Pub Date : 2024-07-23DOI: 10.22331/q-2024-07-23-1422
Andi Gu, Hong-Ye Hu, Di Luo, Taylor L. Patti, Nicholas C. Rubin, Susanne F. Yelin
We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing step, can substantially simplify a Hamiltonian for subsequent analysis on quantum hardware. By design, these transformations can be identified and applied efficiently using purely classical resources. In practice, these transformations allow us to shorten requisite physical circuit-depths, overcoming constraints imposed by imperfect near-term hardware. Importantly, the quality of our transformations is $tunable$: we define a 'ladder' of transformations that yields increasingly simple Hamiltonians at the cost of more classical computation. Using quantum chemistry as a benchmark application, we demonstrate that our protocol leads to significant performance improvements for zero and finite temperature free energy calculations on both digital and analog quantum hardware. Specifically, our energy estimates not only outperform traditional Hartree-Fock solutions, but this performance gap also consistently widens as we tune up the quality of our transformations. In short, our quantum information-based approach opens promising new pathways to realizing useful and feasible quantum chemistry algorithms on near-term hardware.
{"title":"Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic","authors":"Andi Gu, Hong-Ye Hu, Di Luo, Taylor L. Patti, Nicholas C. Rubin, Susanne F. Yelin","doi":"10.22331/q-2024-07-23-1422","DOIUrl":"https://doi.org/10.22331/q-2024-07-23-1422","url":null,"abstract":"We introduce a quantum information theory-inspired method to improve the characterization of many-body Hamiltonians on near-term quantum devices. We design a new class of similarity transformations that, when applied as a preprocessing step, can substantially simplify a Hamiltonian for subsequent analysis on quantum hardware. By design, these transformations can be identified and applied efficiently using purely classical resources. In practice, these transformations allow us to shorten requisite physical circuit-depths, overcoming constraints imposed by imperfect near-term hardware. Importantly, the quality of our transformations is $tunable$: we define a 'ladder' of transformations that yields increasingly simple Hamiltonians at the cost of more classical computation. Using quantum chemistry as a benchmark application, we demonstrate that our protocol leads to significant performance improvements for zero and finite temperature free energy calculations on both digital and analog quantum hardware. Specifically, our energy estimates not only outperform traditional Hartree-Fock solutions, but this performance gap also consistently widens as we tune up the quality of our transformations. In short, our quantum information-based approach opens promising new pathways to realizing useful and feasible quantum chemistry algorithms on near-term hardware.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141755073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-22DOI: 10.22331/q-2024-07-22-1421
Zheng An, Chenfeng Cao, Cheng-Qian Xu, D. L. Zhou
Identifying phases of matter presents considerable challenges, particularly within the domain of quantum theory, where the complexity of ground states appears to increase exponentially with system size. Quantum many-body systems exhibit an array of complex entanglement structures spanning distinct phases. Although extensive research has explored the relationship between quantum phase transitions and quantum entanglement, establishing a direct, pragmatic connection between them remains a critical challenge. In this work, we present a novel and efficient quantum phase transition classifier, utilizing disentanglement with reinforcement learning-optimized variational quantum circuits. We demonstrate the effectiveness of this method on quantum phase transitions in the transverse field Ising model (TFIM) and the XXZ model. Moreover, we observe the algorithm's ability to learn the Kramers-Wannier duality pertaining to entanglement structures in the TFIM. Our approach not only identifies phase transitions based on the performance of the disentangling circuits but also exhibits impressive scalability, facilitating its application in larger and more complex quantum systems. This study sheds light on the characterization of quantum phases through the entanglement structures inherent in quantum many-body systems.
{"title":"Learning quantum phases via single-qubit disentanglement","authors":"Zheng An, Chenfeng Cao, Cheng-Qian Xu, D. L. Zhou","doi":"10.22331/q-2024-07-22-1421","DOIUrl":"https://doi.org/10.22331/q-2024-07-22-1421","url":null,"abstract":"Identifying phases of matter presents considerable challenges, particularly within the domain of quantum theory, where the complexity of ground states appears to increase exponentially with system size. Quantum many-body systems exhibit an array of complex entanglement structures spanning distinct phases. Although extensive research has explored the relationship between quantum phase transitions and quantum entanglement, establishing a direct, pragmatic connection between them remains a critical challenge. In this work, we present a novel and efficient quantum phase transition classifier, utilizing disentanglement with reinforcement learning-optimized variational quantum circuits. We demonstrate the effectiveness of this method on quantum phase transitions in the transverse field Ising model (TFIM) and the XXZ model. Moreover, we observe the algorithm's ability to learn the Kramers-Wannier duality pertaining to entanglement structures in the TFIM. Our approach not only identifies phase transitions based on the performance of the disentangling circuits but also exhibits impressive scalability, facilitating its application in larger and more complex quantum systems. This study sheds light on the characterization of quantum phases through the entanglement structures inherent in quantum many-body systems.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-22DOI: 10.22331/q-2024-07-22-1420
Dimiter Ostrev, Davide Orsucci, Francisco Lázaro, Balazs Matuz
Several notions of code products are known in quantum error correction, such as hypergraph products, homological products, lifted products, balanced products, to name a few. In this paper we introduce a new product code construction which is a natural generalization of classical product codes to quantum codes: starting from a set of component Calderbank-Shor-Steane (CSS) codes, a larger CSS code is obtained where both $X$ parity checks and $Z$ parity checks are associated to classical product codes. We deduce several properties of product CSS codes from the properties of the component codes, including bounds to the code distance, and show that built-in redundancies in the parity checks result in so-called meta-checks which can be exploited to correct syndrome read-out errors. We then specialize to the case of single-parity-check (SPC) product codes which in the classical domain are a common choice for constructing product codes. Logical error rate simulations of a SPC $3$-fold product CSS code having parameters $[[512,174,8]]$ are shown under both a maximum likelihood decoder for the erasure channel and belief propagation decoding for depolarizing noise. We compare the results with other codes of comparable length and dimension, including a code from the family of asymptotically good Tanner codes. We observe that our reference product CSS code outperforms all the other examined codes.
{"title":"Classical product code constructions for quantum Calderbank-Shor-Steane codes","authors":"Dimiter Ostrev, Davide Orsucci, Francisco Lázaro, Balazs Matuz","doi":"10.22331/q-2024-07-22-1420","DOIUrl":"https://doi.org/10.22331/q-2024-07-22-1420","url":null,"abstract":"Several notions of code products are known in quantum error correction, such as hypergraph products, homological products, lifted products, balanced products, to name a few. In this paper we introduce a new product code construction which is a natural generalization of classical product codes to quantum codes: starting from a set of component Calderbank-Shor-Steane (CSS) codes, a larger CSS code is obtained where both $X$ parity checks and $Z$ parity checks are associated to classical product codes. We deduce several properties of product CSS codes from the properties of the component codes, including bounds to the code distance, and show that built-in redundancies in the parity checks result in so-called meta-checks which can be exploited to correct syndrome read-out errors. We then specialize to the case of single-parity-check (SPC) product codes which in the classical domain are a common choice for constructing product codes. Logical error rate simulations of a SPC $3$-fold product CSS code having parameters $[[512,174,8]]$ are shown under both a maximum likelihood decoder for the erasure channel and belief propagation decoding for depolarizing noise. We compare the results with other codes of comparable length and dimension, including a code from the family of asymptotically good Tanner codes. We observe that our reference product CSS code outperforms all the other examined codes.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-19DOI: 10.22331/q-2024-07-19-1419
Shubhayan Sarkar
Quantum networks with multiple sources allow the observation of quantum nonlocality without inputs. Consequently, the incompatibility of measurements is not a necessity for observing quantum nonlocality when one has access to multiple quantum sources. Here we investigate the minimal scenario without inputs where one can observe any form of quantum nonlocality. We show that even two parties with two sources that might be classically correlated can witness a form of quantum nonlocality, in particular quantum steering, in networks without inputs if one of the parties is trusted, that is, performs a fixed known measurement. We term this effect as swap-steering. The scenario presented in this work is minimal to observe such an effect. Consequently, a scenario exists where one can observe quantum steering but not Bell non-locality. We further construct a linear witness to observe swap-steering. Interestingly, this witness enables self-testing of the quantum states generated by the sources and the local measurement of the untrusted party. This in turn allows certifying two bits of randomness that can be obtained from the measurement outcomes of the untrusted device without the requirement of initially feeding the device with randomness.
{"title":"Network quantum steering enables randomness certification without seed randomness","authors":"Shubhayan Sarkar","doi":"10.22331/q-2024-07-19-1419","DOIUrl":"https://doi.org/10.22331/q-2024-07-19-1419","url":null,"abstract":"Quantum networks with multiple sources allow the observation of quantum nonlocality without inputs. Consequently, the incompatibility of measurements is not a necessity for observing quantum nonlocality when one has access to multiple quantum sources. Here we investigate the minimal scenario without inputs where one can observe any form of quantum nonlocality. We show that even two parties with two sources that might be classically correlated can witness a form of quantum nonlocality, in particular quantum steering, in networks without inputs if one of the parties is trusted, that is, performs a fixed known measurement. We term this effect as swap-steering. The scenario presented in this work is minimal to observe such an effect. Consequently, a scenario exists where one can observe quantum steering but not Bell non-locality. We further construct a linear witness to observe swap-steering. Interestingly, this witness enables self-testing of the quantum states generated by the sources and the local measurement of the untrusted party. This in turn allows certifying two bits of randomness that can be obtained from the measurement outcomes of the untrusted device without the requirement of initially feeding the device with randomness.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141730696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-18DOI: 10.22331/q-2024-07-18-1417
Naeimeh Mohseni, Junheng Shi, Tim Byrnes, Michael J. Hartmann
Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural networks in learning the dynamics of physical observables is correlated with the scrambling of quantum information. We train a neural network to find a mapping from the parameters of a model to the evolution of observables in random quantum circuits for various regimes of quantum scrambling and test its $generalization$ and $extrapolation$ capabilities in applying it to unseen circuits. Our results show that a particular type of recurrent neural network is extremely powerful in generalizing its predictions within the system size and time window that it has been trained on for both, localized and scrambled regimes. These include regimes where classical learning approaches are known to fail in sampling from a representation of the full wave function. Moreover, the considered neural network succeeds in $extrapolating$ its predictions beyond the time window and system size that it has been trained on for models that show localization, but not in scrambled regimes.
{"title":"Deep learning of many-body observables and quantum information scrambling","authors":"Naeimeh Mohseni, Junheng Shi, Tim Byrnes, Michael J. Hartmann","doi":"10.22331/q-2024-07-18-1417","DOIUrl":"https://doi.org/10.22331/q-2024-07-18-1417","url":null,"abstract":"Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural networks in learning the dynamics of physical observables is correlated with the scrambling of quantum information. We train a neural network to find a mapping from the parameters of a model to the evolution of observables in random quantum circuits for various regimes of quantum scrambling and test its $generalization$ and $extrapolation$ capabilities in applying it to unseen circuits. Our results show that a particular type of recurrent neural network is extremely powerful in generalizing its predictions within the system size and time window that it has been trained on for both, localized and scrambled regimes. These include regimes where classical learning approaches are known to fail in sampling from a representation of the full wave function. Moreover, the considered neural network succeeds in $extrapolating$ its predictions beyond the time window and system size that it has been trained on for models that show localization, but not in scrambled regimes.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141725853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-18DOI: 10.22331/q-2024-07-18-1418
Stefan Bäuml, Carlos Pascual-García, Victoria Wright, Omar Fawzi, Antonio Acín
Continuous variable quantum key distribution with discrete modulation has the potential to provide information-theoretic security using widely available optical elements and existing telecom infrastructure. While their implementation is significantly simpler than that for protocols based on Gaussian modulation, proving their finite-size security against coherent attacks poses a challenge. In this work we prove finite-size security against coherent attacks for a discrete-modulated quantum key distribution protocol involving four coherent states and heterodyne detection. To do so, and contrary to most of the existing schemes, we first discretize all the continuous variables generated during the protocol. This allows us to use the entropy accumulation theorem, a tool that has previously been used in the setting of discrete variables, to construct the finite-size security proof. We then compute the corresponding finite-key rates through semi-definite programming and under a photon-number cutoff. Our analysis provides asymptotic rates in the range of $0.1-10^{-4}$ bits per round for distances up to hundred kilometres, while in the finite case and for realistic parameters, we get of the order of $10$ Gbits of secret key after $nsim10^{11}$ rounds and distances of few tens of kilometres.
{"title":"Security of discrete-modulated continuous-variable quantum key distribution","authors":"Stefan Bäuml, Carlos Pascual-García, Victoria Wright, Omar Fawzi, Antonio Acín","doi":"10.22331/q-2024-07-18-1418","DOIUrl":"https://doi.org/10.22331/q-2024-07-18-1418","url":null,"abstract":"Continuous variable quantum key distribution with discrete modulation has the potential to provide information-theoretic security using widely available optical elements and existing telecom infrastructure. While their implementation is significantly simpler than that for protocols based on Gaussian modulation, proving their finite-size security against coherent attacks poses a challenge. In this work we prove finite-size security against coherent attacks for a discrete-modulated quantum key distribution protocol involving four coherent states and heterodyne detection. To do so, and contrary to most of the existing schemes, we first discretize all the continuous variables generated during the protocol. This allows us to use the entropy accumulation theorem, a tool that has previously been used in the setting of discrete variables, to construct the finite-size security proof. We then compute the corresponding finite-key rates through semi-definite programming and under a photon-number cutoff. Our analysis provides asymptotic rates in the range of $0.1-10^{-4}$ bits per round for distances up to hundred kilometres, while in the finite case and for realistic parameters, we get of the order of $10$ Gbits of secret key after $nsim10^{11}$ rounds and distances of few tens of kilometres.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141725852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-18DOI: 10.22331/q-2024-07-18-1416
Rahul Sarkar, Theodore J. Yoder
Twist defects in surface codes can be used to encode more logical qubits, improve the code rate, and implement logical gates. In this work we provide a rigorous formalism for constructing surface codes with twists generalizing the well-defined homological formalism introduced by Kitaev for describing CSS surface codes. In particular, we associate a surface code to $any$ graph $G$ embedded on $any$ 2D-manifold, in such a way that (1) qubits are associated to the vertices of the graph, (2) stabilizers are associated to faces, (3) twist defects are associated to odd-degree vertices. In this way, we are able to reproduce the variety of surface codes, with and without twists, in the literature and produce new examples. We also calculate and bound various code properties such as the rate and distance in terms of topological graph properties such as genus, systole, and face-width.
{"title":"A graph-based formalism for surface codes and twists","authors":"Rahul Sarkar, Theodore J. Yoder","doi":"10.22331/q-2024-07-18-1416","DOIUrl":"https://doi.org/10.22331/q-2024-07-18-1416","url":null,"abstract":"Twist defects in surface codes can be used to encode more logical qubits, improve the code rate, and implement logical gates. In this work we provide a rigorous formalism for constructing surface codes with twists generalizing the well-defined homological formalism introduced by Kitaev for describing CSS surface codes. In particular, we associate a surface code to $any$ graph $G$ embedded on $any$ 2D-manifold, in such a way that (1) qubits are associated to the vertices of the graph, (2) stabilizers are associated to faces, (3) twist defects are associated to odd-degree vertices. In this way, we are able to reproduce the variety of surface codes, with and without twists, in the literature and produce new examples. We also calculate and bound various code properties such as the rate and distance in terms of topological graph properties such as genus, systole, and face-width.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141725919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.22331/q-2024-07-17-1413
Poetri Sonya Tarabunga
Non-stabilizerness – commonly known as magic – measures the extent to which a quantum state deviates from stabilizer states and is a fundamental resource for achieving universal quantum computation. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains. To quantify non-stabilizerness, we employ a monotone called mana, based on the negativity of the discrete Wigner function. This measure captures non-stabilizerness for both pure and mixed states. We introduce Rényi generalizations of mana, which are also measures of non-stabilizerness for pure states, and utilize it to compute mana in large quantum systems. We consider the three-state Potts model and its non-integrable extension and we provide strong evidence that the mutual mana exhibits universal logarithmic scaling with distance in conformal field theory, as is the case for entanglement.
非稳定度--通常称为魔力--衡量量子态偏离稳定态的程度，是实现通用量子计算的基本资源。在这项工作中，我们研究了量子自旋链临界附近的非稳定度行为。为了量化非稳定度，我们基于离散维格纳函数的负性，采用了一种称为 mana 的单调。这个量度可以捕捉纯态和混合态的非稳定度。我们引入了mana的雷尼广义，这也是纯态的不稳定性度量，并利用它计算大型量子系统中的mana。我们考虑了三态波茨模型及其不可整合的扩展，并提供了强有力的证据，证明在共形场理论中，相互法力随距离呈现普遍的对数缩放，就像纠缠一样。
{"title":"Critical behaviors of non-stabilizerness in quantum spin chains","authors":"Poetri Sonya Tarabunga","doi":"10.22331/q-2024-07-17-1413","DOIUrl":"https://doi.org/10.22331/q-2024-07-17-1413","url":null,"abstract":"Non-stabilizerness – commonly known as magic – measures the extent to which a quantum state deviates from stabilizer states and is a fundamental resource for achieving universal quantum computation. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains. To quantify non-stabilizerness, we employ a monotone called mana, based on the negativity of the discrete Wigner function. This measure captures non-stabilizerness for both pure and mixed states. We introduce Rényi generalizations of mana, which are also measures of non-stabilizerness for pure states, and utilize it to compute mana in large quantum systems. We consider the three-state Potts model and its non-integrable extension and we provide strong evidence that the mutual mana exhibits universal logarithmic scaling with distance in conformal field theory, as is the case for entanglement.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141631355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.22331/q-2024-07-17-1414
Sara Ditsch, Tobias Haas
We present a general way of quantifying the entropic uncertainty of quantum field configurations in phase space in terms of entropic distinguishability with respect to the vacuum. Our approach is based on the functional Husimi $Q$-distribution and a suitably chosen relative entropy, which we show to be non-trivially bounded from above by the uncertainty principle. The resulting relative entropic uncertainty relation is as general as the concept of coherent states and thus holds for quantum fields of bosonic and fermionic type. Its simple form enables diverse applications, among which we present a complete characterization of the uncertainty surplus of arbitrary states in terms of the total particle number for a scalar field and the fermionic description of the Ising model. Moreover, we provide a quantitative interpretation of the role of the uncertainty principle for quantum phase transitions.
{"title":"Entropic distinguishability of quantum fields in phase space","authors":"Sara Ditsch, Tobias Haas","doi":"10.22331/q-2024-07-17-1414","DOIUrl":"https://doi.org/10.22331/q-2024-07-17-1414","url":null,"abstract":"We present a general way of quantifying the entropic uncertainty of quantum field configurations in phase space in terms of entropic distinguishability with respect to the vacuum. Our approach is based on the functional Husimi $Q$-distribution and a suitably chosen relative entropy, which we show to be non-trivially bounded from above by the uncertainty principle. The resulting relative entropic uncertainty relation is as general as the concept of coherent states and thus holds for quantum fields of bosonic and fermionic type. Its simple form enables diverse applications, among which we present a complete characterization of the uncertainty surplus of arbitrary states in terms of the total particle number for a scalar field and the fermionic description of the Ising model. Moreover, we provide a quantitative interpretation of the role of the uncertainty principle for quantum phase transitions.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141631420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-17DOI: 10.22331/q-2024-07-17-1412
Kyusung Hwang
Quantum spin liquids and anyons, used to be subjects of condensed matter physics, now are realized in various platforms of qubits, offering unprecedented opportunities to investigate fundamental physics of many-body quantum entangled states. Qubits are inevitably exposed to environment effects such as decoherence and dissipation, which are believed to be detrimental to many-body entanglement. Here, we argue that unlike the common belief decoherence and dissipation can give rise to novel topological phenomena in quantum spin liquids. We study open quantum systems of the Kitaev spin liquid and the toric code via the Lindblad master equation approach. By using exact solutions and numerical approaches, we show the dynamical occurrence of anyon condensation by decoherence and dissipation, which results in a topological transition from the initial state spin liquid to the steady state spin liquid. The mechanism of the anyon condensation transition by the Lindblad dynamics is elucidated. We also provide an insight into the relationship between the Kitaev spin liquid and the toric code in the picture of anyon condensation. Our work suggests open quantum systems to be a new venue for topological phenomena of quantum spin liquids and anyons.
{"title":"Mixed-State Quantum Spin Liquids and Dynamical Anyon Condensations in Kitaev Lindbladians","authors":"Kyusung Hwang","doi":"10.22331/q-2024-07-17-1412","DOIUrl":"https://doi.org/10.22331/q-2024-07-17-1412","url":null,"abstract":"Quantum spin liquids and anyons, used to be subjects of condensed matter physics, now are realized in various platforms of qubits, offering unprecedented opportunities to investigate fundamental physics of many-body quantum entangled states. Qubits are inevitably exposed to environment effects such as decoherence and dissipation, which are believed to be detrimental to many-body entanglement. Here, we argue that unlike the common belief decoherence and dissipation can give rise to novel topological phenomena in quantum spin liquids. We study open quantum systems of the Kitaev spin liquid and the toric code via the Lindblad master equation approach. By using exact solutions and numerical approaches, we show the dynamical occurrence of anyon condensation by decoherence and dissipation, which results in a topological transition from the initial state spin liquid to the steady state spin liquid. The mechanism of the anyon condensation transition by the Lindblad dynamics is elucidated. We also provide an insight into the relationship between the Kitaev spin liquid and the toric code in the picture of anyon condensation. Our work suggests open quantum systems to be a new venue for topological phenomena of quantum spin liquids and anyons.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":null,"pages":null},"PeriodicalIF":6.4,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141631419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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