Papers

We investigate the surface flashover voltage threshold for SiO$_2$, SiN, and AlN thin films over micrometre scale lengths. Furthermore, we test the effects of different etching chemistries on SiO$_2$ layers. We find that there is little significant difference between untreated SiO$_2$ samples and those that have been etched with hydrogen fluoride or Transene AlPad Etch 639. SiN and AlN samples performed significantly better than all SiO$_2$ samples giving a 45% increase in surface flashover voltage at a distance of 5 $\mu$m with the difference increasing with electrode spacing.

This paper will deal with isolated laser pulses, those which last for a finite time interval and whose envelope function is strictly zero outside of this interval. We numerically calculate the Fourier transform of this function and study its asymptotic behavior at high frequencies. This work is motivated by recent results on the probability distributions of quadratic operators in second quantized systems. An example is the density of a material which is subject to zero point fluctuations in the phonon vacuum state. These distributions can decrease very slowly, leading to a relatively high probability for large fluctuations. If the operator is measured by a laser pulse, the rate of decrease of the distribution mirrors the rate of decrease of the pulse envelope Fourier transform. We describe a model for the creation of isolated pulses in which this Fourier transform falls as an exponential of a fractional power of frequency and find examples where this fraction is in the range 0.1 to 0.2. The probability distribution for large fluctuation has the same functional form and implies a significant probability for fluctuations very large compared to the variance.

Nonlocal interactions are known to generate volume-law entanglement entropy. However, their deeper impact on the fine structure of quantum correlations remains a key open question. In this work, we explore a bosonic nonlocal field theory, examining correlation measures beyond entanglement entropy, namely, mutual information and tripartite information. Using numerical lattice simulations, we show that the nonlocality scale, \(A\), not only determines the onset of volume-law behavior but also leads to striking features: notably, extremely long-range mutual information and an unusual monogamy structure. In this regime, increasing the separation between large regions can paradoxically enhance their multipartite entanglement. Through holographic duality, we verify that the Ryu-Takayanagi formula correctly captures the volume-law scaling of entropy. Yet, a significant tension emerges: while the field theory reveals rich spatial correlations, the holographic model predicts a complete suppression of both mutual and tripartite information in the volume-law phase. This non-monogamous behavior in the holographic description stands in sharp contrast to the monogamous and highly structured entanglement observed in the field theory. Our results demonstrate that nonlocality gives rise to quantum states of such complexity that conventional geometric models of spacetime fall short. This points to the need for a new framework that goes beyond geometry to fully capture the nature of these correlations.

We combine numerical and experimental approaches to study how impurities affect the maximum superflow in an annular Bose-Einstein condensate. By tuning the impurity density, we achieve precise control over the stability of persistent currents which increases with the impurity number. In the unstable regime, the complex vortex motion within the impurity landscape, characterized by pinning and unpinning events, governs the timescale of the current decay and its final value. Our work establishes atomic superfluids as a pristine platform for exploring universal mechanisms of superflow stabilization and decay, paving the way for atomtronic quantum technologies.

Quantum computing is transitioning from laboratory research to industrial deployment, yet significant challenges persist: system scalability and performance, fabrication yields, and the advancement of algorithms and applications. We emphasize that in building quantum computers – spanning quantum chips, system integration, instruction sets, algorithms, and middleware such as quantum error correction schemes – design is everywhere. In this paper, we advocate for a holistic design perspective in quantum computing, a perspective we argue is pivotal to unlocking innovative co-design opportunities and addressing the aforementioned key challenges. To equip readers with sufficient background for exploring co-optimization opportunities, we detail how interconnected computational methods and tools collaborate to enable end-to-end quantum computer design. This coverage encompasses critical stages – such as chip layout design automation, high-fidelity system-level simulation, Hamiltonian derivation for quantum system modeling, control pulse simulation, decoherence analysis, and physical verification and testing – followed by quantum instruction set design. We then proceed to quantum system and software development, including quantum circuit synthesis, quantum error correction and fault tolerance, and logic verification and testing. Through these discussions, we illustrate with concrete examples – including co-optimizing quantum instruction sets with algorithmic considerations, customizing error correction circuits to hardware-specific constraints, and streamlining quantum chip design through tailored code design, among others. We hope that the detailed end-to-end design workflow as well as these examples will foster dialogue between the hardware and software communities, ultimately facilitating the translation of meaningful research findings into future quantum hardware implementations.

In view of the compelling need for coherent atom transport as a prerequisite for a variety of emerging quantum technologies, we investigate such transport on the example of an adjustable family of two-dimensional optical lattices [L. Tarruell et al., Nature (London) 483, 302 (2012)] that includes square, honeycomb, dimerized, and 1D-chains lattices as its special cases; dynamical optical lattices of this type have already been utilized for the demonstration of topological pumping and the realization of two-qubit quantum gates with neutral atoms. At the outset, we propose the appropriate arrangements of acousto-optic modulators that give rise to a frequency imbalance between counterpropagating laser beams, thus leading to the dynamical-lattice effect in an arbitrary direction in the lattice plane. We subsequently obtain the dynamical-lattice trajectories that enable atom transport in the lattices under consideration using two classes of control schemes: (i) shortcuts to adiabaticity (STA) in the form of inverse engineering based on a dynamical invariant of Lewis-Riesenfeld type, and (ii) their modification, known as enhanced STA (eSTA), which is well-suited for the treatment of anharmonic trapping potentials. We then quantify the resulting atom dynamics using transport fidelities computed from the numerical solutions of the relevant time-dependent Schrödinger equations. By doing so for various choices of the system parameters and transport directions, we demonstrate that – except in the special case of the dimerized lattice – the eSTA method consistently outperforms its STA counterpart, both in terms of the achievable transport times and the robustness of the resulting transport against small variations of optical-lattice depths.

We prove a simple dynamical law for excitation-preserving interactions: the {sum of local Wigner negativities} is upper-bounded by a fixed budget set by the initially excited state. For the single-excitation sector of the XY model (and its beam-splitter analogue), this convexity bound equals the negativity of the seed state and is saturated only when the excitation is fully localized. At intermediate times the sum lies strictly below the bound due to phase-space overlap in local mixtures, quantitatively accounting for entanglement growth as a redistribution of a finite, budgeted resource into shared correlations. We establish the result analytically for two bodies and corroborate it numerically in engineered state-transfer chains, where it reveals a coherence-enabled dark transport: the resource becomes locally invisible while being stored in multi-body coherences. The predicted trajectory of the summed local negativity provides a practical hardware metric: deviations from the ideal, budgeted curve diagnose decoherence and control error.

We study an entanglement phase transition in a class of chaotic non-Hermitian spin chains whose spin-spin coupling terms commute with the non-Hermitian contributions. Two representative models are investigated: the transverse-field Ising model with a complex longitudinal field and the non-Hermitian XX model with a transverse field. By analyzing their complex spectra, we find that both models undergo a dissipation-induced gapless-gapped phase transition when the transverse field exceeds a model-dependent threshold. Interestingly, the complex gap does not vary monotonically with the dissipation rate; instead, it exhibits pronounced oscillations before entering the gapped phase. By simulating their non-unitary dynamics, we show that the steady-state entanglement entropy undergoes a transition from volume-law to area-law scaling as the dissipation rate increases. Moreover, several unexpected features emerge within the volume-law regime: a larger complex gap or dissipation rate may lead to a more entangled steady state. We trace these unusual behaviors of the complex gap and the steady-state entanglement to level crossings between the maximal imaginary level and other spectral levels. Our work uncovers an exotic entanglement transition in chaotic non-Hermitian many-body systems.

Scaling superconducting quantum processors beyond single dilution refrigerators requires efficient optical interconnects, yet integrating microwave-to-optical (M2O) transducers poses challenges due to frequency mismatches and qubit decoherence. We propose a modular architecture using SNAIL-based parametric coupling to interface Brillouin M2O transducers with long-lived 3D cavities, while maintaining plug-and-play compatibility. Through numerical simulations incorporating realistic noises, including laser heating, propagation losses, and detection inefficiency, we demonstrate raw entangled bit fidelities of F~0.8 at kHz-level rates over 30 km using the Duan-Lukin-Cirac-Zoller (DLCZ) protocol. Implementing asymmetric entanglement pumping tailored to amplitude damping errors, we achieve purified fidelities F~0.94 at 0.2 kHz rates. Our cavity-based approach outperforms transmon schemes, providing a practical pathway for distributed superconducting quantum computing.

As quantum hardware advances toward fault-tolerant operation, an intermediate stage known as early fault-tolerant quantum computing (EFTQC) is emerging, where partial error correction enables meaningful computation. In this regime, the ability of quantum processors to scale in size and depth has become a crucial factor shaping their achievable performance. This study investigates how finite scalability influences resource requirements for simulating open-shell catalytic systems using Quantum Phase Estimation (QPE). The analysis compares hardware archetypes distinguished by fidelity or operation speed under two representative scalability models. Finite scalability increases qubit and runtime demands yet leaves overall scaling behavior intact, with high-fidelity architectures requiring lower minimum scalability to solve equally sized problems. These effects are largely independent of the chosen scalability model. Extending this framework, we examine runtime competitiveness across hardware and code configurations, incorporating surface-code and quantum Low-Density Parity-Check (LDPC)-based fault tolerance under finite scalability. The results identify operating regimes where high-fidelity architectures remain competitive despite slower gate speeds and show that LDPC codes further expand this regime by reducing space-time overhead. Together, these findings highlight the central role of scalability in quantifying performance and guiding the design of next-generation quantum hardware. Continued progress in scalable architectures will be essential for extending quantum computing to increasingly complex scientific and industrial applications.

Resolved-sideband cooling is a standard technique in cavity optomechanics enabling quantum control of mechanical motion, but its performance is ultimately limited by quantum backaction heating. This fundamental effect imposes a limit on the minimum achievable mechanical phonon number, establishing a finite-temperature floor regardless of the applied cooling strength. We generalize the semi-classical model for optomechanical cooling to describe universal cavity Hamiltonians incorporating both passive and active nonlinearities. As a concrete demonstration, we analyze the simplest circuit optomechanical system that implements a nonlinear drive via a Josephson junction. Our analysis reveals that this active nonlinear drive can eliminate the residual heating backaction, thereby comparing favorably with alternative optomechanical cooling schemes based on passive nonlinearities arXiv:2202.13228. By successfully overcoming the finite-temperature floor that limits conventional schemes, our method paves the way for unprecedented quantum control over mechanical systems and establishes the experimental viability of zero-heating optomechanical cooling.

From the AdS/CFT dictionary, we derive a bulk dual of the work distribution defined by the two-point measurement on the boundary, yielding a bulk formulation of the Tasaki-Crooks fluctuation theorem. We argue that this does not merely supply a holographic prescription for the work distribution; it encodes the mean energy change and fluctuations of bulk real-time dynamics associated with the two-point measurement.

The measurements of Hanle and polarization recovery effects for localized charge carriers are the basic tools for determining parameters of the spin dynamics, such as strength of the hyperfine interaction, for example, in quantum dots. We describe the dependence of the spin polarization of localized electrons on transverse and longitudinal magnetic fields taking into account the interplay between electron hopping and measurement back action. We show that these two have a qualitatively similar effect in the Faraday geometry, but compete in the Voigt geometry. This allows one to describe a broad range of the experimental results and study the fundamental effects of quantum measurements.

In the paper we developed a procedure for constructing generalized coherent states with shifted argument, as a result of the action of the generalized displacement operator. This was based on the action of a pair of nonlinear ladder operators, which generate nonlinear coherent states. To examine the properties of coherent states with shifted argument, the rules of the normal operator ordering technique (DOOT) were used. The results obtained were verified for a series of particular cases, obtaining expressions consistent with those in the literature. The expressions obtained will be, among others, useful in quantum optics, e.g. for calculating the Wigner operator in the representation of coherent states.

Harnessing a beam of slow free electrons in artificial photonic structures offers a powerful, tunable platform for generating nonclassical light without the need for heavy physical equipment. Here we present a theory of nonclassical lasing, demonstrating how incoherent electrons in photonic crystal cavities can coherently emit photons through collective dynamics. When photon emission rate exceeds cavity losses, nonclassical lasing with sub-Poissonian photon statistics emerges, driven by multi-photon Rabi oscillations. At specific coupling strengths, quantum state trapping effect emerges, producing high-fidelity Fock states at room temperature (e.g. nearly 90%-fidelity of four photon Fock state). Notably, the frequency of the emitted photons can be readily tuned via the velocity of the injected electrons to match cavity modes. This approach supports photonic integration and offers a scalable, energy-efficient platform for room-temperature quantum light sources and advanced studies in quantum electrodynamics.

Simulating non-Hermitian dynamics on quantum computers is often hindered by the decay of success probability and the instability of non-diagonalizable matrices. Here, we present contour-based matrix decomposition (CBMD), a rigorous and versatile quantum functional calculus framework for simulating non-Hermitian matrix functions. By generalizing the matrix Cauchy residue theorem, CBMD decomposes holomorphic non-Hermitian operators into an analytic infinite contour-residue identity, followed by finite truncation with controlled error to yield linear combinations of Hermitian components. For first-order dynamics, CBMD achieves optimal query complexity across all parameters, strictly matching the optimal performance bounds within the linear combination of Hamiltonian simulation (LCHS) paradigm. Beyond first-order systems, the framework naturally generalizes to complex operator functions, including second-order wave dynamics and non-Hermitian special functions such as Bessel and Airy evolutions. Furthermore, CBMD systematically suppresses the asymptotic growth of non-Hermitian components, yielding a significant reduction in the required number of amplitude amplifications compared to the naive scheme of combining monomials via linear combination of unitaries (LCU) after Taylor expansion. Notably, CBMD avoids explicit dependence on matrix diagonalizability, effectively mitigating the long-standing challenges associated with ill-conditioned eigenvectors and Jordan blocks. Our work establishes a systematic matrix calculus that bridges high-performance classical numerics and fault-tolerant quantum algorithms. It should be noted that CBMD inherits standard LCU overheads, and requires the target function to have a bounded growth order on the real axis.

We investigate photon transport and blockade based on the architecture where a waveguide is coupled to a microring resonator at two distinct points. This two-point coupling configuration between the waveguide and resonator gives rise to non-Markovian dynamics, which is induced by the photon transmission delay in the waveguide between the two coupled points. On one hand, by designing the non-Markovian coupling parameters between the waveguide and resonator, single- or two-photon transport and the resulting photon blockade effect can be manipulated according to the output photonic states at the end of waveguide. We for the fist time evaluate the occurrence of photon blockade with scattering matrices and second order correlation functions based on this non-Markovian proposal related to the length of waveguide between two coupled points. On the other hand, when classical driving fields are applied upon the resonator with interactions between its clockwise and counterclockwise modes, the blockade effect of the output field can be determined by the intracavity eigenstates. Then the correlations of the output field as well as the intracavity states can be modulated by the non-Markovian coupling between the microring resonator and waveguide.

Simulation of open quantum systems is an area of active research in quantum algorithms. In this work, we revisit the connection between Markovian open-system dynamics and averages of Hamiltonian real-time evolutions, which we refer to as Hamiltonian twirling channels. By applying the Lévy-Khintchine representation theorem, we clarify when and how a dissipative dynamics can be realized using Hamiltonian twirling channels. Guided by the general theory, we explore Hamiltonian twirling with Gaussian, compound Poisson and symmetric stable distributions and their algorithmic implications. These give wide classes of Lindbladians that can be simulated in $\Theta(t^{1/\alpha})$ Hamiltonian simulation time without any extra ancilla or other quantum gates for $1\le \alpha \le 2$. Moreover, we prove that these time complexities are asymptotically optimal using an information theoretic approach, which, to the best of our knowledge, is the first result of lower bounds on fast-forwarding simulation algorithms.

The quantum geometric tensor (QGT) unifies the Berry curvature (its imaginary part) and the quantum metric (its real part), yet Raman studies of chiral phonons have so far accessed only the former. We perform circularly polarized Raman spectroscopy on the quantum magnet K2Co(SeO3)2, where the field-odd chiral splitting and the field-even center-frequency shift collapse onto a single curve across temperature and magnetic field, revealing a common microscopic origin for both observables. Since the chiral splitting reflects the Berry curvature, the concomitant even component, arising from the same microscopic origin, captures the field-induced change of the quantum metric, corresponding to the diagonal Born-Oppenheimer correction. Across two resolvable Eg modes, the unified data are well captured by a simple empirical quadratic relation. These results establish Raman spectroscopy as a direct probe of the quantum metric and an operational decomposition of quantum geometry within a single measurement.

We study the single-photon scattering in a one-dimensional (1D) waveguide coupled to one transition of a $V$-type giant atom (GA), whose other transition is coherently driven by an classical field. The inelastic scattering of single photons by the GA realizes the single-photon frequency conversion. By applying the Lippmann-Schwinger equation, the scattering coefficients for single photons incident from different directions are obtained, which present different scattering spectra in the Markovian and the non-Markovian regimes. The conversion contrast characterizing the nonreciprocity is also analyzed in both regimes. It is found that the probability of the frequency up- or down-conversion vanishes as long as the emission from either transition pathways for single photons is suppressed, but it is enhanced and even reach unity by introducing the nonreciprocity. It is the quantum self-interference induced by the scale of this two-legged GA and the phase difference between the GA-waveguide couplings that tune the probability of the frequency up- or down-conversion.

We present the first experimental implementation of a polarization-circulation speed meter. In our experiment, the interferometer was reduced to a single-cavity configuration with all mirrors fixed. A green-locking scheme was employed to stabilize the polarization circulation cavity, and a lock-acquisition procedure was demonstrated to realize speed-meter operation. The system was characterized by measuring the transfer function from a pseudo-displacement signal to the photodetector output, confirming that the device measures the speed of mirror motion. These results support the feasibility of polarization-circulation speed meters and suggest that the control scheme could be extended to more complex configurations, such as Michelson interferometers and suspended-mirror systems.

High-energy particle decays naturally realise informationally weak measurements of quantum spin. Decay kinematics act as continuous pointer variables whose overlapping angular distributions encode partial, non-projective information about the parent spin state. Ensemble averages of these pointers yield weak values, linking collider spin-density reconstruction to Aharonov-Vaidman measurement theory. This framework unifies spin tomography, entangled-decay correlations, and spin-correlation algorithms, showing that relativistic decays realise informationally weak measurements of spin and suggesting new ways to probe coherence and interference in high-energy processes.

Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them appealing for practical suppression of noise in near-term quantum computers. In addition to increased qubit-connectivity requirements compared to more conventional topological quantum error correcting codes, qLDPC codes remain notoriously hard to compute with. In this work, we introduce a construction to implement all Clifford quantum gate operations on the recently introduced lift-connected surface (LCS) codes (Old et al. 2024). These codes can be implemented in a 3D-local architecture and achieve asymptotic scaling $[[n, \mathcal{O}(n^{1/3}), \mathcal{O}(n^{1/3})]]$. In particular, LCS codes realize favorable instances with small numbers of qubits: For the $[[15,3,3]]$ LCS code, we provide deterministic fault-tolerant (FT) circuits of the logical gate set $\{\overline{H}_i, \overline{H}_i, \overline{C_i X_j}\}_{i,j \in (0,1,2)}$ based on flag qubits. By adding a procedure for FT magic state preparation, we show quantitatively how to realize an FT universal gate set in $d=3$ LCS codes. Numerical simulations indicate that our gate constructions can attain pseudothresholds in the range $p_{\mathrm{th}} \approx 4.8\cdot 10^{-3}-1.2\cdot 10^{-2}$ for circuit-level noise. The schemes use a moderate number of qubits and are therefore feasible for near-term experiments, facilitating progress for fault-tolerant error corrected logic in high-rate qLPDC codes.

It is well known that all physically relevant states of gauge theories lie in the sectors of the Hilbert space which satisfy the Gauss law. On the lattice, the manifeslty gauge invariant subspace is known to be exactly spanned by gauged tensor networks. In this work, we demonstrate that the continuum limit of certain types of gauged tensor networks is well defined and leads to a new class of states that may be helpful for the non-perturbative study of gauge theories directly in the continuum.

Reinforcement learning (RL) with limited samples is common in real-world applications. However, offline RL performance under this constraint is often suboptimal. We consider an alternative approach to dealing with limited samples by introducing the Quantum Metric Encoder (QME). In this methodology, instead of applying the RL framework directly on the original states and rewards, we embed the states into a more compact and meaningful representation, where the structure of the encoding is inspired by quantum circuits. For classical data, QME is a classically simulable, trainable unitary embedding and thus serves as a quantum-inspired module, on a classical device. For quantum data in the form of quantum states, QME can be implemented directly on quantum hardware, allowing for training without measurement or re-encoding. We evaluated QME on three datasets, each limited to 100 samples. We use Soft-Actor-Critic (SAC) and Implicit-Q-Learning (IQL), two well-known RL algorithms, to demonstrate the effectiveness of our approach. From the experimental results, we find that training offline RL agents on QME-embedded states with decoded rewards yields significantly better performance than training on the original states and rewards. On average across the three datasets, for maximum reward performance, we achieve a 116.2% improvement for SAC and 117.6% for IQL. We further investigate the $\Delta$-hyperbolicity of our framework, a geometric property of the state space known to be important for the RL training efficacy. The QME-embedded states exhibit low $\Delta$-hyperbolicity, suggesting that the improvement after embedding arises from the modified geometry of the state space induced by QME. Thus, the low $\Delta$-hyperbolicity and the corresponding effectiveness of QME could provide valuable information for developing efficient offline RL methods under limited-sample conditions.

We present QuCoWE a framework that learns quantumnative word embeddings by training shallow hardwareefficient parameterized quantum circuits PQCs with a contrastive skipgram objective Words are encoded by datareuploading circuits with controlled ring entanglement similarity is computed via quantum state fidelity and passed through a logitfidelity head that aligns scores with the shiftedPMI scale of SGNSNoiseContrastive Estimation To maintain trainability we introduce an entanglementbudget regularizer based on singlequbit purity that mitigates barren plateaus On Text8 and WikiText2 QuCoWE attains competitive intrinsic WordSim353 SimLex999 and extrinsic SST2 TREC6 performance versus 50100d classical baselines while using fewer learned parameters per token All experiments are run in classical simulation we analyze depolarizingreadout noise and include errormitigation hooks zeronoise extrapolation randomized compiling to facilitate hardware deployment

Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for both bosonic and fermionic systems. As correlated topological insulators (TI) approach experimental realization in quantum simulators, conventional probes, such as transport measurements, are not easily applicable to these synthetic platforms. In this study, we focus on two examples of correlated TI: a bosonic TI protected by $\mathbb{Z}_2\times U(1)$ symmetry and the fermionic quantum spin Hall insulator protected by time-reversal symmetry. We propose a unified, readily implementable protocol based on measuring the disorder parameter $\langle\exp(\mathrm{i}\theta \hat{Q}_A)\rangle$ for a large subregion $A$, with $\hat{Q}_A$ the total charge operator within $A$. Our key finding is that this quantity exhibits non-analytical dependence on $\theta$ for correlated TI, a signature robust against decoherence. We establish this diagnostic through both numerical simulations and analytical derivations. This protocol is well-suited for implementation on near-term quantum simulation platforms, providing a direct route to experimentally confirm correlated TI.

Phase transitions in one-dimensional lattice systems are well established and have been extensively studied within both Hermitian and non-Hermitian frameworks. In this work, we extend this understanding to a more general setting by investigating localization and delocalization transitions and the behavior of the non-Hermitian skin effect (NHSE) using a tight-binding model on a generalized random graph lattice. Our model incorporates three key parameters, asymmetric hopping $\Delta$, on-site disorder $W$, and a random long-range coupling $p$ that together define the underlying random graph structure. By varying $p$, $\Delta$, and the disorder strength, we explore the interplay between topology, randomness, and non-Hermiticity in determining localization properties. Our results show a strong competition between skin effect driven and Anderson driven localizations across parameter regimes. Notably, even in the presence of strong disorder, skin effect driven localization coexists with Anderson-driven localization. We further discuss the relevance of these results to machine-learning architectures and information propagation in complex networks and other real-world problems.

Quantum backflow is a counterintuitive phenomenon in which the probability density of a quantum particle propagates opposite to its momentum. Experimental observation of backflow has remained elusive due to two main challenges: (i) the effect is intrinsically small, with less than 4% of the probability able to flow backward, and (ii) it requires wave packets with a well-defined momentum direction, which are difficult both to prepare and to verify under realistic, noisy conditions. Here, we overcome these challenges by introducing a general formulation of quantum backflow applicable to arbitrary momentum distributions. The framework recovers the standard backflow limit for unidirectional states and identifies general backflow as probability flow exceeding that predicted by the particle's momentum distribution alone. We show that this excess can reach nearly 13%, surpassing the standard backflow bound by more than a factor of three. Furthermore, we extend the framework to the closely related phenomenon of quantum reentry, provide explicit examples of quantum states exhibiting large general backflow and reentry, and discuss the foundational implications of these nonclassical effects. Our results open a pathway toward the experimental observation of quantum backflow in realistic settings.

In this work, we present a geometrical formulation of quantum thermodynamics based on contact geometry and principal fiber bundles. The quantum thermodynamic state space is modeled as a contact manifold, with equilibrium Gibbs states forming a Legendrian submanifold that encodes the fundamental thermodynamic relations. A principal fiber bundle over the manifold of density operators distinguishes the quantum state structure from thermodynamic labels: its fibers represent non-equilibrium configurations, and their unique intersections with the equilibrium submanifold enforce thermodynamic consistency. Quasistatic processes correspond to minimizing geodesics under the Bures-Wasserstein metric, leading to minimal dissipation, while the divergence of geodesic length toward rank-deficient states geometrically derives the unattainability aspect of the third law. Non-equilibrium extensions, formulated through pseudo-Riemannian metrics and connections on the principal bundle, introduce curvature-induced holonomy that quantifies a geometric source of irreversibility in cyclic processes. In this framework, the thermodynamic laws in the quantum regime emerge naturally as geometric consequences.