{"title":"Complexity of Gaussian quantum optics with a limited number of non-linearities","authors":"Michael G Jabbour and Leonardo Novo","doi":"10.1088/2058-9565/adf6d4","DOIUrl":null,"url":null,"abstract":"It is well known in quantum optics that any process involving the preparation of a multimode Gaussian state, followed by a Gaussian operation and Gaussian measurements, can be efficiently simulated by classical computers. Here, we provide evidence that computing transition amplitudes of Gaussian processes with a single-layer of non-linearities is hard for classical computers. To this end, we show how an efficient algorithm to solve this problem could be used to efficiently approximate outcome probabilities of a Gaussian boson sampling experiment. We also extend this complexity result to the problem of computing transition probabilities of Gaussian processes with two layers of non-linearities, by developing a Hadamard test for continuous-variable systems that may be of independent interest. Given recent experimental developments in the implementation of photon-photon interactions, our results may inspire new schemes showing quantum computational advantage or algorithmic applications of non-linear quantum optical systems realizable in the near-term.","PeriodicalId":20821,"journal":{"name":"Quantum Science and Technology","volume":"10 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Science and Technology","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/2058-9565/adf6d4","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
It is well known in quantum optics that any process involving the preparation of a multimode Gaussian state, followed by a Gaussian operation and Gaussian measurements, can be efficiently simulated by classical computers. Here, we provide evidence that computing transition amplitudes of Gaussian processes with a single-layer of non-linearities is hard for classical computers. To this end, we show how an efficient algorithm to solve this problem could be used to efficiently approximate outcome probabilities of a Gaussian boson sampling experiment. We also extend this complexity result to the problem of computing transition probabilities of Gaussian processes with two layers of non-linearities, by developing a Hadamard test for continuous-variable systems that may be of independent interest. Given recent experimental developments in the implementation of photon-photon interactions, our results may inspire new schemes showing quantum computational advantage or algorithmic applications of non-linear quantum optical systems realizable in the near-term.
期刊介绍:
Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics.
Quantum Science and Technology is a new multidisciplinary, electronic-only journal, devoted to publishing research of the highest quality and impact covering theoretical and experimental advances in the fundamental science and application of all quantum-enabled technologies.