arXiv subjects

Naga Dileep Varikuti

Publications and source records attributed to Naga Dileep Varikuti.

13 recordsLinked to original sources

arXiv2026

Non-Kolmogorov-Arnold-Moser Quantum Sensors for Quantum Parameter Estimation

Non-KAM (Kolmogorov-Arnold-Moser) systems, when subjected to weak time-dependent perturbations, exhibit an abrupt transition to classical chaos through the breakdown of invariant phase-space tori. We showcase the utilization of non-KAM systems in the quantum regime as quantum sensors, leveraging their sensitivity at \textit{resonances}. Quantum Fisher information (QFI) is a central quantity in quantum parameter estimation theory that measures how much information a quantum state contains about an unknown parameter that is encoded into it. In other words, it quantifies the sensitivity of a quantum state to small changes in that parameter. In this work, through numerical analysis in conjunction with analytical results, we study the performance of the non-KAM systems for quantum sensing applications by computing the QFI. We find that the growth of the QFI is remarkably enhanced when the resonance condition is satisfied. For frequency estimation under Floquet unitary encodings, we derive a transport bound: if the mean excitation number grows as $\langle\hat n(t)\rangle\sim t^α$, the QFI obeys $I(t)\lesssim t^{2α+2}$. The quantum kicked harmonic oscillator, a paradigmatic non-KAM system, realizes the full hierarchy: localized dynamics ($α=0$) yield quadratic growth, delocalized diffusion along stochastic webs ($α=1$) yields quartic growth, and translationally invariant resonances ($α=2$) saturate the bound with anomalous hexic growth, $I(t)\sim t^{6}$, established analytically at resonance $R=2$ and numerically at $R=4$. The enhancement stems from resonance-induced translational symmetry rather than exponential instability, identifying non-KAM resonances as a metrological resource distinct from chaos-assisted and criticality-based sensing.

quant-ph↗

arXiv2026

Deep Thermalization and Measurements of Quantum Resources

Quantum resource theories provide a unified framework for characterizing useful quantum phenomena subject to physical constraints but are notoriously hard to assess in experimental systems. In this letter, we introduce a unified protocol for quantifying the resource-generating power of arbitrary quantum evolutions applicable to multiple resource theories. It is based on deep thermalization, which has recently gained attention for its role in the emergence of quantum state designs from partial projective measurements. Central to our approach is the use of projected ensembles, recently employed to probe deep thermalization, together with new twirling identities that allow us to directly infer the resource-generating powers of the underlying dynamics. These identities further reveal how resources build up and thermalize in generic quantum circuits. Finally, we show that quantum resources themselves undergo deep thermalization at the subsystem level, offering a complementary and another experimentally accessible route to infer the resource-generating powers. Our work connects deep thermalization to resource quantification, offering a new perspective on the essential role of various resources in generating state designs and enabling efficient estimation of quantum resources in experiment.

quant-ph↗

arXiv2026

Instabilities in a Non-KAM System via Information Scrambling: A Note

We study operator growth in quantized non-KAM systems using out-of-time-ordered correlators (OTOCs), focusing on the kicked harmonic oscillator as a representative example. Since the classical harmonic oscillator is degenerate, the dynamics fall outside the usual Kolmogorov-Arnold-Moser (KAM) framework, and resonances play a central role in shaping the phase space. We examine the system near resonances, where the ratio between the oscillator and driving frequencies takes integer values. Even though the classical Lyapunov exponent remains small at these points, and hence no conventional chaos, the phase space still undergoes strong structural changes. The OTOCs are particularly sensitive to these resonances, with a quadratic-in-time growth at resonance compared to linear growth away from it. Within a perturbative treatment, we derive closed-form expressions for the OTOCs and uncover a number-theoretic structure emerging in the behavior of OTOCs, governed by the Euler totient function of the frequency ratio. Overall, the results we present in this short note imply that resonant structures can play an important role in controlling information spreading.

quant-ph↗

arXiv2026

Quantum resources in non-stoquastic quantum annealing

Quantum annealing promises to solve combinatorial optimization problems by preparing the ground state of a target Hamiltonian. Standard annealing protocols are, however, stoquastic and can thus be simulated by sign-problem-free quantum Monte-Carlo methods. To obtain a true quantum advantage, it has been proposed to use non-stoquastic catalyst Hamiltonians. Active only at intermediate stages of the protocol, these can, for certain problems, convert first-order into second-order quantum phase transitions and thus permit an exponential speedup over the stoquastic protocol. At the same time, the non-stoquastic catalyst renders quantum Monte-Carlo methods inefficient. It remains, however, an open question how other classical computation methods are affected by the non-stoquastic terms. We address this question by computing quantum resources -- entanglement entropy and stabilizer Rényi entropy -- whose presence makes classical computations based on tensor networks and stabilizer-tableau methods exponentially hard. We compare these with the spectral gap along the annealing path for two paradigmatic benchmark models, the fully connected $p$-spin model and a geometrically local Ising model. While the exact behavior shows a subtle dependency on the underlying model and the annealing path, our numerics suggest consistently that the scaling of entanglement and non-stabilizerness is at least maintained in the deeply non-stoquastic regime and in some cases even significantly enhanced. Our results thus suggest that improvements of quantum performance in non-stoquastic annealing coincide with significant presence of quantum computational resources.

quant-ph↗

arXiv2026

Loschmidt echo and scrambling of systematic errors in tomography -- a quantum signature of chaos

How does quantum chaos lead to rapid scrambling of information as well as systematic errors across a system when one introduces perturbations in the dynamics? What are its consequences for the reliability of quantum simulations and quantum information processing? We employ continuous measurement quantum tomography as a paradigm to study these questions. The measurement record is generated as a sequence of expectation values of a Hermitian observable evolving under repeated application of the Floquet map of the quantum kicked top. We construct a quantity to capture the scrambling of systematic errors, an out-of-time-ordered correlator (OTOC), that serves as a signature of chaos and quantifies the spread of errors. We show that the spread of errors, as quantified by the OTOC, is related to the operator Loschmidt echo (OLE), which is defined as the Hilbert-Schmidt inner product of the operators $\mathcal{O}_n$ and $\mathcal{O'}_n$ generated from repeated application of the Floquet map for ideal (unperturbed) dynamics and the \emph{true} (perturbed) dynamics, respectively. This also gives us an operational interpretation of the Loschmidt echo for operators by connecting it to the performance of quantum tomography. We show how our results demonstrate not only a link between LE and scrambling of errors different than previous studies, but that such a link can have operational consequences in quantum information processing.

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arXiv2026

Impact of Clifford operations on non-stabilizing power and quantum chaos

Non-stabilizerness, alongside entanglement, is a crucial ingredient for fault-tolerant quantum computation and achieving a genuine quantum advantage. Despite recent progress, a complete understanding of the generation and thermalization of non-stabilizerness in circuits that mix Clifford and non-Clifford operations remains elusive. While Clifford operations do not generate non-stabilizerness, their interplay with non-Clifford gates can strongly impact the overall non-stabilizing dynamics of generic quantum circuits. In this work, we establish a direct relationship between the final non-stabilizing power and the individual powers of the non-Clifford gates, in circuits where these gates are interspersed with random Clifford operations. By leveraging this result, we unveil the thermalization of non-stabilizing power to its Haar-averaged value in generic circuits. As a precursor, we analyze two-qubit gates and illustrate this thermalization in analytically tractable systems. Extending this, we explore the operator-space non-stabilizing power and demonstrate its behavior in physical models. Finally, we examine the role of non-stabilizing power in the emergence of quantum chaos in brick-wall quantum circuits. Our work elucidates how non-stabilizing dynamics evolve and thermalize in quantum circuits and thus contributes to a better understanding of quantum computational resources and of their role in quantum chaos.

quant-ph↗

arXiv2024

Information acquisition, scrambling, and sensitivity to errors in quantum chaos

Signatures of chaos can be understood by studying quantum systems whose classical counterpart is chaotic. However, the concepts of integrability, non-integrability and chaos extend to systems without a classical analogue. Here, we first review the classical route from order into chaos. Since nature is fundamentally quantum, we discuss how chaos manifests in the quantum domain. We briefly describe semi-classical methods, and discuss the consequences of chaos in quantum information processing. We review the quantum version of Lyapunov exponents, as quantified by the out-of-time ordered correlators (OTOC), Kolmogorov-Sinai (KS) entropy and sensitivity to errors. We then review the study of signatures of quantum chaos using quantum tomography. Classically, if we know the dynamics exactly, as we maintain a constant coarse-grained tracking of the trajectory, we gain exponentially fine-grained information about the initial condition. In the quantum setting,as we track the measurement record with fixed signal-to-noise, we gain increasing information about the initial condition. In the process, we have given a new quantification of operator spreading in Krylov subspaces with quantum state reconstruction. The study of these signatures is not only of theoretical interest but also of practical importance.

quant-ph↗

arXiv2024

Quantum Information Scrambling, Chaos, Sensitivity, and Emergent State Designs

Understanding quantum chaos is of profound theoretical interest and carries significant implications for various applications, from condensed matter physics to quantum error correction. Recently, out-of-time ordered correlators (OTOCs) have emerged as a powerful tool to quantify quantum chaos. For a given quantum system, the OTOCs measure incompatibility between an operator evolved in the Heisenberg picture and an unevolved operator. In the first part of this thesis, we employ OTOCs to study the dynamical sensitivity of a perturbed non-Komogorov-Arnold-Moser (non-KAM) system in the quantum limit as the parameter that characterizes the $\textit{resonance}$ condition is slowly varied. For this purpose, we consider a quantized kicked harmonic oscillator (KHO) model that displays stochastic webs in the phase space. The OTOC analysis is followed by a study of quantum Fisher information (QFI) at the resonances and a comparison with the non-resonance cases. We shall show that scaling of the QFI in time is enhanced at the resonances, making the dynamics of the non-KAM systems good candidates for quantum sensing. In the following chapter, we study the OTOCs in a bipartite system of kicked coupled tops with a special focus on the mixed phase space OTOC dynamics. The last part of the thesis is devoted to the study of the emergence of quantum state designs as a signature of quantum chaos and the role of symmetries in this phenomenon. Recently proposed projected ensemble framework utilizes quantum chaos as a resource to construct approximate higher-order state designs. Despite being ubiquitous, the effects of symmetries on the emergence of quantum state designs remain under-explored. We thoroughly investigate this by demonstrating the interplay between symmetries and measurements in constructing approximate state designs. Finally, we outline a few open directions relevant to the current thesis.

quant-ph↗

arXiv2024

Unraveling the emergence of quantum state designs in systems with symmetry

Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and benchmarking various quantum protocols with broad applications ranging from circuit designs to black hole physics. Symmetries, on the other hand, are expected to reduce the randomness of a state. Despite being ubiquitous, the effects of symmetry on quantum state designs remain an outstanding question. The recently introduced projected ensemble framework generates efficient approximate state $t$-designs by hinging on projective measurements and many-body quantum chaos. In this work, we examine the emergence of state designs from the random generator states exhibiting symmetries. Leveraging on translation symmetry, we analytically establish a sufficient condition for the measurement basis leading to the state $t$-designs. Then, by making use of the trace distance measure, we numerically investigate the convergence to the designs. Subsequently, we inspect the violation of the sufficient condition to identify bases that fail to converge. We further demonstrate the emergence of state designs in a physical system by studying the dynamics of a chaotic tilted field Ising chain with translation symmetry. We find faster convergence of the trace distance during the early time evolution in comparison to the cases when the symmetry is broken. To delineate the general applicability of our results, we extend our analysis to other symmetries. We expect our findings to pave the way for further exploration of deep thermalization and equilibration of closed and open quantum many-body systems.

quant-ph↗

arXiv2024

Out-of-Time Ordered Correlators in Kicked Coupled Tops: Information Scrambling in Mixed Phase Space and the Role of Conserved Quantities

We study operator growth in a bipartite kicked coupled tops (KCT) system using out-of-time ordered correlators (OTOCs), which quantify ``information scrambling" due to chaotic dynamics and serve as a quantum analog of classical Lyapunov exponents. In the KCT system, chaos arises from the hyper-fine coupling between the spins. Due to a conservation law, the system's dynamics decompose into distinct invariant subspaces. Focusing initially on the largest subspace, we numerically verify that the OTOC growth rate aligns well with the classical Lyapunov exponent for fully chaotic dynamics. While previous studies have largely focused on scrambling in fully chaotic dynamics, works on mixed-phase space scrambling are sparse. We explore scrambling behavior in both mixed-phase space and globally chaotic dynamics. In the mixed phase space, we use Percival's conjecture to partition the eigenstates of the Floquet map into ``regular" and ``chaotic." Using these states as the initial states, we examine how their mean phase space locations affect the growth and saturation of the OTOCs. Beyond the largest subspace, we study the OTOCs across the entire system, including all other smaller subspaces. For certain initial operators, we analytically derive the OTOC saturation using random matrix theory (RMT). When the initial operators are chosen randomly from the unitarily invariant random matrix ensembles, the averaged OTOC relates to the linear entanglement entropy of the Floquet operator, as found in earlier works. For the diagonal Gaussian initial operators, we provide a simple expression for the OTOC.

quant-ph↗

arXiv2023

Quantifying operator spreading and chaos in Krylov subspaces with quantum state reconstruction

We study operator spreading in many-body quantum systems by its potential to generate an informationally complete measurement record in quantum tomography. We adopt continuous weak measurement tomography for this purpose. We generate the measurement record as a series of expectation values of an observable evolving under the desired dynamics, which can show a transition from integrability to complete chaos. We find that the amount of operator spreading, as quantified by the fidelity in quantum tomography, increases with the degree of chaos in the system. We also observe a remarkable increase in information gain when the dynamics transitions from integrable to nonintegrable. We find our approach in quantifying operator spreading is a more consistent indicator of quantum chaos than Krylov complexity as the latter may correlate/anti-correlate or show no explicit behavior with the level of chaos in the dynamics. We support our argument through various metrics of information gain for two models: the Ising spin chain with a tilted magnetic field and the Heisenberg XXZ spin chain with an integrability-breaking field. Our paper gives an operational interpretation for operator spreading in quantum chaos.

quant-ph↗

arXiv2023

Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators

Non-KAM (Kolmogorov-Arnold-Moser) systems, when perturbed by weak time-dependent fields, offer a fast route to classical chaos through an abrupt breaking of invariant phase space tori. In this work, we employ out-of-time-order correlators (OTOCs) to study the dynamical sensitivity of a perturbed non-KAM system in the quantum limit as the parameter that characterizes the $\textit{resonance}$ condition is slowly varied. For this purpose, we consider a quantized kicked harmonic oscillator (KHO) model, which displays stochastic webs resembling Arnold's diffusion that facilitate large-scale diffusion in the phase space. Although the Lyapunov exponent of the KHO at resonances remains close to zero in the weak perturbative regime, making the system weakly chaotic in the conventional sense, the classical phase space undergoes significant structural changes. Motivated by this, we study the OTOCs when the system is in resonance and contrast the results with the non-resonant case. At resonances, we observe that the long-time dynamics of the OTOCs are sensitive to these structural changes, where they grow quadratically as opposed to linear or stagnant growth at non-resonances. On the other hand, our findings suggest that the short-time dynamics remain relatively more stable and show the exponential growth found in the literature for unstable fixed points. The numerical results are backed by analytical expressions derived for a few special cases. We will then extend our findings concerning the non-resonant cases to a broad class of near-integrable KAM systems.

nlin.CD↗

arXiv2020

Exponential speedup in measuring out-of-time-ordered correlators with a single bit of quantum information

Out-of-time-ordered correlators (OTOC) are a quantifier of quantum information scrambling and quantum chaos. We propose an efficient quantum algorithm to measure OTOCs that provides an exponential speed-up over the best known classical algorithm provided the OTOC operator to be estimated admits an efficient gate decomposition. We also discuss a scheme to obtain information about the eigenvalue spectrum and the spectral density of OTOCs.

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