-4171-92a8-920048e331d8","canonical_identity":{"paper_id":635908,"paper_uid":"aba345c0-51de-4171-92a8-920048e331d8","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/41550628"}