Kenneth Goodenough;Sébastian de Bone;Vaishnavi Addala;Stefan Krastanov;Sarah Jansen;Dion Gijswijt;David Elkouss
{"title":"使用图代码的 n 到 k 近程蒸馏协议","authors":"Kenneth Goodenough;Sébastian de Bone;Vaishnavi Addala;Stefan Krastanov;Sarah Jansen;Dion Gijswijt;David Elkouss","doi":"10.1109/JSAC.2024.3380094","DOIUrl":null,"url":null,"abstract":"Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant class of distillation protocols, which distill \n<inline-formula> <tex-math>$n$ </tex-math></inline-formula>\n to \n<inline-formula> <tex-math>$k$ </tex-math></inline-formula>\n end-to-end entangled pairs using bilocal Clifford operations, a single round of communication and a possible final local operation depending on the observed measurement outcomes. In the case of permutationally invariant depolarizing noise on the input states, we find a correspondence between these distillation protocols and graph codes. We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet. This correspondence allows us to investigate use cases for so-called non-trivial measurement syndromes. Furthermore, we detail a recipe to construct the circuit used for the distillation protocol given a graph code. We use this to find circuits of short depth and small number of two-qubit gates. Additionally, we develop a black-box circuit optimization algorithm, and find that both approaches yield comparable circuits. Finally, we investigate the teleportation of encoded states and find protocols which jointly improve the rate and fidelities with respect to prior art.","PeriodicalId":73294,"journal":{"name":"IEEE journal on selected areas in communications : a publication of the IEEE Communications Society","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10479665","citationCount":"0","resultStr":"{\"title\":\"Near-Term n to k Distillation Protocols Using Graph Codes\",\"authors\":\"Kenneth Goodenough;Sébastian de Bone;Vaishnavi Addala;Stefan Krastanov;Sarah Jansen;Dion Gijswijt;David Elkouss\",\"doi\":\"10.1109/JSAC.2024.3380094\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant class of distillation protocols, which distill \\n<inline-formula> <tex-math>$n$ </tex-math></inline-formula>\\n to \\n<inline-formula> <tex-math>$k$ </tex-math></inline-formula>\\n end-to-end entangled pairs using bilocal Clifford operations, a single round of communication and a possible final local operation depending on the observed measurement outcomes. In the case of permutationally invariant depolarizing noise on the input states, we find a correspondence between these distillation protocols and graph codes. We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet. This correspondence allows us to investigate use cases for so-called non-trivial measurement syndromes. Furthermore, we detail a recipe to construct the circuit used for the distillation protocol given a graph code. We use this to find circuits of short depth and small number of two-qubit gates. Additionally, we develop a black-box circuit optimization algorithm, and find that both approaches yield comparable circuits. Finally, we investigate the teleportation of encoded states and find protocols which jointly improve the rate and fidelities with respect to prior art.\",\"PeriodicalId\":73294,\"journal\":{\"name\":\"IEEE journal on selected areas in communications : a publication of the IEEE Communications Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10479665\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IEEE journal on selected areas in communications : a publication of the IEEE Communications Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/10479665/\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE journal on selected areas in communications : a publication of the IEEE Communications Society","FirstCategoryId":"1085","ListUrlMain":"https://ieeexplore.ieee.org/document/10479665/","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Near-Term n to k Distillation Protocols Using Graph Codes
Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant class of distillation protocols, which distill
$n$
to
$k$
end-to-end entangled pairs using bilocal Clifford operations, a single round of communication and a possible final local operation depending on the observed measurement outcomes. In the case of permutationally invariant depolarizing noise on the input states, we find a correspondence between these distillation protocols and graph codes. We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet. This correspondence allows us to investigate use cases for so-called non-trivial measurement syndromes. Furthermore, we detail a recipe to construct the circuit used for the distillation protocol given a graph code. We use this to find circuits of short depth and small number of two-qubit gates. Additionally, we develop a black-box circuit optimization algorithm, and find that both approaches yield comparable circuits. Finally, we investigate the teleportation of encoded states and find protocols which jointly improve the rate and fidelities with respect to prior art.