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Yoshihiko Hasegawa

Publications and source records attributed to Yoshihiko Hasegawa.

At least 19 recordsLinked to original sources
arXiv2026

Thermodynamics of classifiers

The rise of artificial intelligence has led to a growing demand for computational power. In this situation, energy-efficient computing methods are being actively investigated, which raises a fundamental question: what is the relationship between computational error and thermodynamic cost? Here, we derive the error-cost trade-off in the binary classifier by considering classification based on nonequilibrium thermodynamics. We derive trade-off relations showing that classification error cannot be lower than fundamental bounds set by thermodynamic quantities: entropy production, which measures irreversibility, and dynamical activity, which quantifies the activity of the system. Our results show that when entropy production or dynamical activity vanishes, the classification error reaches $1/2$, equivalent to random guessing, whereas greater thermodynamic costs enable lower error. The results establish a quantitative trade-off in physical information processing, potentially leading to the development of energy-efficient computing devices.

cond-mat.stat-mech↗
arXiv2026

Heisenberg Scaling in Many-Body Kinetic Uncertainty Relation via Quantum Feedback

Kinetic uncertainty relations impose a fundamental constraint on counting precision by requiring large dynamical activity to suppress fluctuations. For $N$ independent constituents, the activity is additive and scales as $O(N)$, so the corresponding precision bound improves only as $O(1/N)$. A central question is whether many-body quantum systems can instead achieve Heisenberg scaling, with relative variance suppressed as $O(1/N^{2})$. Such scaling could enable substantially enhanced precision in quantum devices, including quantum clocks. Superradiance appears to provide a natural route because its collective emission activity can scale as $O(N^2)$. We show, however, that superradiance alone fails to achieve Heisenberg scaling because this enhanced activity is transient. We then demonstrate that jump-conditioned quantum feedback stabilizes the superradiant high-activity regime and converts this collective enhancement into Heisenberg scaling. We establish this mechanism analytically using a many-body kinetic uncertainty relation and mean-field analysis, and demonstrate through quantum-trajectory simulations that the actual relative counting fluctuation scales as $O(1/N^{2})$.

quant-ph↗
arXiv2026

Anisotropic information geometry of entropy production

We reveal that the information geometry of entropy production exhibits an intrinsic anisotropy, providing a unified origin for the inequivalent geometric constraints obeyed by its different components. Using a hierarchical projection structure of quantum relative entropy, we derive an exact orthogonal decomposition of entropy production into three distinct geometric contributions associated with the deviation of the Gibbs projection temperature from the reference temperature, the deviation of the environment from its Gibbs projection state, and system--environment correlations. We demonstrate that these contributions obey fundamentally different geometric bounds: the first reduces to a classical Kullback--Leibler divergence and admits no universal upper bound in terms of the trace distance and the system and environment dimensions alone, whereas the latter two admit rigorous distance-based bounds with dimension-dependent factors. The framework also applies to classical Markovian dynamics described solely in terms of the system state, for which the system--environment correlation contribution is absent from the decomposition. Combining this geometric decomposition with dynamical speed limits, we obtain rigorous bounds on entropy production expressed solely in terms of physically accessible quantities, such as the mean energy and Hamiltonian variance.

quant-ph↗
arXiv2026

Trade-off between Cooling-Step Count and Geometric Implementation Cost in Non-Markovian Algorithmic Cooling

Quantum cooling is important for reliable quantum computation but involves a trade-off between cooling performance and implementation resources. Although reservoir memory can improve particular aspects of cooling performance, the associated resource cost, particularly for circuit implementation, remains insufficiently understood. Here, we investigate how reservoir memory affects the trade-off between cooling performance quantified by the cooling-step count and geometric implementation cost in single-qubit heat-bath algorithmic cooling. Using a pseudomode mapping, we represent the non-Markovian damped Jaynes--Cummings dynamics by a repeated collision circuit and evaluate its geometric implementation cost. Using matrix-based simulations and an implementation on the ibm_kawasaki Heron r2 processor, we identify a trade-off: suppressing reservoir memory reduces the cooling-step count but generally increases the geometric protocol cost. Our work provides a resource-based perspective on reservoir engineering for algorithmic cooling.

quant-ph↗
arXiv2026

Unified quantification of entanglement and magic in information scrambling and their trade-off relation

Entanglement and magic are among the most fundamental properties unique to quantum systems. Each quantity captures a different aspect of non-classical behavior, and each can be regarded as a resource within its own operational setting. However, the interrelation between them has not yet been fully clarified, and whether a more fundamental measure exists remains an open question. Addressing these issues is essential for deepening our understanding of quantumness. In this study, we establish a unified resource theory of information scrambling, consisting of two types: entanglement scrambling and magic scrambling. We introduce a measure that jointly characterizes both types of scrambling. This unified approach reveals a rigorous trade-off relation between entanglement and magic scrambling, as the exact maximum value of the proposed measure can be derived analytically. Furthermore, we quantify the scrambling capability of unitary transformations in terms of their ability to amplify this measure. We also discuss the relevance of our framework to the Pauli propagation method as a practical application. Our work provides insights into the connection between entanglement and magic that extend beyond the context of information scrambling.

quant-ph↗
arXiv2026

Lie-Algebraic Subspace Quantization for Zero-Shot Quantum Learning and Barren-Plateau Mitigation

The barren plateau phenomenon severely limits the scalability of parameterized quantum circuits (PQCs). We present an analytical framework for zero-shot classical-to-quantum parameter transfer and manifold-based model merging without quantum-side optimization. Our parameter transfer map converts classical neural-network weights into low-dimensional quantum evolutions using Stiefel subspace selection, nearest-unitary polar projection, and logarithmic generator extraction. We prove a Subspace Quantization Theorem that bounds the reconstruction error by geometric truncation and exact non-unitarity, with the latter becoming second order in the near-unitary regime. Identity-centered architectures naturally produce generators near the identity, avoiding logarithm branch-cut singularities and mitigating initialization-time gradient concentration. We further derive an explicit error bound for manifold-based model merging and show that the same construction provides a warm-start initialization whose active dynamics remain confined to a k-dimensional subspace. Experiments on IBM ibm_kobe demonstrate Hellinger fidelity of 0.987 at k=8, while subspace gradients remain resolvable up to 128 physical qubits.

quant-ph↗
arXiv2026

Thermodynamic uncertainty relation for generalized time-reversal observables

Time-reversal symmetry plays an essential role in the thermodynamic uncertainty relations, which bound the fluctuations of observables in terms of the associated dissipation. In fact, thermodynamic uncertainty relations are typically derived under the assumption that the observable of interest is antisymmetric under time reversal. This also suggests that existing thermodynamic uncertainty relations are restricted to a limited class of observables. In this paper, we mitigate this restriction by introducing a new class of observables that do not exhibit the exact antisymmetry but change the sign under time reversal. We call it generalized time reversal and derive a broadly applicable thermodynamic uncertainty relation for observables with this condition. The generalization is achieved by direct statistical arguments on the observable distributions and holds for both deterministic and stochastic dynamics. We demonstrate the derived thermodynamic uncertainty relation with observables subjected to rectifications, showing that the precision of generalized observables remains expressible in terms of the dissipative cost. The result extends the scope of thermodynamic uncertainty relations beyond the reach of previous frameworks relying on the exact antisymmetry.

cond-mat.stat-mech↗
arXiv2026

Trade-off Relation for Black Hole Entropy Fluctuations

Black holes respond to infalling quantum matter fields by changing their entropy. Since such matter is quantum in nature, the entropy response should be sensitive to its quantum fluctuations. We show, within stochastic semiclassical gravity, that a horizon cannot record relevant quantum information with arbitrarily small entropy fluctuations. For the infalling photons encoding which-path information in the Danielson-Satishchandran-Wald decoherence experiment, we derive a trade-off relation between the stochastic variance of the black hole entropy change and the photon number.

gr-qc↗
arXiv2026

Structural $f$-divergence: Tight universal bounds for cost function moments and gradients in parameterized quantum circuits

The barren plateau phenomenon, in which cost-function gradients of variational quantum algorithms vanish exponentially, remains a central obstacle for near-term quantum computing. Existing analyses typically depend on t-design or Haar-random assumptions and bound quantities at the level of unitary distributions, offering limited insight for designing probability measures on the parameter space of parameterized quantum circuits. In this paper, we introduce the structural $f$-divergence, a symmetric $f$-divergence-based measure between probability distributions on the parameter space. We establish analytically trade-off inequalities that bound the discrepancies in the expected gradient magnitude and in the cost-function moments between a distribution on PQC and a reference distribution; equality is attained by a minimal one-qubit, one-layer ansatz. As applications, we derive necessary conditions on probability measures for avoiding BPs and cost concentration, and sufficient conditions that suppress noise-induced deviations.

quant-ph↗
arXiv2026

Thermodynamic Recycling of Algorithmic Failure Branches: Quantum-Computer Demonstration with Quantum Error Correction

Thermodynamic trade-off relations dictate fundamental limits on the performance of thermodynamic tasks through costs such as heat dissipation. Here, we propose a framework called thermodynamic recycling to circumvent these limits in quantum processors by exploiting failure branches of quantum algorithms, which are usually discarded. The key component is an athermal bath naturally generated during the resetting of a failure branch. By coupling this bath to a target system prior to relaxation, thermodynamic tasks can be performed beyond conventional thermodynamic limits. We apply this framework to information erasure and derive the reduction in heat dissipation analytically. As a demonstration, we implement our framework on IBM's superconducting quantum processor by combining the Harrow--Hassidim--Lloyd algorithm with three-qubit quantum error correction, thereby reducing the heat dissipated in erasing syndrome information. Despite substantial noise and errors in current hardware, our method achieves erasure with heat dissipation below the Landauer limit. This work establishes an operational connection between quantum computing and quantum thermodynamics for resource-efficient quantum computation.

quant-ph↗
arXiv2026

Optimal Control to Minimize Dissipation and Fluctuations in Open Quantum Systems Beyond Slow and Rapid Regimes

Optimal control is a central problem in quantum thermodynamics. When minimizing dissipated work and work fluctuations defined via the two-point measurement scheme in open quantum systems, existing approaches largely focus on the rapid- and slow-driving limits, leaving the behavior at intermediate timescales elusive. In this work, by numerically optimizing the driving protocols, we demonstrate that the open quantum systems exhibit distinct optimal structures not captured by the conventional limits. Specifically, in the coherent spin-boson model, we find that the optimal protocol switches discontinuously between distinct locally optimal solutions as the relative weight between dissipation and fluctuations is varied. Furthermore, for a single-level quantum dot coupled to a fermionic reservoir, the optimized protocol develops a characteristic multi-step structure.

quant-ph↗
arXiv2026

Kinetic Uncertainty Relation in Collective Dissipative Quantum Many-Body Systems

Attaining the ultimate precision remains a central objective in the engineering of nanoscale systems and the investigation of nonequilibrium processes. While thermodynamic and kinetic uncertainty relations establish fundamental precision bounds, prior derivations in the quantum regime have remained confined to single-body systems. Consequently, the ultimate precision limits for interacting many-body systems have been unknown. In this Letter, we analytically formulate a kinetic uncertainty relation for a many-body system undergoing collective dissipation, a paradigmatic model of boundary time crystals. By applying a mean-field approximation, we derive lower bounds for relative fluctuations expressed in terms of clear physical quantities. Our analysis identifies a cooperative enhancement mechanism, demonstrating that collective interactions allow the precision to scale with the number of particles. We validate these findings through numerical simulations across the stationary, critical, and boundary time crystal phases. Our work presents the first theoretical description of precision bounds in collective dissipative quantum many-body systems for an arbitrary particle number $N$, providing a solid foundation for designing future quantum technologies that exploit many-body phenomena.

quant-ph↗
arXiv2026

High-order interactions in quantum optomechanics: fluctuations, dynamics and thermodynamics

Quantum optomechanics describes the interaction between a confined field and a fluctuating wall due to radiation pressure. The dynamics of this system is typically understood using perturbation theory up to second order in the small coupling. Improving beyond this regime can shed light onto new phenomena. In this work we study high-order resonant wall-field interactions characterized by two- and three-phonon scattering processes. We obtain the Hamiltonian, compute the perturbed energy spectrum and explicitly calculate corrections to the ground state. Finally, we study the dynamics of the system when second- and third-order resonance conditions are activated, showing that the presence of high-order terms in the Hamiltonian drastically affects the populations of all particles, as well as the entropy production rate.

quant-ph↗
arXiv2026

Unified speed limits in classical and quantum dynamics via temporal Fisher information

The importance of Fisher information is increasing in nonequilibrium thermodynamics, as it has played a fundamental role in trade-off relations such as thermodynamic uncertainty relations and speed limits. In this work, we investigate temporal Fisher information, which measures the temporal information content encoded in probability distributions, for both classical and quantum systems. We establish that temporal Fisher information is bounded from above by physical costs, such as entropy production in classical Langevin and Markov processes and the variance of interaction Hamiltonians in open quantum systems. Conversely, temporal Fisher information is bounded from below by statistical distances (e.g., the Bhattacharyya arccos distance), leading to classical and quantum speed limits that constrain the minimal time required for state transformations. We perform numerical simulations on two quantum dot models to validate the obtained bounds. Our work provides a unified perspective on speed limits from the point of view of temporal Fisher information in both classical and quantum dynamics.

quant-ph↗
arXiv2026

Entropic trade-off relations in stochastic thermodynamics via replica Markov processes

Traditional thermodynamic trade-off relations usually apply to quantities that depend linearly on probability distributions. In contrast, many important information-theoretic measures, such as entropies, are nonlinear and therefore difficult to analyze with existing frameworks. Motivated by replica methods in quantum information and spin-glass theory, we introduce replica Markov processes, i.e., Markovian dynamics of $K$ independent, identical copies, and derive trade-off relations that bound relative moments of replica observables in terms of the dynamical activity. By choosing appropriate replica observables, these inequalities translate into bounds on nonlinear quantities of the original single process. Focusing on entropic measures of uncertainty, we obtain upper bounds on both the time derivative and the value of the Tsallis entropy for general trajectory-observable distributions. Moreover, we derive upper bounds on the Rényi and Tsallis entropies, where the bounds involve the initial dynamical activity. Analogous bounds can be derived for the entropies of the state distribution. In particular, we provide upper bounds on both the time derivative and the value of the Tsallis entropy of state distributions. Moreover, we show that the Rényi and Tsallis entropies of the state distribution are bounded from above by terms involving the local escape rate from the initial node. We also illustrate how replicas can be used to study other nonlinear functionals such as extreme-value observables. Finally, we extend the construction to continuously monitored open quantum systems, where the bounds are expressed in terms of the quantum dynamical activity. These results provide entropic counterparts to activity-based uncertainty relations and establish a general method for constraining nonlinear information-theoretic quantities in stochastic and quantum thermodynamics.

cond-mat.stat-mech↗
arXiv2026

Gradient Analysis of Barren Plateau in Parameterized Quantum Circuits with multi-qubit gates

The emergence of the Barren Plateau phenomenon poses a significant challenge to quantum machine learning. While most Barren Plateau analyses focus on single-qubit rotation gates, the gradient behavior of Parameterized Quantum Circuits built from multi-qubit gates remains largely unexplored. In this work, we present a general theoretical framework for analyzing the gradient properties of Parameterized Quantum Circuits with multi-qubit gates. Our method generalizes the direct computation framework, bypassing the Haar random assumption on parameters and enabling the calculation of the gradient expectation and variance. We apply this framework to single-layer and deep-layer circuits, deriving analytical results that quantify how gradient variance is co-determined by the size of the multi-qubit gate and the number of qubits, layers, and effective parameters. Numerical simulations validate our findings. Our study provides a refined framework for analyzing and optimizing Parameterized Quantum Circuits with complex multi-qubit gates.

quant-ph↗
arXiv2026

Unified entropy production in finite quantum systems

In finite-dimensional quantum systems, temperature cannot be uniquely defined. This, in turn, implies that there are several ways to define entropy production in finite-dimensional quantum systems, because the classical entropy production depends on temperature. We propose a unified definition of entropy production based on the difference in quantum relative entropy with respect to reference states characterized by effective temperatures. We demonstrate that the proposed definition naturally decomposes into a Clausius-type entropy production and an additional contribution arising from the time dependence of the effective temperature. Furthermore, we show that requiring the entropy production rate to take the conventional form as the sum of the entropy change and the heat flow constrains the effective temperature to be either constant or equal to a specific energy-matching effective temperature. For general initial states, entropy production can become negative, in which case we derive lower bounds on entropy production and establish sufficient conditions for its non-negativity using the trace distance.

quant-ph↗
arXiv2026

Sparse QUBO Formulation for Efficient Embedding via Network-Based Decomposition of Equality and Inequality Constraints

Quantum annealing is a promising approach for solving combinatorial optimization problems. However, its performance is often limited by the overhead of additional qubits required for embedding logical QUBO models onto quantum annealers. This overhead becomes severe when logical QUBO models have dense connectivity. Such dense structures frequently arise when formulating equality and inequality constraints. To address this issue, we propose a method to construct a significantly sparser logical QUBO model for these constraints. By adding auxiliary variables based on specific network structures, our approach decomposes the original constraint into smaller, more manageable constraints. We demonstrate that this method reduces the number of edges (quadratic terms) from $O(N^2)$ to $O(N)$ for the one-hot constraint and to $O(N\log N)$ in the worst case for general equality constraints, where $N$ is the number of variables. Experimental results on D-Wave's hardware show that our formulation leads to substantial reductions in the number of qubits required for embedding, shorter average chain lengths, lower chain break rates, and higher feasible solution rates compared to conventional methods. This work provides a practical tool for efficiently solving constrained optimization problems on current and future quantum annealers.

quant-ph↗