Pub Date : 2026-01-14DOI: 10.22331/q-2026-01-14-1965
Marius A. Oancea, Thomas B. Mieling, Giandomenico Palumbo
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. In this work, we use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. This construction is based on a general connection on a Hermitian vector bundle, which defines a notion of quantum state transport in parameter space, and a sub-bundle projector, which constrains the set of accessible quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by generalized Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor that contains an additional curvature contribution. To illustrate our results, we describe the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor, with its additional curvature contributions, is obtained in this case. As a concrete example, we consider Dirac fermions confined to a hyperbolic plane and demonstrate how spatial curvature influences the quantum geometry. This work sets the stage for further exploration of quantum systems in curved geometries, with applications in both high-energy physics and condensed matter systems.
{"title":"Quantum geometric tensors from sub-bundle geometry","authors":"Marius A. Oancea, Thomas B. Mieling, Giandomenico Palumbo","doi":"10.22331/q-2026-01-14-1965","DOIUrl":"https://doi.org/10.22331/q-2026-01-14-1965","url":null,"abstract":"The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor, which unifies the Berry curvature and the quantum metric. In this work, we use the differential-geometric framework of vector bundles to analyze the properties of parameter-dependent quantum states and generalize the quantum geometric tensor to this setting. This construction is based on a general connection on a Hermitian vector bundle, which defines a notion of quantum state transport in parameter space, and a sub-bundle projector, which constrains the set of accessible quantum states. We show that the sub-bundle geometry is similar to that of submanifolds in Riemannian geometry and is described by generalized Gauss-Codazzi-Mainardi equations. This leads to a novel definition of the quantum geometric tensor that contains an additional curvature contribution. To illustrate our results, we describe the sub-bundle geometry arising in the semiclassical treatment of Dirac fields propagating in curved spacetime and show how the quantum geometric tensor, with its additional curvature contributions, is obtained in this case. As a concrete example, we consider Dirac fermions confined to a hyperbolic plane and demonstrate how spatial curvature influences the quantum geometry. This work sets the stage for further exploration of quantum systems in curved geometries, with applications in both high-energy physics and condensed matter systems.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"81 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145968854","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 : 2026-01-14DOI: 10.22331/q-2026-01-14-1963
Sridhar Prabhu, Vladimir Kremenetski, Saeed A. Khan, Ryotatsu Yanagimoto, Peter L. McMahon
Conventionally in quantum sensing, the goal is to estimate one or more unknown parameters that are assumed to be deterministic – that is, they do not change between shots of the quantum-sensing protocol. We instead consider the setting where the parameters are stochastic: each shot of the quantum-sensing protocol senses parameter values that come from independent random draws. In this work, we explore three examples where the stochastic parameters are correlated and show how using entanglement provides a benefit in classification or estimation tasks: (1) a two-parameter classification task, for which there is an advantage in the low-shot regime; (2) an $N$-parameter estimation task and a classification variant of it, for which an entangled sensor requires just a constant number (independent of $N$) shots to achieve the same accuracy as an unentangled sensor using exponentially many (${sim}2^N$) shots; (3) classifying the magnetization of a spin chain in thermal equilibrium, where the individual spins fluctuate but the total spin in one direction is conserved – this gives a practical setting in which stochastic parameters are correlated in a way that an entangled sensor can be designed to exploit. We also present a theoretical framework for assessing, for a given choice of entangled sensing protocol and distributions to discriminate between, how much advantage the entangled sensor would have over an unentangled sensor. Our work motivates the further study of sensing correlated stochastic parameters using entangled quantum sensors – and since classical sensors by definition cannot be entangled, our work shows the possibility for entangled quantum sensors to achieve an exponential advantage in sample complexity over classical sensors, in contrast to the typical quadratic advantage.
{"title":"Exponential advantage in quantum sensing of correlated parameters","authors":"Sridhar Prabhu, Vladimir Kremenetski, Saeed A. Khan, Ryotatsu Yanagimoto, Peter L. McMahon","doi":"10.22331/q-2026-01-14-1963","DOIUrl":"https://doi.org/10.22331/q-2026-01-14-1963","url":null,"abstract":"Conventionally in quantum sensing, the goal is to estimate one or more unknown parameters that are assumed to be deterministic – that is, they do not change between shots of the quantum-sensing protocol. We instead consider the setting where the parameters are stochastic: each shot of the quantum-sensing protocol senses parameter values that come from independent random draws. In this work, we explore three examples where the stochastic parameters are correlated and show how using entanglement provides a benefit in classification or estimation tasks: (1) a two-parameter classification task, for which there is an advantage in the low-shot regime; (2) an $N$-parameter estimation task and a classification variant of it, for which an entangled sensor requires just a constant number (independent of $N$) shots to achieve the same accuracy as an unentangled sensor using exponentially many (${sim}2^N$) shots; (3) classifying the magnetization of a spin chain in thermal equilibrium, where the individual spins fluctuate but the total spin in one direction is conserved – this gives a practical setting in which stochastic parameters are correlated in a way that an entangled sensor can be designed to exploit. We also present a theoretical framework for assessing, for a given choice of entangled sensing protocol and distributions to discriminate between, how much advantage the entangled sensor would have over an unentangled sensor. Our work motivates the further study of sensing correlated stochastic parameters using entangled quantum sensors – and since classical sensors by definition cannot be entangled, our work shows the possibility for entangled quantum sensors to achieve an exponential advantage in sample complexity over classical sensors, in contrast to the typical quadratic advantage.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"37 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962801","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 : 2026-01-14DOI: 10.22331/q-2026-01-14-1962
Qilin Li, Atharva Vidwans, Yazhen Wang, Micheline B. Soley
We establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this framework to harness Bayesian statistics for improved measurement efficiency with rigorous interval estimates at all iterations of Iterative Quantum Amplitude Estimation. We demonstrate the resulting method, Bayesian Iterative Quantum Amplitude Estimation (BIQAE), accurately and efficiently estimates both quantum amplitudes and molecular ground-state energies to high accuracy, and show in analytic and numerical sample complexity analyses that BIQAE outperforms all other QAE approaches considered. Both rigorous mathematical proofs and numerical simulations conclusively indicate Bayesian statistics is the source of this advantage, a finding that invites further inquiry into the power of statistics to expedite the search for quantum utility.
{"title":"Harnessing Bayesian Statistics to Accelerate Iterative Quantum Amplitude Estimation","authors":"Qilin Li, Atharva Vidwans, Yazhen Wang, Micheline B. Soley","doi":"10.22331/q-2026-01-14-1962","DOIUrl":"https://doi.org/10.22331/q-2026-01-14-1962","url":null,"abstract":"We establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this framework to harness Bayesian statistics for improved measurement efficiency with rigorous interval estimates at all iterations of Iterative Quantum Amplitude Estimation. We demonstrate the resulting method, Bayesian Iterative Quantum Amplitude Estimation (BIQAE), accurately and efficiently estimates both quantum amplitudes and molecular ground-state energies to high accuracy, and show in analytic and numerical sample complexity analyses that BIQAE outperforms all other QAE approaches considered. Both rigorous mathematical proofs and numerical simulations conclusively indicate Bayesian statistics is the source of this advantage, a finding that invites further inquiry into the power of statistics to expedite the search for quantum utility.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"15 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962803","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 : 2026-01-08DOI: 10.22331/q-2026-01-08-1960
Roy Araiza, Yidong Chen, Marius Junge, Peixue Wu
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By leveraging Lipschitz norms inspired by quantum optimal transport theory, we rigorously establish the fundamental properties of this complexity measure. The flexibility in selecting the resource set allows us to derive effective lower bounds for gate complexities and simulation costs of both Hamiltonian simulations and dynamics of open quantum systems. Additionally, we demonstrate that this complexity measure exhibits linear growth for random quantum circuits and finite-dimensional quantum simulations, up to the Brown-Susskind threshold.
{"title":"Resource-Dependent Complexity of Quantum Channels","authors":"Roy Araiza, Yidong Chen, Marius Junge, Peixue Wu","doi":"10.22331/q-2026-01-08-1960","DOIUrl":"https://doi.org/10.22331/q-2026-01-08-1960","url":null,"abstract":"We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By leveraging Lipschitz norms inspired by quantum optimal transport theory, we rigorously establish the fundamental properties of this complexity measure. The flexibility in selecting the resource set allows us to derive effective lower bounds for gate complexities and simulation costs of both Hamiltonian simulations and dynamics of open quantum systems. Additionally, we demonstrate that this complexity measure exhibits linear growth for random quantum circuits and finite-dimensional quantum simulations, up to the Brown-Susskind threshold.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"25 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145919798","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 : 2026-01-08DOI: 10.22331/q-2026-01-08-1961
Uta Isabella Meyer, Ivan Šupić, Frédéric Grosshans, Damian Markham
Self-testing identifies quantum states and correlations that exhibit nonlocality, distinguishing them, up to local transformations, from other quantum states. Due to their strong nonlocality, it is known that all graph states can be self-tested in the standard setting – where parties are not allowed to communicate. Recently it has been shown that graph states display nonlocal correlations even when bounded classical communication on the underlying graph is permitted, a feature that has found applications in proving a circuit-depth separation between classical and quantum computing. In this work, we develop self testing in the framework of bounded classical communication, and we show that certain graph states can be robustly self-tested even allowing for communication. In particular, we provide an explicit self-test for the circular graph state and the honeycomb cluster state – the latter known to be a universal resource for measurement based quantum computation. Since communication generally obstructs self-testing of graph states, we further provide a procedure to robustly self-test any graph state from larger ones that exhibit nonlocal correlations in the communication scenario.
{"title":"Self-Testing Graph States Permitting Bounded Classical Communication","authors":"Uta Isabella Meyer, Ivan Šupić, Frédéric Grosshans, Damian Markham","doi":"10.22331/q-2026-01-08-1961","DOIUrl":"https://doi.org/10.22331/q-2026-01-08-1961","url":null,"abstract":"Self-testing identifies quantum states and correlations that exhibit nonlocality, distinguishing them, up to local transformations, from other quantum states. Due to their strong nonlocality, it is known that all graph states can be self-tested in the standard setting – where parties are not allowed to communicate. Recently it has been shown that graph states display nonlocal correlations even when bounded classical communication on the underlying graph is permitted, a feature that has found applications in proving a circuit-depth separation between classical and quantum computing. In this work, we develop self testing in the framework of bounded classical communication, and we show that certain graph states can be robustly self-tested even allowing for communication. In particular, we provide an explicit self-test for the circular graph state and the honeycomb cluster state – the latter known to be a universal resource for measurement based quantum computation. Since communication generally obstructs self-testing of graph states, we further provide a procedure to robustly self-test any graph state from larger ones that exhibit nonlocal correlations in the communication scenario.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"34 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145919882","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 : 2026-01-07DOI: 10.22331/q-2026-01-07-1959
Matthias Salzger, John H. Selby
There has been a recent surge of interest within the field of quantum foundations regarding incorporating ideas from general relativity and quantum gravity. However, many quantum information tools remain agnostic to the underlying spacetime. For instance, whenever we draw a quantum circuit the effective spacetime imposed by the connectivity of the physical qubits which will realize this circuit is not taken into account. In this work, we aim to address this limitation by extending the framework of process theories to include a background spacetime structure. We introduce the notion of process implementations, i.e., decompositions of a process. A process is then embeddable if and only if one of its implementations can be embedded in such a way that all the component processes are localized and all wires follow timelike paths. While conceptually simple, checking for embeddability is generally computationally intractable. We therefore work towards simplifying this problem as much as possible, identifying a canonical subset of implementations that determine both the embeddability of a process and the causal structures distinguishable at least in some process theory. Notably, we discover countably infinite ''zigzag'' causal structures beyond those typically considered. While these can be ignored in classical theory, they seem to be essential in quantum theory, as the quantum CNOT gate can be implemented by all zigzag structures but not in a standard causal structure, except in the trivial undecomposed way. These zigzags could be significant for quantum causal modeling and the study of novel quantum resources.
{"title":"A decompositional framework for process theories in spacetime","authors":"Matthias Salzger, John H. Selby","doi":"10.22331/q-2026-01-07-1959","DOIUrl":"https://doi.org/10.22331/q-2026-01-07-1959","url":null,"abstract":"There has been a recent surge of interest within the field of quantum foundations regarding incorporating ideas from general relativity and quantum gravity. However, many quantum information tools remain agnostic to the underlying spacetime. For instance, whenever we draw a quantum circuit the effective spacetime imposed by the connectivity of the physical qubits which will realize this circuit is not taken into account. In this work, we aim to address this limitation by extending the framework of process theories to include a background spacetime structure. We introduce the notion of process implementations, i.e., decompositions of a process. A process is then embeddable if and only if one of its implementations can be embedded in such a way that all the component processes are localized and all wires follow timelike paths. While conceptually simple, checking for embeddability is generally computationally intractable. We therefore work towards simplifying this problem as much as possible, identifying a canonical subset of implementations that determine both the embeddability of a process and the causal structures distinguishable at least in some process theory. Notably, we discover countably infinite ''zigzag'' causal structures beyond those typically considered. While these can be ignored in classical theory, they seem to be essential in quantum theory, as the quantum CNOT gate can be implemented by all zigzag structures but not in a standard causal structure, except in the trivial undecomposed way. These zigzags could be significant for quantum causal modeling and the study of novel quantum resources.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"14 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145919797","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 : 2025-12-31DOI: 10.22331/q-2025-12-31-1958
Fernando Lledó, Carlos Palazuelos, Julio I. de Vicente
Quantum networks are promising venues for quantum information processing. This motivates the study of the entanglement properties of the particular multipartite quantum states that underpin these structures. In particular, it has been recently shown that when the links are noisy two drastically different behaviors can occur regarding the global entanglement properties of the network. While in certain configurations the network displays genuine multipartite entanglement (GME) for any system size provided the noise level is below a certain threshold, in others GME is washed out if the system size is big enough for any fixed non-zero level of noise. However, this difference has only been established considering the two extreme cases of maximally and minimally connected networks (i.e. complete graphs versus trees, respectively). In this article we investigate this question much more in depth and relate this behavior to the growth of several graph theoretic parameters that measure the connectivity of the graph sequence that codifies the structure of the network as the number of parties increases. The strongest conditions are obtained when considering the degree growth. Our main results are that a sufficiently fast degree growth (i.e. $Omega(N)$, where $N$ is the size of the network) is sufficient for asymptotic robustness of GME, while if it is sufficiently slow (i.e. $o(log N)$) then the network becomes asymptotically biseparable. We also present several explicit constructions related to the optimality of these results.
{"title":"Asymptotic robustness of entanglement in noisy quantum networks and graph connectivity","authors":"Fernando Lledó, Carlos Palazuelos, Julio I. de Vicente","doi":"10.22331/q-2025-12-31-1958","DOIUrl":"https://doi.org/10.22331/q-2025-12-31-1958","url":null,"abstract":"Quantum networks are promising venues for quantum information processing. This motivates the study of the entanglement properties of the particular multipartite quantum states that underpin these structures. In particular, it has been recently shown that when the links are noisy two drastically different behaviors can occur regarding the global entanglement properties of the network. While in certain configurations the network displays genuine multipartite entanglement (GME) for any system size provided the noise level is below a certain threshold, in others GME is washed out if the system size is big enough for any fixed non-zero level of noise. However, this difference has only been established considering the two extreme cases of maximally and minimally connected networks (i.e. complete graphs versus trees, respectively). In this article we investigate this question much more in depth and relate this behavior to the growth of several graph theoretic parameters that measure the connectivity of the graph sequence that codifies the structure of the network as the number of parties increases. The strongest conditions are obtained when considering the degree growth. Our main results are that a sufficiently fast degree growth (i.e. $Omega(N)$, where $N$ is the size of the network) is sufficient for asymptotic robustness of GME, while if it is sufficiently slow (i.e. $o(log N)$) then the network becomes asymptotically biseparable. We also present several explicit constructions related to the optimality of these results.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"28 1","pages":"1958"},"PeriodicalIF":6.4,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894230","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 : 2025-12-30DOI: 10.22331/q-2025-12-30-1957
Sutapa Samanta, Derek S. Wang, Armin Rahmani, Aditi Mitra
Investigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the transverse-field Ising model, which can host a topological defect that performs the Kramers-Wannier duality transformation. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and binds a single zero mode. This zero mode is unusual as it lacks a localized partner in the same $mathbb{Z}_2$ sector and has an infinite lifetime, even in finite systems. Using Floquet driving of a closed Ising chain with a duality defect, we generate this zero mode in a digital quantum computer. We detect the mode by measuring its associated persistent autocorrelation function using an efficient sampling protocol and a compound strategy for error mitigation. We also show that the zero mode resides at the domain wall between two regions related by a Kramers-Wannier duality transformation. Finally, we highlight the robustness of the isolated zero mode to integrability- and symmetry-breaking perturbations. Our findings provide a method for exploring exotic topological defects, associated with noninvertible generalized symmetries, in digitized quantum devices.
{"title":"Isolated zero mode in a quantum computer from a duality twist","authors":"Sutapa Samanta, Derek S. Wang, Armin Rahmani, Aditi Mitra","doi":"10.22331/q-2025-12-30-1957","DOIUrl":"https://doi.org/10.22331/q-2025-12-30-1957","url":null,"abstract":"Investigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the transverse-field Ising model, which can host a topological defect that performs the Kramers-Wannier duality transformation. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and binds a single zero mode. This zero mode is unusual as it lacks a localized partner in the same $mathbb{Z}_2$ sector and has an infinite lifetime, even in finite systems. Using Floquet driving of a closed Ising chain with a duality defect, we generate this zero mode in a digital quantum computer. We detect the mode by measuring its associated persistent autocorrelation function using an efficient sampling protocol and a compound strategy for error mitigation. We also show that the zero mode resides at the domain wall between two regions related by a Kramers-Wannier duality transformation. Finally, we highlight the robustness of the isolated zero mode to integrability- and symmetry-breaking perturbations. Our findings provide a method for exploring exotic topological defects, associated with noninvertible generalized symmetries, in digitized quantum devices.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"6 1","pages":"1957"},"PeriodicalIF":6.4,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145894232","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 : 2025-12-24DOI: 10.22331/q-2025-12-24-1956
Beatrice Magni, Xhek Turkeshi
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results and perform large-scale simulations in regimes challenging for tensor network and Pauli-based methods. We begin by analyzing generalized stabilizer entropies, computable magic monotones in many-qudit systems, and identify a dynamical phase transition in the doping rate, marking the breakdown of classical simulability and the onset of Haar-random behavior. The critical behavior is governed by the qudit dimension and the magic content of the non-Clifford gate. Using the qudit $T$-gate as a benchmark, we show that higher-dimensional qudits converge faster to Haar-typical stabilizer entropies. For qutrits ($d=3$), analytical predictions match numerics on brickwork circuits, showing that locality plays a limited role in magic spreading. We also examine anticoncentration and entanglement growth, showing that $O(log N)$ non-Clifford gates suffice for approximating Haar expectation values to precision $varepsilon$, and relate antiflatness measures to stabilizer entropies in qutrit systems. Finally, we analyze out-of-time-order correlators and show that a finite density of non-Clifford gates is needed to induce chaos, with a sharp transition fixed by the local dimension, twice that of the magic transition. Altogether, these results establish a unified framework for diagnosing complexity in doped Clifford circuits and deepen our understanding of resource theories in multiqudit systems.
{"title":"Quantum Complexity and Chaos in Many-Qudit Doped Clifford Circuits","authors":"Beatrice Magni, Xhek Turkeshi","doi":"10.22331/q-2025-12-24-1956","DOIUrl":"https://doi.org/10.22331/q-2025-12-24-1956","url":null,"abstract":"We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results and perform large-scale simulations in regimes challenging for tensor network and Pauli-based methods. We begin by analyzing generalized stabilizer entropies, computable magic monotones in many-qudit systems, and identify a dynamical phase transition in the doping rate, marking the breakdown of classical simulability and the onset of Haar-random behavior. The critical behavior is governed by the qudit dimension and the magic content of the non-Clifford gate. Using the qudit $T$-gate as a benchmark, we show that higher-dimensional qudits converge faster to Haar-typical stabilizer entropies. For qutrits ($d=3$), analytical predictions match numerics on brickwork circuits, showing that locality plays a limited role in magic spreading. We also examine anticoncentration and entanglement growth, showing that $O(log N)$ non-Clifford gates suffice for approximating Haar expectation values to precision $varepsilon$, and relate antiflatness measures to stabilizer entropies in qutrit systems. Finally, we analyze out-of-time-order correlators and show that a finite density of non-Clifford gates is needed to induce chaos, with a sharp transition fixed by the local dimension, twice that of the magic transition. Altogether, these results establish a unified framework for diagnosing complexity in doped Clifford circuits and deepen our understanding of resource theories in multiqudit systems.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"20 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813652","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 : 2025-12-23DOI: 10.22331/q-2025-12-23-1955
Nhat A. Nghiem, Xianfeng David Gu, Tzu-Chieh Wei
Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be identified. Given a simplex, an important feature is called the Betti numbers, which roughly count the number of `holes' in different dimensions. Calculating Betti numbers exactly can be $#$P-hard, and approximating them can be NP-hard, which rules out the possibility of any generic efficient algorithms and unconditional exponential quantum speedup. Here, we explore the specific setting of a triangulated manifold. In contrast to most known methods to estimate Betti numbers, which rely on homology, we exploit the `dual' approach, namely, cohomology, combining the insight of the Hodge theory and de Rham cohomology. Our proposed algorithm can calculate its $r$-th normalized Betti number $beta_r/|S_r|$ up to some additive error $epsilon$ with running time $mathcal{O}Big(frac{log(|S_r^K| |S_{r+1}^K|)}{epsilon^2} log (log |S_r^K|) big( rlog |S_r^K| big) Big)$, where $|S_r|$ is the number of $r$-simplexes in the given complex. For the estimation of $r$-th Betti number $beta_r$ to a chosen multiplicative accuracy $epsilon'$, our algorithm has complexity $ mathcal{O}Big(frac{log(|S_r^K| |S_{r+1}^K|)}{epsilon'^2} big( frac{ Gamma}{beta_r}big)^2 (log |S_r^K|) log big( rlog |S_r^K| big) Big)$, where $Gamma leq |S_r^K|$ can be chosen. A detailed analysis is provided, showing that our cohomology framework can even perform exponentially faster than previous homology methods in several regimes. In particular, our method is most effective when $beta_r ll |S_r^K|$, which can offer more flexibility and practicability than existing quantum algorithms that achieve the best performance in the regime $beta_r approx |S_r^K|$.
{"title":"Quantum Algorithm for Estimating Betti Numbers Using Cohomology Approach","authors":"Nhat A. Nghiem, Xianfeng David Gu, Tzu-Chieh Wei","doi":"10.22331/q-2025-12-23-1955","DOIUrl":"https://doi.org/10.22331/q-2025-12-23-1955","url":null,"abstract":"Topological data analysis has emerged as a powerful tool for analyzing large-scale data. An abstract simplicial complex, in principle, can be built from data points, and by using tools from homology, topological features could be identified. Given a simplex, an important feature is called the Betti numbers, which roughly count the number of `holes' in different dimensions. Calculating Betti numbers exactly can be $#$P-hard, and approximating them can be NP-hard, which rules out the possibility of any generic efficient algorithms and unconditional exponential quantum speedup. Here, we explore the specific setting of a triangulated manifold. In contrast to most known methods to estimate Betti numbers, which rely on homology, we exploit the `dual' approach, namely, cohomology, combining the insight of the Hodge theory and de Rham cohomology. Our proposed algorithm can calculate its $r$-th normalized Betti number $beta_r/|S_r|$ up to some additive error $epsilon$ with running time $mathcal{O}Big(frac{log(|S_r^K| |S_{r+1}^K|)}{epsilon^2} log (log |S_r^K|) big( rlog |S_r^K| big) Big)$, where $|S_r|$ is the number of $r$-simplexes in the given complex. For the estimation of $r$-th Betti number $beta_r$ to a chosen multiplicative accuracy $epsilon'$, our algorithm has complexity $ mathcal{O}Big(frac{log(|S_r^K| |S_{r+1}^K|)}{epsilon'^2} big( frac{ Gamma}{beta_r}big)^2 (log |S_r^K|) log big( rlog |S_r^K| big) Big)$, where $Gamma leq |S_r^K|$ can be chosen. A detailed analysis is provided, showing that our cohomology framework can even perform exponentially faster than previous homology methods in several regimes. In particular, our method is most effective when $beta_r ll |S_r^K|$, which can offer more flexibility and practicability than existing quantum algorithms that achieve the best performance in the regime $beta_r approx |S_r^K|$.","PeriodicalId":20807,"journal":{"name":"Quantum","volume":"118 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145813651","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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