{"title":"Quantum multi-state Swap Test: an algorithm for estimating overlaps of arbitrary number quantum states","authors":"Wen Liu, Yang-Zhi Li, Han-Wen Yin, Zhi-Rao Wang, Jiang Wu","doi":"10.1140/epjqt/s40507-024-00259-5","DOIUrl":null,"url":null,"abstract":"<div><p>Estimating the overlap between two states is an important task with several applications in quantum information. However, the typical swap test circuit can only measure a sole pair of quantum states at a time. In this study, a recursive quantum circuit is designed to measure overlaps of <i>n</i> quantum states <span>\\(\\left | {\\phi _{1} } \\right \\rangle ,\\left | {\\phi _{2} } \\right \\rangle ,\\ldots\\left | {\\phi _{n} }\\right \\rangle \\)</span> concurrently with <span>\\(O(k2^{k})\\)</span> controlled-swap(CSWAP) gates and <span>\\(O(k)\\)</span> ancillary qubits, where <span>\\(k=\\left \\lceil {\\log n} \\right \\rceil \\)</span>. All pairwise overlaps among input quantum states <span>\\(|\\langle \\phi _{i}|\\phi _{j}\\rangle |^{2}\\)</span> can be obtained in this circuit. Compared with existing scheme for measuring the overlap of multiple quantum states, the circuit provides higher precision and less consumption of ancillary qubits. In addition, some simulation experiments are performed on IBM quantum cloud platform to verify the superiority of this algorithm.</p></div>","PeriodicalId":547,"journal":{"name":"EPJ Quantum Technology","volume":"11 1","pages":""},"PeriodicalIF":5.8000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-024-00259-5","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPJ Quantum Technology","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1140/epjqt/s40507-024-00259-5","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
Abstract
Estimating the overlap between two states is an important task with several applications in quantum information. However, the typical swap test circuit can only measure a sole pair of quantum states at a time. In this study, a recursive quantum circuit is designed to measure overlaps of n quantum states \(\left | {\phi _{1} } \right \rangle ,\left | {\phi _{2} } \right \rangle ,\ldots\left | {\phi _{n} }\right \rangle \) concurrently with \(O(k2^{k})\) controlled-swap(CSWAP) gates and \(O(k)\) ancillary qubits, where \(k=\left \lceil {\log n} \right \rceil \). All pairwise overlaps among input quantum states \(|\langle \phi _{i}|\phi _{j}\rangle |^{2}\) can be obtained in this circuit. Compared with existing scheme for measuring the overlap of multiple quantum states, the circuit provides higher precision and less consumption of ancillary qubits. In addition, some simulation experiments are performed on IBM quantum cloud platform to verify the superiority of this algorithm.
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.
EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following:
Quantum measurement, metrology and lithography
Quantum complex systems, networks and cellular automata
Quantum electromechanical systems
Quantum optomechanical systems
Quantum machines, engineering and nanorobotics
Quantum control theory
Quantum information, communication and computation
Quantum thermodynamics
Quantum metamaterials
The effect of Casimir forces on micro- and nano-electromechanical systems
Quantum biology
Quantum sensing
Hybrid quantum systems
Quantum simulations.