[{"date_published":"2026-05-22T00:00:00Z","_id":"21917","corr_author":"1","quality_controlled":"1","date_updated":"2026-06-02T09:15:13Z","DOAJ_listed":"1","status":"public","volume":10,"title":"Tensor cross interpolation of purities in quantum many-body systems","oa":1,"file_date_updated":"2026-06-02T09:12:11Z","project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","call_identifier":"H2020","grant_number":"850899"}],"month":"05","arxiv":1,"ddc":["530"],"OA_type":"gold","author":[{"full_name":"Kolisnyk, Dmytro","id":"530a7320-5355-11ee-ae5a-82a46997aaa7","last_name":"Kolisnyk","orcid":"0000-0002-8612-8202","first_name":"Dmytro"},{"full_name":"Medina Ramos, Raimel A","id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos","orcid":"0000-0002-5383-2869","first_name":"Raimel A"},{"full_name":"Vasseur, Romain","last_name":"Vasseur","first_name":"Romain"},{"last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","full_name":"Serbyn, Maksym","first_name":"Maksym","orcid":"0000-0002-2399-5827"}],"date_created":"2026-05-26T19:39:12Z","OA_place":"publisher","publication_identifier":{"eissn":["2521-327X"]},"article_number":"2114","article_type":"original","abstract":[{"lang":"eng","text":"A defining feature of quantum many-body systems is the exponential scaling of the Hilbert space with the number of degrees of freedom. This exponential complexity naïvely renders a complete state characterization, for instance via the complete set of bipartite Renyi entropies for all disjoint regions, a challenging task. Recently, a compact way of storing subregions' purities by encoding them as amplitudes of a fictitious quantum wave function, known as entanglement feature, was proposed. Notably, the entanglement feature can be a simple object even for highly entangled quantum states. However the complexity and practical usage of the entanglement feature for general quantum states has not been explored. In this work, we demonstrate that the entanglement feature can be efficiently learned using only a polynomial amount of samples in the number of degrees of freedom through the so-called tensor cross interpolation (TCI) algorithm, assuming it is expressible as a finite bond dimension MPS. We benchmark this learning process on Haar and random MPS states, confirming analytic expectations. Applying the TCI algorithm to quantum eigenstates of various one dimensional quantum systems, we identify cases where eigenstates have entanglement feature learnable with TCI. We conclude with possible applications of the learned entanglement feature, such as quantifying the distance between different entanglement patterns and finding the optimal one-dimensional ordering of physical indices in a given state, highlighting the potential utility of the proposed purity interpolation method."}],"file":[{"file_size":3284798,"checksum":"f8ce78607ad06120cdf894dc8cef55da","success":1,"date_updated":"2026-06-02T09:12:11Z","date_created":"2026-06-02T09:12:11Z","relation":"main_file","file_name":"2026_Quantum_Kolisnyk.pdf","content_type":"application/pdf","creator":"dernst","file_id":"21939","access_level":"open_access"}],"fulldoi":"https://doi.org/10.22331/q-2026-05-22-2114","acknowledgement":"We acknowledge useful discussions with Richard Küng\r\non the interpolation methods and error spreading, Ilia\r\nA. Luchnikov, Margarita Davydova, and, in particular, Hiroshi Shinaoka, Marc Ritter, Yuriel Nuñez\r\nfor useful discussions about TCI and the various\r\nworkarounds within the TensorCrossInterpolation.jl\r\nlibrary. We also acknowledge the comments of anonymous Referee B, that encouraged us to expand the\r\nmanuscript with discussion of additional applications\r\nof entanglement feature in Section 4.3. M.S. acknowledges discussions with D. V. Savostyanov at the 2nd\r\nInternational Quantum Tensor Networks (IQTN) plenary meeting at Flatiron Institute’s Center for Computational Quantum Physics (CCQ) for introduction\r\nto the TCI approach. D.K and M.S. acknowledge support by the European Research Council (ERC) under We acknowledge useful discussions with Richard Küng\r\non the interpolation methods and error spreading, Ilia\r\nA. Luchnikov, Margarita Davydova, and, in particular, Hiroshi Shinaoka, Marc Ritter, Yuriel Nuñez\r\nfor useful discussions about TCI and the various\r\nworkarounds within the TensorCrossInterpolation.jl\r\nlibrary. We also acknowledge the comments of anonymous Referee B, that encouraged us to expand the\r\nmanuscript with discussion of additional applications\r\nof entanglement feature in Section 4.3. M.S. acknowledges discussions with D. V. Savostyanov at the 2nd\r\nInternational Quantum Tensor Networks (IQTN) plenary meeting at Flatiron Institute’s Center for Computational Quantum Physics (CCQ) for introduction\r\nto the TCI approach. D.K and M.S. acknowledge support by the European Research Council (ERC) under We acknowledge useful discussions with Richard Küng\r\non the interpolation methods and error spreading, Ilia\r\nA. Luchnikov, Margarita Davydova, and, in particular, Hiroshi Shinaoka, Marc Ritter, Yuriel Nuñez\r\nfor useful discussions about TCI and the various\r\nworkarounds within the TensorCrossInterpolation.jl\r\nlibrary. We also acknowledge the comments of anonymous Referee B, that encouraged us to expand the\r\nmanuscript with discussion of additional applications\r\nof entanglement feature in Section 4.3. M.S. acknowledges discussions with D. V. Savostyanov at the 2nd\r\nInternational Quantum Tensor Networks (IQTN) plenary meeting at Flatiron Institute’s Center for Computational Quantum Physics (CCQ) for introduction\r\nto the TCI approach. D.K and M.S. acknowledge support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899).\r\nR.V. acknowledges partial support from the US Department of Energy, Office of Science, Basic Energy\r\nSciences, under award No. DE-SC0023999, and the\r\nSwiss National Science Foundation (grant 10008234).\r\nThis research was supported in part by grant NSF\r\nPHY-2309135 to the Kavli Institute for Theoretical\r\nPhysics (KITP)","type":"journal_article","year":"2026","department":[{"_id":"MaSe"},{"_id":"GradSch"}],"publication_status":"published","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften","doi":"10.22331/q-2026-05-22-2114","ec_funded":1,"citation":{"ista":"Kolisnyk D, Medina Ramos RA, Vasseur R, Serbyn M. 2026. Tensor cross interpolation of purities in quantum many-body systems. Quantum. 10, 2114.","mla":"Kolisnyk, Dmytro, et al. “Tensor Cross Interpolation of Purities in Quantum Many-Body Systems.” <i>Quantum</i>, vol. 10, 2114, Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2026, doi:<a href=\"https://doi.org/10.22331/q-2026-05-22-2114\">10.22331/q-2026-05-22-2114</a>.","apa":"Kolisnyk, D., Medina Ramos, R. A., Vasseur, R., &#38; Serbyn, M. (2026). Tensor cross interpolation of purities in quantum many-body systems. <i>Quantum</i>. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften. <a href=\"https://doi.org/10.22331/q-2026-05-22-2114\">https://doi.org/10.22331/q-2026-05-22-2114</a>","short":"D. Kolisnyk, R.A. Medina Ramos, R. Vasseur, M. Serbyn, Quantum 10 (2026).","chicago":"Kolisnyk, Dmytro, Raimel A Medina Ramos, Romain Vasseur, and Maksym Serbyn. “Tensor Cross Interpolation of Purities in Quantum Many-Body Systems.” <i>Quantum</i>. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2026. <a href=\"https://doi.org/10.22331/q-2026-05-22-2114\">https://doi.org/10.22331/q-2026-05-22-2114</a>.","ama":"Kolisnyk D, Medina Ramos RA, Vasseur R, Serbyn M. Tensor cross interpolation of purities in quantum many-body systems. <i>Quantum</i>. 2026;10. doi:<a href=\"https://doi.org/10.22331/q-2026-05-22-2114\">10.22331/q-2026-05-22-2114</a>","ieee":"D. Kolisnyk, R. A. Medina Ramos, R. Vasseur, and M. Serbyn, “Tensor cross interpolation of purities in quantum many-body systems,” <i>Quantum</i>, vol. 10. Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, 2026."},"has_accepted_license":"1","publication":"Quantum","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"article_processing_charge":"Yes","external_id":{"arxiv":["2503.17230"]},"intvolume":"        10","oa_version":"Published Version","day":"22","PlanS_conform":"1"},{"article_processing_charge":"No","publication":"2025 IEEE International Conference on Quantum Computing and Engineering","conference":{"start_date":"2025-08-30","name":"QCE: International Conference on Quantum Computing and Engineering","end_date":"2025-09-05","location":"Albuquerque, NM, United States"},"citation":{"apa":"Eder, P. J., Kerschbaumer, A., Finžgar, J. R., Medina Ramos, R. A., Schuetz, M. J. A., Katzgraber, H. G., … Mendl, C. B. (2025). Quantum-guided cluster algorithms for combinatorial optimization. In <i>2025 IEEE International Conference on Quantum Computing and Engineering</i>. Albuquerque, NM, United States: IEEE. <a href=\"https://doi.org/10.1109/qce65121.2025.00033\">https://doi.org/10.1109/qce65121.2025.00033</a>","short":"P.J. Eder, A. Kerschbaumer, J.R. Finžgar, R.A. Medina Ramos, M.J.A. Schuetz, H.G. Katzgraber, S. Braun, C.B. Mendl, in:, 2025 IEEE International Conference on Quantum Computing and Engineering, IEEE, 2025.","chicago":"Eder, Peter J., Aron Kerschbaumer, Jernej Rudi Finžgar, Raimel A Medina Ramos, Martin J. A. Schuetz, Helmut G. Katzgraber, Sarah Braun, and Christian B. Mendl. “Quantum-Guided Cluster Algorithms for Combinatorial Optimization.” In <i>2025 IEEE International Conference on Quantum Computing and Engineering</i>. IEEE, 2025. <a href=\"https://doi.org/10.1109/qce65121.2025.00033\">https://doi.org/10.1109/qce65121.2025.00033</a>.","ama":"Eder PJ, Kerschbaumer A, Finžgar JR, et al. Quantum-guided cluster algorithms for combinatorial optimization. In: <i>2025 IEEE International Conference on Quantum Computing and Engineering</i>. IEEE; 2025. doi:<a href=\"https://doi.org/10.1109/qce65121.2025.00033\">10.1109/qce65121.2025.00033</a>","ieee":"P. J. Eder <i>et al.</i>, “Quantum-guided cluster algorithms for combinatorial optimization,” in <i>2025 IEEE International Conference on Quantum Computing and Engineering</i>, Albuquerque, NM, United States, 2025.","mla":"Eder, Peter J., et al. “Quantum-Guided Cluster Algorithms for Combinatorial Optimization.” <i>2025 IEEE International Conference on Quantum Computing and Engineering</i>, IEEE, 2025, doi:<a href=\"https://doi.org/10.1109/qce65121.2025.00033\">10.1109/qce65121.2025.00033</a>.","ista":"Eder PJ, Kerschbaumer A, Finžgar JR, Medina Ramos RA, Schuetz MJA, Katzgraber HG, Braun S, Mendl CB. 2025. Quantum-guided cluster algorithms for combinatorial optimization. 2025 IEEE International Conference on Quantum Computing and Engineering. QCE: International Conference on Quantum Computing and Engineering."},"publication_status":"published","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1109/qce65121.2025.00033","publisher":"IEEE","type":"conference","year":"2025","department":[{"_id":"MaSe"}],"day":"01","oa_version":"Preprint","external_id":{"arxiv":["2508.10656"]},"month":"09","arxiv":1,"title":"Quantum-guided cluster algorithms for combinatorial optimization","status":"public","oa":1,"date_updated":"2026-02-18T08:45:56Z","corr_author":"1","quality_controlled":"1","date_published":"2025-09-01T00:00:00Z","_id":"21272","abstract":[{"text":"Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a Monte Carlo (MC)-based algorithm that updates spins one at a time. Yet, these localized updates can cause the system to become trapped in local minima. Cluster algorithms (CAs) were developed to address this limitation and have demonstrated considerable success in studying ferromagnetic systems; however, they tend to encounter percolation issues when applied to generic spin glasses. In this work, we introduce a novel CA designed to tackle these challenges by leveraging precomputed two-point correlations, aiming solve combinatorial optimization problems in the form of Max-Cut more efficiently. In our approach, clusters are formed probabilistically based on these correlations. Various classical and quantum algorithms can be employed to generate correlations that embody information about the energy landscape of the problem. By utilizing this information, the algorithm aims to identify groups of spins whose simultaneous flipping induces large transitions in configuration space with high acceptance probability - even at low energy levels - thereby escaping local minima more effectively. Notably, clusters generated using correlations from the Quantum Approximate Optimization Algorithm exhibit high acceptance rates at low temperatures. These acceptance rates often increase with circuit depth, accelerating the algorithm and enabling more efficient exploration of the solution space.","lang":"eng"}],"publication_identifier":{"eisbn":["9798331557362"]},"acknowledgement":"P.J.E was partially funded by the German BMWK project QCHALLenge (Grant No. 01MQ22008B).\r\n","fulldoi":"https://doi.org/10.1109/qce65121.2025.00033","OA_place":"repository","date_created":"2026-02-17T08:00:17Z","author":[{"first_name":"Peter J.","full_name":"Eder, Peter J.","last_name":"Eder"},{"id":"ade85a9c-3200-11ee-973b-91c1eb240410","last_name":"Kerschbaumer","full_name":"Kerschbaumer, Aron","first_name":"Aron","orcid":"0009-0002-2370-8661"},{"last_name":"Finžgar","full_name":"Finžgar, Jernej Rudi","first_name":"Jernej Rudi"},{"id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos","full_name":"Medina Ramos, Raimel A","first_name":"Raimel A","orcid":"0000-0002-5383-2869"},{"full_name":"Schuetz, Martin J. A.","last_name":"Schuetz","first_name":"Martin J. A."},{"first_name":"Helmut G.","full_name":"Katzgraber, Helmut G.","last_name":"Katzgraber"},{"last_name":"Braun","full_name":"Braun, Sarah","first_name":"Sarah"},{"first_name":"Christian B.","full_name":"Mendl, Christian B.","last_name":"Mendl"}],"OA_type":"green","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2508.10656"}]},{"keyword":["Quantum computing","Variational Quantum Algorithms","Optimization"],"citation":{"mla":"Medina Ramos, Raimel A. <i>Exploring the Optimization Landscape of Variational Quantum Algorithms</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17208\">10.15479/at:ista:17208</a>.","chicago":"Medina Ramos, Raimel A. “Exploring the Optimization Landscape of Variational Quantum Algorithms.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17208\">https://doi.org/10.15479/at:ista:17208</a>.","short":"R.A. Medina Ramos, Exploring the Optimization Landscape of Variational Quantum Algorithms, Institute of Science and Technology Austria, 2024.","apa":"Medina Ramos, R. A. (2024). <i>Exploring the optimization landscape of variational quantum algorithms</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17208\">https://doi.org/10.15479/at:ista:17208</a>","ieee":"R. A. Medina Ramos, “Exploring the optimization landscape of variational quantum algorithms,” Institute of Science and Technology Austria, 2024.","ama":"Medina Ramos RA. Exploring the optimization landscape of variational quantum algorithms. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17208\">10.15479/at:ista:17208</a>","ista":"Medina Ramos RA. 2024. Exploring the optimization landscape of variational quantum algorithms. Institute of Science and Technology Austria."},"article_processing_charge":"No","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"MaSe"}],"year":"2024","type":"dissertation","publisher":"Institute of Science and Technology Austria","doi":"10.15479/at:ista:17208","ec_funded":1,"alternative_title":["ISTA Thesis"],"acknowledged_ssus":[{"_id":"ScienComp"}],"publication_status":"published","language":[{"iso":"eng"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","supervisor":[{"first_name":"Maksym","orcid":"0000-0002-2399-5827","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","last_name":"Serbyn","full_name":"Serbyn, Maksym"}],"day":"09","oa_version":"Published Version","oa":1,"file_date_updated":"2024-07-17T09:23:24Z","page":"133","status":"public","title":"Exploring the optimization landscape of variational quantum algorithms","project":[{"grant_number":"850899","call_identifier":"H2020","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control"}],"month":"07","_id":"17208","date_published":"2024-07-09T00:00:00Z","corr_author":"1","date_updated":"2026-04-07T12:43:22Z","OA_place":"publisher","date_created":"2024-07-09T09:14:24Z","fulldoi":"https://doi.org/10.15479/at:ista:17208","related_material":{"record":[{"relation":"part_of_dissertation","id":"10545","status":"public"},{"status":"public","id":"10067","relation":"part_of_dissertation"},{"id":"17222","relation":"part_of_dissertation","status":"public"},{"id":"13125","relation":"part_of_dissertation","status":"public"},{"id":"11471","relation":"part_of_dissertation","status":"public"}]},"file":[{"file_size":"14218691","checksum":"6f45273d04f4418bc2adc018baed0525","date_updated":"2024-07-10T11:34:09Z","date_created":"2024-07-09T09:21:44Z","relation":"source_file","file_name":"Raimel_Thesis-Final.zip","creator":"rmedinar","content_type":"application/zip","access_level":"closed","file_id":"17212"},{"date_updated":"2024-07-17T09:23:24Z","checksum":"6724a95bec772dbabc0111b9f08a805e","file_size":11253627,"success":1,"content_type":"application/pdf","creator":"rmedinar","file_id":"17275","access_level":"open_access","relation":"main_file","file_name":"Raimel_Thesis-20_pdfa.pdf","date_created":"2024-07-17T09:23:24Z"}],"publication_identifier":{"issn":["2663-337X"]},"abstract":[{"text":"Can current quantum computers provide a speedup over their classical counterparts for some kinds of problems? In this thesis, with a focus on ground state search/preparation, we address some of the challenges that both quantum annealing and variational quantum algorithms suffer from, hindering any possible practical speedup in comparison to the best classical counterparts. \r\n\r\nIn the first part of the thesis, we study the performance of quantum annealing for solving a particular combinatorial optimization problem called 3-XOR satisfability (3-XORSAT). The classical problem is mapped into a ground state search of a 3-local classical Hamiltonian $H_C$. We consider how modifying the initial problem, by adding more interaction terms to the corresponding Hamiltonian, leads to the emergence of a first-order phase transition during the annealing process. This phenomenon causes the total annealing duration, $T$, required to prepare the ground state of $H_C$ with a high probability to increase exponentially with the size of the problem. Our findings indicate that with the growing complexity of problem instances, the likelihood of encountering first-order phase transitions also increases, making quantum annealing an impractical solution for these types of combinatorial optimization problems.\r\n\r\nIn the second part, we focus on the problem of barren plateaus in generic variational quantum algorithms. Barren plateaus correspond to flat regions in the parameter space where the gradient of the cost function is zero in expectation, and with the variance decaying exponentially with the system size, thus obstructing an efficient parameter optimization.  We propose an algorithm to circumvent Barren Plateaus by monitoring the entanglement entropy of k-local reduced density matrices, alongside a method for estimating entanglement entropy via classical shadow tomography. We illustrate the approach with the paradigmatic example of the variational quantum eigensolver, and show that our algorithm effectively avoids barren plateaus in the initialization as well as during the optimization stage. \r\n\r\nLastly, in the last two Chapters of this thesis, we focus on the quantum approximate optimization algorithm (QAOA), originally introduced as an algorithm for solving generic combinatorial optimization problems in near-term quantum devices. Specifically, we focus on how to develop rigorous initialization strategies with guarantee improvement. Our motivation for this study lies in that for random initialization, the optimization typically leads to local minima with poor performance. Our main result corresponds to the analytical construction of index-1 saddle points or transition states, stationary points with a single direction of descent, as a tool for systematically exploring the QAOA optimization landscape. This leads us to propose a novel greedy parameter initialization strategy that guarantees for the energy to decrease with an increasing number of circuit layers. Furthermore, with precise estimates for the negative Hessian eigenvalue and its eigenvector, we establish a lower bound for energy improvement following a QAOA iteration.","lang":"eng"}],"ddc":["539"],"author":[{"full_name":"Medina Ramos, Raimel A","id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos","orcid":"0000-0002-5383-2869","first_name":"Raimel A"}],"degree_awarded":"PhD"},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.10125"}],"author":[{"orcid":"0000-0002-5383-2869","first_name":"Raimel A","full_name":"Medina Ramos, Raimel A","id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos"},{"orcid":"0000-0002-2399-5827","first_name":"Maksym","full_name":"Serbyn, Maksym","last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2024-07-10T13:12:09Z","OA_place":"repository","related_material":{"record":[{"id":"17208","status":"public","relation":"dissertation_contains"}]},"fulldoi":"https://doi.org/10.48550/arXiv.2405.10125","article_number":"2405.10125","abstract":[{"lang":"eng","text":"The quantum approximate optimization algorithm (QAOA) uses a quantum computer\r\nto implement a variational method with $2p$ layers of alternating unitary\r\noperators, optimized by a classical computer to minimize a cost function. While\r\nrigorous performance guarantees exist for the QAOA at small depths $p$, the\r\nbehavior at large depths remains less clear, though simulations suggest\r\nexponentially fast convergence for certain problems. In this work, we gain\r\ninsights into the deep QAOA using an analytic expansion of the cost function\r\naround transition states. Transition states are constructed in a recursive\r\nmanner: from the local minima of the QAOA with $p$ layers we obtain transition\r\nstates of the QAOA with $p+1$ layers, which are stationary points characterized\r\nby a unique direction of negative curvature. We construct an analytic estimate\r\nof the negative curvature and the corresponding direction in parameter space at\r\neach transition state. The expansion of the QAOA cost function along the\r\nnegative direction to the quartic order gives a lower bound of the QAOA cost\r\nfunction improvement. We provide physical intuition behind the analytic\r\nexpressions for the local curvature and quartic expansion coefficient. Our\r\nnumerical study confirms the accuracy of our approximations and reveals that\r\nthe obtained bound and the true value of the QAOA cost function gain have a\r\ncharacteristic exponential decrease with the number of layers $p$, with the\r\nbound decreasing more rapidly. Our study establishes an analytical method for\r\nrecursively studying the QAOA that is applicable in the regime of high circuit\r\ndepth."}],"_id":"17222","date_published":"2024-05-16T00:00:00Z","corr_author":"1","date_updated":"2026-04-07T12:43:22Z","oa":1,"status":"public","title":"A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm","arxiv":1,"month":"05","external_id":{"arxiv":["2405.10125"]},"day":"16","oa_version":"Preprint","department":[{"_id":"MaSe"}],"year":"2024","type":"preprint","doi":"10.48550/arXiv.2405.10125","publication_status":"draft","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"citation":{"ista":"Medina Ramos RA, Serbyn M. A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. arXiv, 2405.10125.","chicago":"Medina Ramos, Raimel A, and Maksym Serbyn. “A Recursive Lower Bound on the Energy Improvement of the Quantum Approximate Optimization Algorithm.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2405.10125\">https://doi.org/10.48550/arXiv.2405.10125</a>.","apa":"Medina Ramos, R. A., &#38; Serbyn, M. (n.d.). A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2405.10125\">https://doi.org/10.48550/arXiv.2405.10125</a>","short":"R.A. Medina Ramos, M. Serbyn, ArXiv (n.d.).","ama":"Medina Ramos RA, Serbyn M. A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2405.10125\">10.48550/arXiv.2405.10125</a>","ieee":"R. A. Medina Ramos and M. Serbyn, “A recursive lower bound on the energy improvement of the quantum approximate optimization algorithm,” <i>arXiv</i>. .","mla":"Medina Ramos, Raimel A., and Maksym Serbyn. “A Recursive Lower Bound on the Energy Improvement of the Quantum Approximate Optimization Algorithm.” <i>ArXiv</i>, 2405.10125, doi:<a href=\"https://doi.org/10.48550/arXiv.2405.10125\">10.48550/arXiv.2405.10125</a>."},"publication":"arXiv","article_processing_charge":"No","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"}},{"citation":{"ama":"Sack S, Medina Ramos RA, Kueng R, Serbyn M. Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement. <i>Physical Review A</i>. 2023;107(6). doi:<a href=\"https://doi.org/10.1103/physreva.107.062404\">10.1103/physreva.107.062404</a>","ieee":"S. Sack, R. A. Medina Ramos, R. Kueng, and M. Serbyn, “Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement,” <i>Physical Review A</i>, vol. 107, no. 6. American Physical Society, 2023.","apa":"Sack, S., Medina Ramos, R. A., Kueng, R., &#38; Serbyn, M. (2023). Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement. <i>Physical Review A</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physreva.107.062404\">https://doi.org/10.1103/physreva.107.062404</a>","chicago":"Sack, Stefan, Raimel A Medina Ramos, Richard Kueng, and Maksym Serbyn. “Recursive Greedy Initialization of the Quantum Approximate Optimization Algorithm with Guaranteed Improvement.” <i>Physical Review A</i>. American Physical Society, 2023. <a href=\"https://doi.org/10.1103/physreva.107.062404\">https://doi.org/10.1103/physreva.107.062404</a>.","short":"S. Sack, R.A. Medina Ramos, R. Kueng, M. Serbyn, Physical Review A 107 (2023).","mla":"Sack, Stefan, et al. “Recursive Greedy Initialization of the Quantum Approximate Optimization Algorithm with Guaranteed Improvement.” <i>Physical Review A</i>, vol. 107, no. 6, 062404, American Physical Society, 2023, doi:<a href=\"https://doi.org/10.1103/physreva.107.062404\">10.1103/physreva.107.062404</a>.","ista":"Sack S, Medina Ramos RA, Kueng R, Serbyn M. 2023. Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement. Physical Review A. 107(6), 062404."},"has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"article_processing_charge":"No","publication":"Physical Review A","type":"journal_article","isi":1,"issue":"6","year":"2023","department":[{"_id":"MaSe"}],"language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","ec_funded":1,"doi":"10.1103/physreva.107.062404","publisher":"American Physical Society","intvolume":"       107","oa_version":"Published Version","day":"02","external_id":{"isi":["001016927100012"],"arxiv":["2209.01159"]},"title":"Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement","status":"public","volume":107,"file_date_updated":"2023-06-13T07:28:36Z","oa":1,"month":"06","project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","call_identifier":"H2020","grant_number":"850899"}],"arxiv":1,"date_published":"2023-06-02T00:00:00Z","scopus_import":"1","_id":"13125","date_updated":"2026-09-11T22:31:10Z","quality_controlled":"1","corr_author":"1","date_created":"2023-06-07T06:57:32Z","abstract":[{"lang":"eng","text":"The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of p layers of alternating unitary operators and a classical computer is used to optimize the variational parameters. For a random initialization, the optimization typically leads to local minima with poor performance, motivating the search for initialization strategies of QAOA variational parameters. Although numerous heuristic initializations exist, an analytical understanding and performance guarantees for large p remain evasive.We introduce a greedy initialization of QAOA which guarantees improving performance with an increasing number of layers. Our main result is an analytic construction of 2p + 1 transition states—saddle points with a unique negative curvature direction—for QAOA with p + 1 layers that use the local minimum of QAOA with p layers. Transition states connect to new local minima, which are guaranteed to lower the energy compared to the minimum found for p layers. We use the GREEDY procedure to navigate the exponentially increasing with p number of local minima resulting from the recursive application of our analytic construction. The performance of the GREEDY procedure matches available initialization strategies while providing a guarantee for the minimal energy to decrease with an increasing number of layers p. "}],"article_type":"original","publication_identifier":{"issn":["2469-9926"],"eissn":["2469-9934"]},"article_number":"062404","acknowledgement":"We thank V. Verteletskyi for a joint collaboration on numerical studies of the QAOA during his internship at ISTA that inspired analytic results on TS reported in this work. We acknowledge A. A. Mele and M. Brooks for discussions and D. Egger, P. Love, and D. Wierichs for valuable feedback on the manuscript. S.H.S., R.A.M., and M.S. acknowledge support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899). R.K. is supported by the SFB BeyondC (Grant No. F7107-N38) and the project QuantumReady (FFG 896217). ","related_material":{"record":[{"id":"17208","status":"public","relation":"dissertation_contains"},{"id":"14622","status":"public","relation":"dissertation_contains"}]},"fulldoi":"https://doi.org/10.1103/physreva.107.062404","file":[{"access_level":"open_access","file_id":"13131","content_type":"application/pdf","creator":"dernst","file_name":"2023_PhysRevA_Sack.pdf","relation":"main_file","date_created":"2023-06-13T07:28:36Z","date_updated":"2023-06-13T07:28:36Z","success":1,"file_size":2524611,"checksum":"0d71423888eeccaa60d8f41197f26306"}],"ddc":["530"],"author":[{"orcid":"0000-0001-5400-8508","first_name":"Stefan","full_name":"Sack, Stefan","id":"dd622248-f6e0-11ea-865d-ce382a1c81a5","last_name":"Sack"},{"first_name":"Raimel A","orcid":"0000-0002-5383-2869","id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos","full_name":"Medina Ramos, Raimel A"},{"first_name":"Richard","last_name":"Kueng","full_name":"Kueng, Richard"},{"first_name":"Maksym","orcid":"0000-0002-2399-5827","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","last_name":"Serbyn","full_name":"Serbyn, Maksym"}]},{"OA_type":"gold","author":[{"first_name":"L.","full_name":"Daguerre, L.","last_name":"Daguerre"},{"first_name":"G.","last_name":"Torroba","full_name":"Torroba, G."},{"orcid":"0000-0002-5383-2869","first_name":"Raimel A","full_name":"Medina Ramos, Raimel A","last_name":"Medina Ramos","id":"CE680B90-D85A-11E9-B684-C920E6697425"},{"first_name":"M.","last_name":"Solís","full_name":"Solís, M."}],"ddc":["530"],"abstract":[{"lang":"eng","text":"studiamos aspectos de Teoría Cuántica de Campos a densidad finita usando técnicas y conceptos de información cuántica. Nos enfocamos en fermiones de Dirac masivos con potencial químico en 1+1 dimensiones espacio-temporales. Usando la entropía de entrelazamiento en un intervalo, construimos la función c entrópica que es finita. Esta función c no es monótona, e incorpora el entrelazamiento de largo alcance proveniente de la superficie de Fermi. Motivados por trabajos previos de modelos en la red, calculamos numéricamente las entropías de Renyi y encontramos oscilaciones de Friedel. Seguidamente, analizamos la información mutua como una medida de correlación entre diferentes regiones. Usando una expansión de distancia grande desarrollada por Cardy, argumentamos que la información mutua detecta las correlaciones inducidas por la superficie de Fermi todavía al orden dominante en la expansión. Finalmente, analizamos la entropía relativa y sus generalizaciones de Renyi para distinguir estados con diferente carga. Encontramos que estados en diferentes sectores de superselección dan origen a un comportamiento super-extensivo en la entropía relativa."}],"article_type":"original","publication_identifier":{"eissn":["1850-1168"]},"acknowledgement":"Se agradece a Horacio Casini por distintas discusiones y comentarios a lo largo del trabajo. LD cuenta con el apoyo de CNEA y UNCuyo, Inst. GT cuenta con el apoyo de CONICET,\r\nANPCyT, CNEA, y UNCuyo, Inst. Balseiro. RM cuenta con el apoyo de IST Austria. MS cuenta con el apoyode CONICET y UNCuyo, Inst. Balseiro. También se agradece a la Asociación Argentina de Física por la posibilidad de presentar este artículo en el marco de una Mención Especial por el Premio Luis Másperi 2020.","fulldoi":"https://doi.org/10.31527/analesafa.2021.32.4.93","file":[{"date_created":"2022-02-21T09:32:44Z","relation":"main_file","file_name":"2022_AnalesAFA_Daguerre.pdf","content_type":"application/pdf","creator":"dernst","file_id":"10782","access_level":"open_access","checksum":"ca66a3017205677c5b4d22b3bb74fb0b","file_size":4505751,"success":1,"date_updated":"2022-02-21T09:32:44Z"}],"date_created":"2022-02-20T23:01:32Z","OA_place":"publisher","date_updated":"2026-04-02T12:30:12Z","DOAJ_listed":"1","quality_controlled":"1","date_published":"2022-01-13T00:00:00Z","scopus_import":"1","_id":"10769","month":"01","title":"Non relativistic quantum field theory: Dynamics and irreversibility","volume":32,"status":"public","file_date_updated":"2022-02-21T09:32:44Z","page":"93-98","oa":1,"day":"13","oa_version":"Published Version","intvolume":"        32","language":[{"iso":"spa"}],"publication_status":"published","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.31527/analesafa.2021.32.4.93","publisher":"Asociación Física Argentina","type":"journal_article","year":"2022","department":[{"_id":"MaSe"}],"issue":"4","has_accepted_license":"1","article_processing_charge":"No","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publication":"Anales de la Asociacion Fisica Argentina","citation":{"ista":"Daguerre L, Torroba G, Medina Ramos RA, Solís M. 2022. Non relativistic quantum field theory: Dynamics and irreversibility. Anales de la Asociacion Fisica Argentina. 32(4), 93–98.","apa":"Daguerre, L., Torroba, G., Medina Ramos, R. A., &#38; Solís, M. (2022). Non relativistic quantum field theory: Dynamics and irreversibility. <i>Anales de la Asociacion Fisica Argentina</i>. Asociación Física Argentina. <a href=\"https://doi.org/10.31527/analesafa.2021.32.4.93\">https://doi.org/10.31527/analesafa.2021.32.4.93</a>","chicago":"Daguerre, L., G. Torroba, Raimel A Medina Ramos, and M. Solís. “Non relativistic quantum field theory: Dynamics and irreversibility.” <i>Anales de la Asociacion Fisica Argentina</i>. Asociación Física Argentina, 2022. <a href=\"https://doi.org/10.31527/analesafa.2021.32.4.93\">https://doi.org/10.31527/analesafa.2021.32.4.93</a>.","short":"L. Daguerre, G. Torroba, R.A. Medina Ramos, M. Solís, Anales de la Asociacion Fisica Argentina 32 (2022) 93–98.","ieee":"L. Daguerre, G. Torroba, R. A. Medina Ramos, and M. Solís, “Non relativistic quantum field theory: Dynamics and irreversibility,” <i>Anales de la Asociacion Fisica Argentina</i>, vol. 32, no. 4. Asociación Física Argentina, pp. 93–98, 2022.","ama":"Daguerre L, Torroba G, Medina Ramos RA, Solís M. Non relativistic quantum field theory: Dynamics and irreversibility. <i>Anales de la Asociacion Fisica Argentina</i>. 2022;32(4):93-98. doi:<a href=\"https://doi.org/10.31527/analesafa.2021.32.4.93\">10.31527/analesafa.2021.32.4.93</a>","mla":"Daguerre, L., et al. “Non relativistic quantum field theory: Dynamics and irreversibility.” <i>Anales de la Asociacion Fisica Argentina</i>, vol. 32, no. 4, Asociación Física Argentina, 2022, pp. 93–98, doi:<a href=\"https://doi.org/10.31527/analesafa.2021.32.4.93\">10.31527/analesafa.2021.32.4.93</a>."}},{"quality_controlled":"1","corr_author":"1","date_updated":"2026-09-11T22:31:10Z","_id":"11471","scopus_import":"1","date_published":"2022-06-29T00:00:00Z","arxiv":1,"project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","call_identifier":"H2020","grant_number":"850899","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E"}],"month":"06","oa":1,"file_date_updated":"2022-06-30T07:14:48Z","volume":3,"status":"public","title":"Avoiding barren plateaus using classical shadows","author":[{"last_name":"Sack","id":"dd622248-f6e0-11ea-865d-ce382a1c81a5","full_name":"Sack, Stefan","first_name":"Stefan","orcid":"0000-0001-5400-8508"},{"orcid":"0000-0002-5383-2869","first_name":"Raimel A","full_name":"Medina Ramos, Raimel A","id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos"},{"last_name":"Michailidis","id":"36EBAD38-F248-11E8-B48F-1D18A9856A87","full_name":"Michailidis, Alexios","first_name":"Alexios","orcid":"0000-0002-8443-1064"},{"last_name":"Kueng","full_name":"Kueng, Richard","first_name":"Richard"},{"id":"47809E7E-F248-11E8-B48F-1D18A9856A87","last_name":"Serbyn","full_name":"Serbyn, Maksym","first_name":"Maksym","orcid":"0000-0002-2399-5827"}],"ddc":["530"],"fulldoi":"https://doi.org/10.1103/prxquantum.3.020365","file":[{"date_created":"2022-06-30T07:14:48Z","file_name":"2022_PRXQuantum_Sack.pdf","relation":"main_file","file_id":"11472","access_level":"open_access","content_type":"application/pdf","creator":"dernst","success":1,"file_size":4231591,"checksum":"a7706b28d24a0e32a55ea04b82a2df43","date_updated":"2022-06-30T07:14:48Z"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"17208"},{"relation":"dissertation_contains","id":"14622","status":"public"}]},"acknowledgement":"We thank Marco Cerezo, Zoe Holmes, and Nicholas Hunter-Jones for fruitful discussion and valuable feedback. We also acknowledge Adam Smith, Johannes Jakob Meyer, and Victor V. Albert for comments on the paper. The simulations were performed in the Julia programming\r\nlanguage [65] using the Yao module [66]. S.H.S., R.A.M., A.A.M. and M.S. acknowledge support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899).","publication_identifier":{"issn":["2691-3399"]},"article_number":"020365","article_type":"original","abstract":[{"lang":"eng","text":"Variational quantum algorithms are promising algorithms for achieving quantum advantage on nearterm devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ansätze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients, which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBPs) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows WBPs to be avoided during the optimization process. This paves the way for efficient barren plateau-free optimization on near-term devices. "}],"date_created":"2022-06-29T20:21:32Z","publisher":"American Physical Society","ec_funded":1,"doi":"10.1103/prxquantum.3.020365","publication_status":"published","language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"2","year":"2022","department":[{"_id":"MaSe"}],"isi":1,"type":"journal_article","publication":"PRX Quantum","article_processing_charge":"No","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","keyword":["General Medicine"],"citation":{"ista":"Sack S, Medina Ramos RA, Michailidis A, Kueng R, Serbyn M. 2022. Avoiding barren plateaus using classical shadows. PRX Quantum. 3(2), 020365.","mla":"Sack, Stefan, et al. “Avoiding Barren Plateaus Using Classical Shadows.” <i>PRX Quantum</i>, vol. 3, no. 2, 020365, American Physical Society, 2022, doi:<a href=\"https://doi.org/10.1103/prxquantum.3.020365\">10.1103/prxquantum.3.020365</a>.","short":"S. Sack, R.A. Medina Ramos, A. Michailidis, R. Kueng, M. Serbyn, PRX Quantum 3 (2022).","chicago":"Sack, Stefan, Raimel A Medina Ramos, Alexios Michailidis, Richard Kueng, and Maksym Serbyn. “Avoiding Barren Plateaus Using Classical Shadows.” <i>PRX Quantum</i>. American Physical Society, 2022. <a href=\"https://doi.org/10.1103/prxquantum.3.020365\">https://doi.org/10.1103/prxquantum.3.020365</a>.","apa":"Sack, S., Medina Ramos, R. A., Michailidis, A., Kueng, R., &#38; Serbyn, M. (2022). Avoiding barren plateaus using classical shadows. <i>PRX Quantum</i>. American Physical Society. <a href=\"https://doi.org/10.1103/prxquantum.3.020365\">https://doi.org/10.1103/prxquantum.3.020365</a>","ama":"Sack S, Medina Ramos RA, Michailidis A, Kueng R, Serbyn M. Avoiding barren plateaus using classical shadows. <i>PRX Quantum</i>. 2022;3(2). doi:<a href=\"https://doi.org/10.1103/prxquantum.3.020365\">10.1103/prxquantum.3.020365</a>","ieee":"S. Sack, R. A. Medina Ramos, A. Michailidis, R. Kueng, and M. Serbyn, “Avoiding barren plateaus using classical shadows,” <i>PRX Quantum</i>, vol. 3, no. 2. American Physical Society, 2022."},"external_id":{"arxiv":["2201.08194"],"isi":["000822564300001"]},"day":"29","oa_version":"Published Version","intvolume":"         3"},{"_id":"15269","date_published":"2021-03-08T00:00:00Z","scopus_import":"1","date_updated":"2025-09-10T10:15:02Z","corr_author":"1","quality_controlled":"1","file_date_updated":"2024-04-10T09:18:38Z","oa":1,"title":"Aspects of quantum information in finite density field theory","status":"public","volume":2021,"arxiv":1,"month":"03","ddc":["530"],"author":[{"first_name":"Lucas","full_name":"Daguerre, Lucas","last_name":"Daguerre"},{"first_name":"Raimel A","orcid":"0000-0002-5383-2869","id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos","full_name":"Medina Ramos, Raimel A"},{"first_name":"Mario","full_name":"Solís, Mario","last_name":"Solís"},{"first_name":"Gonzalo","full_name":"Torroba, Gonzalo","last_name":"Torroba"}],"date_created":"2024-04-03T07:51:06Z","acknowledgement":"We thank H. Casini for many interesting discussions and comments on the manuscript.\r\nLD is supported by CNEA and UNCuyo, Inst. Balseiro. RM is supported by IST Austria.\r\nMS is supported by CONICET and UNCuyo, Inst. Balseiro. GT is supported by CONICET\r\n(PIP grant 11220150100299), ANPCyT (PICT 2018-2517), CNEA, and UNCuyo,\r\nInst. Balseiro.","file":[{"file_id":"15310","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_name":"2021_JourHighEnergyPhysics_Daguerre.pdf","relation":"main_file","date_created":"2024-04-10T09:18:38Z","date_updated":"2024-04-10T09:18:38Z","success":1,"checksum":"4f540e63988ee87173e02f51a19a6672","file_size":5389195}],"fulldoi":"https://doi.org/10.1007/jhep03(2021)079","abstract":[{"text":"We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic <jats:italic>c</jats:italic>-function that is finite. Unlike what happens in Lorentz-invariant theories, this <jats:italic>c</jats:italic>-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.","lang":"eng"}],"publication_identifier":{"issn":["1029-8479"]},"article_number":"79","article_type":"original","department":[{"_id":"MaSe"}],"issue":"3","year":"2021","type":"journal_article","isi":1,"doi":"10.1007/jhep03(2021)079","publisher":"Springer Nature","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","language":[{"iso":"eng"}],"keyword":["Nuclear and High Energy Physics"],"citation":{"mla":"Daguerre, Lucas, et al. “Aspects of Quantum Information in Finite Density Field Theory.” <i>Journal of High Energy Physics</i>, vol. 2021, no. 3, 79, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/jhep03(2021)079\">10.1007/jhep03(2021)079</a>.","apa":"Daguerre, L., Medina Ramos, R. A., Solís, M., &#38; Torroba, G. (2021). Aspects of quantum information in finite density field theory. <i>Journal of High Energy Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/jhep03(2021)079\">https://doi.org/10.1007/jhep03(2021)079</a>","short":"L. Daguerre, R.A. Medina Ramos, M. Solís, G. Torroba, Journal of High Energy Physics 2021 (2021).","chicago":"Daguerre, Lucas, Raimel A Medina Ramos, Mario Solís, and Gonzalo Torroba. “Aspects of Quantum Information in Finite Density Field Theory.” <i>Journal of High Energy Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/jhep03(2021)079\">https://doi.org/10.1007/jhep03(2021)079</a>.","ieee":"L. Daguerre, R. A. Medina Ramos, M. Solís, and G. Torroba, “Aspects of quantum information in finite density field theory,” <i>Journal of High Energy Physics</i>, vol. 2021, no. 3. Springer Nature, 2021.","ama":"Daguerre L, Medina Ramos RA, Solís M, Torroba G. Aspects of quantum information in finite density field theory. <i>Journal of High Energy Physics</i>. 2021;2021(3). doi:<a href=\"https://doi.org/10.1007/jhep03(2021)079\">10.1007/jhep03(2021)079</a>","ista":"Daguerre L, Medina Ramos RA, Solís M, Torroba G. 2021. Aspects of quantum information in finite density field theory. Journal of High Energy Physics. 2021(3), 79."},"article_processing_charge":"Yes","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"publication":"Journal of High Energy Physics","has_accepted_license":"1","external_id":{"isi":["000627376600004"],"arxiv":["2011.01252"]},"intvolume":"      2021","oa_version":"Published Version","day":"08"},{"external_id":{"isi":["000704414400002"],"arxiv":["2107.05735"]},"day":"30","oa_version":"Preprint","intvolume":"       104","doi":"10.1103/physrevb.104.104205","ec_funded":1,"publisher":"American Physical Society","language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","year":"2021","department":[{"_id":"MaSe"}],"issue":"10","type":"journal_article","isi":1,"article_processing_charge":"No","publication":"Physical Review B","citation":{"ieee":"R. A. Medina Ramos, R. Vasseur, and M. Serbyn, “Entanglement transitions from restricted Boltzmann machines,” <i>Physical Review B</i>, vol. 104, no. 10. American Physical Society, 2021.","ama":"Medina Ramos RA, Vasseur R, Serbyn M. Entanglement transitions from restricted Boltzmann machines. <i>Physical Review B</i>. 2021;104(10). doi:<a href=\"https://doi.org/10.1103/physrevb.104.104205\">10.1103/physrevb.104.104205</a>","apa":"Medina Ramos, R. A., Vasseur, R., &#38; Serbyn, M. (2021). Entanglement transitions from restricted Boltzmann machines. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevb.104.104205\">https://doi.org/10.1103/physrevb.104.104205</a>","short":"R.A. Medina Ramos, R. Vasseur, M. Serbyn, Physical Review B 104 (2021).","chicago":"Medina Ramos, Raimel A, Romain Vasseur, and Maksym Serbyn. “Entanglement Transitions from Restricted Boltzmann Machines.” <i>Physical Review B</i>. American Physical Society, 2021. <a href=\"https://doi.org/10.1103/physrevb.104.104205\">https://doi.org/10.1103/physrevb.104.104205</a>.","mla":"Medina Ramos, Raimel A., et al. “Entanglement Transitions from Restricted Boltzmann Machines.” <i>Physical Review B</i>, vol. 104, no. 10, 104205, American Physical Society, 2021, doi:<a href=\"https://doi.org/10.1103/physrevb.104.104205\">10.1103/physrevb.104.104205</a>.","ista":"Medina Ramos RA, Vasseur R, Serbyn M. 2021. Entanglement transitions from restricted Boltzmann machines. Physical Review B. 104(10), 104205."},"author":[{"full_name":"Medina Ramos, Raimel A","id":"CE680B90-D85A-11E9-B684-C920E6697425","last_name":"Medina Ramos","orcid":"0000-0002-5383-2869","first_name":"Raimel A"},{"first_name":"Romain","full_name":"Vasseur, Romain","last_name":"Vasseur"},{"id":"47809E7E-F248-11E8-B48F-1D18A9856A87","last_name":"Serbyn","full_name":"Serbyn, Maksym","first_name":"Maksym","orcid":"0000-0002-2399-5827"}],"main_file_link":[{"url":"https://arxiv.org/abs/2107.05735","open_access":"1"}],"acknowledgement":"We would like to thank S. De Nicola, P. Brighi, and V. Karle for fruitful discussions and valuable feedback on the manuscript. R.M. and M.S. acknowledge support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 850899). R.V. acknowledges support from the US Department of Energy, Office of Science, Basic Energy Sciences, under Early Career Award No. DE-SC0019168, and the Alfred P. Sloan Foundation through a Sloan Research Fellowship.","related_material":{"record":[{"id":"17208","status":"public","relation":"dissertation_contains"}]},"fulldoi":"https://doi.org/10.1103/physrevb.104.104205","abstract":[{"text":"The search for novel entangled phases of matter has lead to the recent discovery of a new class of “entanglement transitions,” exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free-energy cost of inserting a domain wall. In this paper we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural-network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite-size effects in finite-size numerical simulations. Introducing phases with correlations decaying as 1/r^α in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent α. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.","lang":"eng"}],"publication_identifier":{"eissn":["2469-9969"],"issn":["2469-9950"]},"article_type":"original","article_number":"104205","date_created":"2021-10-02T09:03:42Z","date_updated":"2026-04-07T12:43:22Z","corr_author":"1","quality_controlled":"1","_id":"10067","date_published":"2021-09-30T00:00:00Z","scopus_import":"1","arxiv":1,"month":"09","project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","grant_number":"850899","call_identifier":"H2020"}],"oa":1,"title":"Entanglement transitions from restricted Boltzmann machines","volume":104,"status":"public"},{"title":"Duality approach to quantum annealing of the 3-variable exclusive-or satisfiability problem (3-XORSAT)","status":"public","volume":104,"oa":1,"month":"12","project":[{"name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","grant_number":"850899","call_identifier":"H2020","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E"}],"arxiv":1,"date_published":"2021-12-14T00:00:00Z","scopus_import":"1","_id":"10545","date_updated":"2026-04-07T12:43:22Z","quality_controlled":"1","date_created":"2021-12-14T20:46:07Z","abstract":[{"text":"Classical models with complex energy landscapes represent a perspective avenue for the near-term application of quantum simulators. Until now, many theoretical works studied the performance of quantum algorithms for models with a unique ground state. However, when the classical problem is in a so-called clustering phase, the ground state manifold is highly degenerate. As an example, we consider a 3-XORSAT model defined on simple hypergraphs. The degeneracy of classical ground state manifold translates into the emergence of an extensive number of Z2 symmetries, which remain intact even in the presence of a quantum transverse magnetic field. We establish a general duality approach that restricts the quantum problem to a given sector of conserved Z2 charges and use it to study how the outcome of the quantum adiabatic algorithm depends on the hypergraph geometry. We show that the tree hypergraph which corresponds to a classically solvable instance of the 3-XORSAT problem features a constant gap, whereas the closed hypergraph encounters a second-order phase transition with a gap vanishing as a power-law in the problem size. The duality developed in this work provides a practical tool for studies of quantum models with classically degenerate energy manifold and reveals potential connections between glasses and gauge theories.","lang":"eng"}],"article_type":"original","article_number":"062423","publication_identifier":{"issn":["2469-9926"],"eissn":["2469-9934"]},"acknowledgement":"We would like to thank S. De Nicola, A. Michaidilis, T. Gulden, Y. Nez-Fernndez, P. Brighi, and S. Sack for fruitful discussions and valuable feedback on the manuscript. M.S. acknowledges useful discussions with E. Altman, L. Cugliandolo, and C. Laumann. We acknowledge support from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme Grant Agreement No. 850899.","related_material":{"record":[{"id":"17208","relation":"dissertation_contains","status":"public"}]},"fulldoi":"https://doi.org/10.1103/physreva.104.062423","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2106.06344"}],"author":[{"full_name":"Medina Ramos, Raimel A","last_name":"Medina Ramos","id":"CE680B90-D85A-11E9-B684-C920E6697425","orcid":"0000-0002-5383-2869","first_name":"Raimel A"},{"orcid":"0000-0002-2399-5827","first_name":"Maksym","full_name":"Serbyn, Maksym","last_name":"Serbyn","id":"47809E7E-F248-11E8-B48F-1D18A9856A87"}],"citation":{"mla":"Medina Ramos, Raimel A., and Maksym Serbyn. “Duality Approach to Quantum Annealing of the 3-Variable Exclusive-or Satisfiability Problem (3-XORSAT).” <i>Physical Review A</i>, vol. 104, no. 6, 062423, American Physical Society, 2021, doi:<a href=\"https://doi.org/10.1103/physreva.104.062423\">10.1103/physreva.104.062423</a>.","ieee":"R. A. Medina Ramos and M. Serbyn, “Duality approach to quantum annealing of the 3-variable exclusive-or satisfiability problem (3-XORSAT),” <i>Physical Review A</i>, vol. 104, no. 6. American Physical Society, 2021.","ama":"Medina Ramos RA, Serbyn M. Duality approach to quantum annealing of the 3-variable exclusive-or satisfiability problem (3-XORSAT). <i>Physical Review A</i>. 2021;104(6). doi:<a href=\"https://doi.org/10.1103/physreva.104.062423\">10.1103/physreva.104.062423</a>","chicago":"Medina Ramos, Raimel A, and Maksym Serbyn. “Duality Approach to Quantum Annealing of the 3-Variable Exclusive-or Satisfiability Problem (3-XORSAT).” <i>Physical Review A</i>. American Physical Society, 2021. <a href=\"https://doi.org/10.1103/physreva.104.062423\">https://doi.org/10.1103/physreva.104.062423</a>.","apa":"Medina Ramos, R. A., &#38; Serbyn, M. (2021). Duality approach to quantum annealing of the 3-variable exclusive-or satisfiability problem (3-XORSAT). <i>Physical Review A</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physreva.104.062423\">https://doi.org/10.1103/physreva.104.062423</a>","short":"R.A. Medina Ramos, M. Serbyn, Physical Review A 104 (2021).","ista":"Medina Ramos RA, Serbyn M. 2021. Duality approach to quantum annealing of the 3-variable exclusive-or satisfiability problem (3-XORSAT). Physical Review A. 104(6), 062423."},"article_processing_charge":"No","publication":"Physical Review A","type":"journal_article","isi":1,"issue":"6","year":"2021","department":[{"_id":"MaSe"}],"language":[{"iso":"eng"}],"publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ec_funded":1,"doi":"10.1103/physreva.104.062423","publisher":"American Physical Society","intvolume":"       104","oa_version":"Preprint","day":"14","external_id":{"isi":["000753659200004"],"arxiv":["2106.06344"]}}]