Pramod Padmanabhan, Fumihiko Sugino, Diego Trancanelli
Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.
{"title":"Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation","authors":"Pramod Padmanabhan, Fumihiko Sugino, Diego Trancanelli","doi":"10.26421/QIC20.1-2-3","DOIUrl":"https://doi.org/10.26421/QIC20.1-2-3","url":null,"abstract":"Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"6 1","pages":"37-64"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83422691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
XUEXUAN HAO, FENGRONG ZHANGa School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China; State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China; Mine Digitization Engineering Research Center of Ministry of Education of the People’s Republic of China, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China
{"title":"Quantum period finding based on the Bernstein-Vazirani algorithm","authors":"Xuexuan Hao, Fengrong Zhang, Yongzhuang Wei, Yong Zhou","doi":"10.26421/QIC20.1-2-4","DOIUrl":"https://doi.org/10.26421/QIC20.1-2-4","url":null,"abstract":"XUEXUAN HAO, FENGRONG ZHANGa School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China; State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China; Mine Digitization Engineering Research Center of Ministry of Education of the People’s Republic of China, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"14 1","pages":"65-84"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87129491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The contemporary development of Quantum Computers has opened new possibilities for computation improvements, but the limits of Moore’s law validity are starting to show. We analyze here the possibility that miniaturization will continue to be the source of Moore’s law validity in the near future, and our conclusion is that miniaturization is no longer a reliable answer for the future development of computer science, but instead we suggest that lateralization is the correct approach. By lateralization, we mean the use of biology as the correct format for the implementation of ubiquitous computerized systems, a format that might in many circumstances eschew miniaturization as an overly expensive useless advantage whereas in other cases miniaturization might play a key role. Thus, the future of computer science is not towards a miniaturization that goes from the atom-scale (its present application scale) towards the nucleus-scale, but rather in developing more integrated circuits at the micrometer to nanometer scale, so as to better mimic and interact with biological systems. We analyze some ”almost sci-fi” approaches to the development of better computer systems near the Bekenstein bound limit, and unsurprisingly they fail to have any realistic feasibility. Then, we use the difference between the classical vs. quantum version of the Hammerstein-Clifford theorem to explain why biological systems eschewed quantum computation to represent the world but have chosen classical computation instead. Finally, we analyze examples of recent work which indicate future possibilities of integration between computers and biological systems. As a corollary of that choice by the biological systems, we propose that the predicted lateralization-driven evolution in computer science will not be based in quantum computers, but rather in classical computers.
{"title":"Some considerations on quantum computing at sub-atomic scales and its impact in the future of Moore's law","authors":"N. Lori, J. Neves, A. Blin, Victor Alves","doi":"10.26421/QIC20.1-2-1","DOIUrl":"https://doi.org/10.26421/QIC20.1-2-1","url":null,"abstract":"The contemporary development of Quantum Computers has opened new possibilities for computation improvements, but the limits of Moore’s law validity are starting to show. We analyze here the possibility that miniaturization will continue to be the source of Moore’s law validity in the near future, and our conclusion is that miniaturization is no longer a reliable answer for the future development of computer science, but instead we suggest that lateralization is the correct approach. By lateralization, we mean the use of biology as the correct format for the implementation of ubiquitous computerized systems, a format that might in many circumstances eschew miniaturization as an overly expensive useless advantage whereas in other cases miniaturization might play a key role. Thus, the future of computer science is not towards a miniaturization that goes from the atom-scale (its present application scale) towards the nucleus-scale, but rather in developing more integrated circuits at the micrometer to nanometer scale, so as to better mimic and interact with biological systems. We analyze some ”almost sci-fi” approaches to the development of better computer systems near the Bekenstein bound limit, and unsurprisingly they fail to have any realistic feasibility. Then, we use the difference between the classical vs. quantum version of the Hammerstein-Clifford theorem to explain why biological systems eschewed quantum computation to represent the world but have chosen classical computation instead. Finally, we analyze examples of recent work which indicate future possibilities of integration between computers and biological systems. As a corollary of that choice by the biological systems, we propose that the predicted lateralization-driven evolution in computer science will not be based in quantum computers, but rather in classical computers.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"46 1","pages":"1-13"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84635002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by cite{AG17} showing a quantum-inspired interactive protocol ($IP$) for $PreciseBQP$ where the prover is only assumed to be a $PreciseBQP$ machine, and show that the result can be strengthened to show an $IP$ for $NP^{PP}$ with a prover which is only assumed to be an $NP^{PP}$ machine - which was not known before. We also show how the protocol can be used to directly verify $QMA$ computations, thus connecting the sum-check protocol by cite{AAV13} with the result of cite{AG17,LFKN90}. Our results shed light on a quantum-inspired proof for $IP=PSPACE$, as $PreciseQMA$ captures the full $PSPACE$ power.
{"title":"Towards a quantum-inspired proof for IP = PSPACE","authors":"A. Green, Yupan Liu, Guy Kindler","doi":"10.26421/QIC21.5-6-2","DOIUrl":"https://doi.org/10.26421/QIC21.5-6-2","url":null,"abstract":"We explore quantum-inspired interactive proof systems where the prover is limited. Namely, we improve on a result by cite{AG17} showing a quantum-inspired interactive protocol ($IP$) for $PreciseBQP$ where the prover is only assumed to be a $PreciseBQP$ machine, and show that the result can be strengthened to show an $IP$ for $NP^{PP}$ with a prover which is only assumed to be an $NP^{PP}$ machine - which was not known before. We also show how the protocol can be used to directly verify $QMA$ computations, thus connecting the sum-check protocol by cite{AAV13} with the result of cite{AG17,LFKN90}. Our results shed light on a quantum-inspired proof for $IP=PSPACE$, as $PreciseQMA$ captures the full $PSPACE$ power.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"22 1","pages":"377-386"},"PeriodicalIF":0.0,"publicationDate":"2019-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83452536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hongxiang Chen, M. Vasmer, N. P. Breuckmann, Edward Grant
Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure that generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimization. We test the procedure by simulating small quantum codes of four to fifteen qubits showing that our procedure finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, the [[8,3,2]] code, and the [[10,1,2]] code.
{"title":"Automated discovery of logical gates for quantum error correction","authors":"Hongxiang Chen, M. Vasmer, N. P. Breuckmann, Edward Grant","doi":"10.26421/QIC22.11-12-3","DOIUrl":"https://doi.org/10.26421/QIC22.11-12-3","url":null,"abstract":"Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure that generates logical operations given known encoding and correcting procedures. Our technique is to use variational circuits for learning both the logical gates and the physical operations implementing them. This procedure can be implemented on near-term quantum computers via quantum process tomography. It enables automatic discovery of logical gates from analytically designed error correcting codes and can be extended to error correcting codes found by numerical optimization. We test the procedure by simulating small quantum codes of four to fifteen qubits showing that our procedure finds most logical gates known in the current literature. Additionally, it generates logical gates not found in the current literature for the [[5,1,2]] code, the [[6,3,2]] code, the [[8,3,2]] code, and the [[10,1,2]] code.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"1 1","pages":"947-964"},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90311122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Several ways have been proposed in the literature to define a coherence measure based on Tsallis relative entropy. One of them is defined as a distance between a state and a set of incoherent states with Tsallis relative entropy taken as a distance measure. Unfortunately, this measure does not satisfy the required strong monotonicity, but a modification of this coherence has been proposed that does. We introduce three new Tsallis coherence measures coming from a more general definition that also satisfy the strong monotonicity, and compare all five definitions between each other. Using three coherence measures that we discuss, one can also define a discord. Two of these have been used in the literature, and another one is new. We also discuss two correlation measures based on Tsallis relative entropy. We provide explicit expressions for all three discord and two correlation measure on pure states. Lastly, we provide tight upper and lower bounds on two discord and correlations measures on any quantum state, with the condition for equality.
{"title":"Quantum coherence, discord and correlation measures based on Tsallis relative entropy","authors":"Anna Vershynina","doi":"10.26421/QIC20.7-8-2","DOIUrl":"https://doi.org/10.26421/QIC20.7-8-2","url":null,"abstract":"Several ways have been proposed in the literature to define a coherence measure based on Tsallis relative entropy. One of them is defined as a distance between a state and a set of incoherent states with Tsallis relative entropy taken as a distance measure. Unfortunately, this measure does not satisfy the required strong monotonicity, but a modification of this coherence has been proposed that does. We introduce three new Tsallis coherence measures coming from a more general definition that also satisfy the strong monotonicity, and compare all five definitions between each other. Using three coherence measures that we discuss, one can also define a discord. Two of these have been used in the literature, and another one is new. We also discuss two correlation measures based on Tsallis relative entropy. We provide explicit expressions for all three discord and two correlation measure on pure states. Lastly, we provide tight upper and lower bounds on two discord and correlations measures on any quantum state, with the condition for equality.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"48 1","pages":"553-569"},"PeriodicalIF":0.0,"publicationDate":"2019-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83669036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have definite locations. The local Turing machines are shown to be equivalent to the corresponding circuit models and standard models of Turing machines by simulation methods. This work reveals the fundamental connection between tensor-network states and information processing.
{"title":"A local model of quantum Turing machines","authors":"Dongsheng Wang","doi":"10.26421/QIC20.3-4","DOIUrl":"https://doi.org/10.26421/QIC20.3-4","url":null,"abstract":"The model of local Turing machines is introduced, including classical and quantum ones, in the framework of matrix-product states. The locality refers to the fact that at any instance of the computation the heads of a Turing machine have definite locations. The local Turing machines are shown to be equivalent to the corresponding circuit models and standard models of Turing machines by simulation methods. This work reveals the fundamental connection between tensor-network states and information processing.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"11 1","pages":"213-229"},"PeriodicalIF":0.0,"publicationDate":"2019-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88002045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point of view. In particular, a new quantitative measure of an entanglement of the geometrical nature, has been proposed. Using the invented Gram matrix approach, a version of a non-linear purification of mixed states describing the system analysed has been presented.
{"title":"A Gramian approach to entanglement in bipartite finite dimensional systems: the case of pure states","authors":"R. Gielerak, Marek Sawerwain","doi":"10.26421/QIC20.13-14-1","DOIUrl":"https://doi.org/10.26421/QIC20.13-14-1","url":null,"abstract":"It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point of view. In particular, a new quantitative measure of an entanglement of the geometrical nature, has been proposed. Using the invented Gram matrix approach, a version of a non-linear purification of mixed states describing the system analysed has been presented.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"34 1","pages":"1081-1108"},"PeriodicalIF":0.0,"publicationDate":"2019-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81057543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Superunsteerability is a particular kind of spatial quantum correlation that can be observed in a steering scenario in the presence of limited shared randomness. In this work, we define an experimentally measurable quantity in a steering scenario to certify superunsteerability. In the context of certification of randomness with this scenario, we demonstrate that such certification of superunsteerability provides a bound on the amount of genuine randomness generation. On the other hand, superlocality is another kind of spatial quantum correlation that can be observed in a Bell scenario in the presence of limited shared randomness. We identify inequalities to certify superlocality in the Bell scenarios that can be adopted to implement $2$-to-$1$ and $3$-to-$1$ random-access codes. We observe that such certification of superlocality acts as resource for the random-access codes in the presence of limited shared randomness. As a by-product of our certification of superunsteerability and superlocality, we identify a new classification of separable states having quantumness.
{"title":"Certifying quantumness beyond steering and nonlocality and its implications on quantum information processing","authors":"C. Jebarathinam, D. Das","doi":"10.26421/QIC23.5-6-2","DOIUrl":"https://doi.org/10.26421/QIC23.5-6-2","url":null,"abstract":"Superunsteerability is a particular kind of spatial quantum correlation that can be observed in a steering scenario in the presence of limited shared randomness. In this work, we define an experimentally measurable quantity in a steering scenario to certify superunsteerability. In the context of certification of randomness with this scenario, we demonstrate that such certification of superunsteerability provides a bound on the amount of genuine randomness generation. On the other hand, superlocality is another kind of spatial quantum correlation that can be observed in a Bell scenario in the presence of limited shared randomness. We identify inequalities to certify superlocality in the Bell scenarios that can be adopted to implement $2$-to-$1$ and $3$-to-$1$ random-access codes. We observe that such certification of superlocality acts as resource for the random-access codes in the presence of limited shared randomness. As a by-product of our certification of superunsteerability and superlocality, we identify a new classification of separable states having quantumness.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"107 1","pages":"379-401"},"PeriodicalIF":0.0,"publicationDate":"2019-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84958922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A quantum key distribution protocol is proposed that is a variation of BB84 that provides raw key generation from correlations that violate a Bell-type inequality for single qubit systems and not entangled pairs. Additionally, it 1) is state-independent, 2) involves two-way classical communication, and 3) does not require basis matching between the two parties. The Brukner-Taylor-Cheung-Vedral (BTCV) time-like form of the Bell-CHSH inequality [C. Brukner, S. Taylor, S. Cheung, V. Vedral arXiv:quant-ph/0402127] is employed as an eavesdropping check; sequential measurements lead to an inequality identical in form to the Bell-CHSH inequality, which relies only on the measurements performed with no regard for the qubit states. We show that this form manifests naturally from the non-commutativity of observables.
提出了一种量子密钥分发协议，该协议是BB84的一种变体，它从违反单量子比特系统的贝尔不等式的相关性中生成原始密钥，而不是纠缠对。此外，它1)与状态无关，2)涉及双向经典通信，3)不需要双方之间的基础匹配。Bell-CHSH不等式的Brukner-Taylor-Cheung-Vedral (BTCV)类时形式[j]。Brukner, S. Taylor, S. Cheung, V. Vedral [j]: quantum -ph/0402127];顺序测量导致的不等式在形式上与Bell-CHSH不等式相同，后者仅依赖于执行的测量，而不考虑量子位状态。我们从可观察对象的非交换性中证明了这种形式的自然表现。
{"title":"State-independent quantum key distribution with two-way classical communication","authors":"R. P. Sandhir","doi":"10.26421/QIC19.15-16-2","DOIUrl":"https://doi.org/10.26421/QIC19.15-16-2","url":null,"abstract":"A quantum key distribution protocol is proposed that is a variation of BB84 that provides raw key generation from correlations that violate a Bell-type inequality for single qubit systems and not entangled pairs. Additionally, it 1) is state-independent, 2) involves two-way classical communication, and 3) does not require basis matching between the two parties. The Brukner-Taylor-Cheung-Vedral (BTCV) time-like form of the Bell-CHSH inequality [C. Brukner, S. Taylor, S. Cheung, V. Vedral arXiv:quant-ph/0402127] is employed as an eavesdropping check; sequential measurements lead to an inequality identical in form to the Bell-CHSH inequality, which relies only on the measurements performed with no regard for the qubit states. We show that this form manifests naturally from the non-commutativity of observables.","PeriodicalId":20904,"journal":{"name":"Quantum Inf. Comput.","volume":"38 1","pages":"1279-1293"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86246856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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