Papers

Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement, their rapidly growing error limits access to long-time observables. We present a framework for constructing efficient high-order Trotter-Suzuki schemes by identifying their structure and directly optimizing their parameters over a high-dimensional space. This method enables the discovery of new schemes with significantly improved efficiency compared to traditional constructions, such as those by Suzuki and Yoshida. Based on the theoretical efficiency and practical performance, we recommend two novel highly efficient schemes at $4^{\textrm{th}}$ and $6^{\textrm{th}}$ order. We also demonstrate the effectiveness of these decompositions on the Heisenberg model and the quantum harmonic oscillator, and find that for a fixed final time they perform better across the computational cost. Even when using large time steps, they surpass established low-order schemes like the Leapfrog. Finally, we investigate the in-practice performance of different Trotter schemes and find the decompositions with more uniform coefficients tend to feature improved error accumulation over long times. We have included this observation into our choice of recommended schemes.

Genuine quantum interference between independent nonlinear processes of different order provides a route to coherent control that cannot be reduced to a classical field interference. Here we present an all-optical analogue of coherent carrier injection by exploiting interference between second- and third-order quantum nonlinear processes in an integrated photonic platform. Photon pairs generated via spontaneous parametric down-conversion and spontaneous four-wave mixing coherently contribute to the same final two-photon state, resulting in a phase-dependent modulation of both the generation rate and the spectral structure of the emitted biphoton state. We illustrate the features of such interference and how it can be used to shape biphoton wavefunctions and their quantum correlations. These results identify interference between nonlinear processes of different order as a distinct form of coherent quantum control within quantum nonlinear optics.

Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated codes have recently attracted attention due to theoretical advances in fault-tolerant protocols with constant-space-overhead and polylogarithmic-time-overhead, as well as practical developments of high-rate many-hypercube codes equipped with a high-performance level-by-level minimum-distance decoder (LMDD). We propose a general, high-performance decoder for high-rate concatenated stabilizer codes that extends LMDD by leveraging the Chase algorithm to generate a suitable set of candidate errors. Our simulation results demonstrate that the proposed decoder outperforms conventional decoders for high-rate concatenated Hamming codes under bit-flip noise.

This paper aims to first explain, somewhat more clearly, the Stochastic-Quantum correspondence put forward in by Barandes in 2023. Specifically, the quantum-mechanical bra-ket notation is used, illuminating some results of previous results. With this, we prove the six axioms of textbook quantum mechanics from a single axiom: every physical system evolves according to a, generally indivisible, stochastic law. Afterwards, we generalise the treatment to continuous bases, which showcases a problem with them, indicating that space (and other physical variables) may be discrete in nature. Some concrete examples are also given, including the generalisation to classical and quantum fields. Then, we treat some practical issues of this new stochastic approach, regarding the solving of problems in physics, which turns out to still be most tractable in the traditional way. Finally, we explain the classical limit, where a system of many particles is found to behave classically according to Newton's second law. Along with that, we present a way of solving the measurement problem, characterising what is an environment and a measuring device and explaining how the wavefunction collapse comes about. Specifically, it is found that what distinguishes an environment is its number of degrees of freedom, while a measuring device is a low-entropy type of environment.

We establish an exponentially decaying upper bound on the average energy that can be extracted in quantum energy teleportation (QET) protocols executed on finite-range {gapped} lattice systems possessing a unique ground state. Under mild regularity assumptions on the Hamiltonian and uniform operator-norm bounds on the local measurement operators, there exist positive constants $C$ and $\mu$ (determined by the spectral gap, interaction range and local operator norms) such that for any local measurement performed in a region $A$ and any outcome-dependent local unitaries implemented in a disjoint region $B$ separated by distance $d=\operatorname{dist}(A,B)$ one has $|E_A-E_B|\le C\,e^{-\mu d}$. The bound is nonperturbative, explicit up to model-dependent constants, and follows from the variational characterization of the ground state combined with exponential clustering implied by the spectral gap. We emphasize that the constants deteriorate as the gap closes (equivalently, as the correlation length diverges), so the estimate is intended for the gapped regime.

This paper presents a feasibility study demonstrating that quantum machine learning (QML) algorithms achieve competitive performance on real-world medical imaging despite operating under severe constraints. We evaluate Equilibrium Propagation (EP), an energy-based learning method that does not use backpropagation (incompatible with quantum systems due to state-collapsing measurements) and Variational Quantum Circuits (VQCs) for automated detection of Acute Myeloid Leukemia (AML) from blood cell microscopy images using binary classification (2 classes: AML vs. Healthy). Key Result: Using limited subsets (50-250 samples per class) of the AML-Cytomorphology dataset (18,365 expert-annotated images), quantum methods achieve performance only 12-15% below classical CNNs despite reduced image resolution (64x64 pixels), engineered features (20D), and classical simulation via Qiskit. EP reaches 86.4% accuracy (only 12% below CNN) without backpropagation, while the 4-qubit VQC attains 83.0% accuracy with consistent data efficiency: VQC maintains stable 83% performance with only 50 samples per class, whereas CNN requires 250 samples (5x more data) to reach 98%. These results establish reproducible baselines for QML in healthcare, validating NISQ-era feasibility.

Quantum computing requires the optimization of control pulses to achieve high-fidelity quantum gates. We propose a machine learning-based protocol to address the challenges of evaluating gradients and modeling complex system dynamics. By training a recurrent neural network (RNN) to predict qubit behavior, our approach enables efficient gradient-based pulse optimization without the need for a detailed system model. First, we sample qubit dynamics using random control pulses with weak prior assumptions. We then train the RNN on the system's observed responses, and use the trained model to optimize high-fidelity control pulses. We demonstrate the effectiveness of this approach through simulations on a single $ST_0$ qubit.

Assessing whether a noisy quantum device can potentially exhibit quantum advantage is essential for selecting practical quantum utility tasks that are not efficiently verifiable by classical means. For optimization, a prominent candidate for quantum advantage, entropy benchmarking provides insights based concomitantly on the specifics of the application and its implementation, as well as hardware noise. However, such an approach still does not account for finite-shot effects or for quantum error mitigation (QEM), a key near-term error suppression strategy that reduces estimation bias at the cost of increased sampling overhead. We address this limitation by developing a benchmarking framework that explicitly incorporates finite-shot statistics and the resource overhead induced by QEM. Our framework quantifies quantum advantage through the confidence that an estimated energy lies within an interval defined by the best-known classical upper and lower bounds. Using a proof-of-principle numerical study of the two-dimensional Fermi-Hubbard model at size $8\times8$, we demonstrate that the framework effectively identifies noise and shot-budget regimes in which the probabilistic error cancellation (PEC), a representative QEM method, is operationally advantageous, and potential quantum advantage is not hindered by finite-shot effects. Overall, our approach equips end-users with a framework based on lightweight numerics for assessing potential practical quantum advantage in optimization on near-future quantum hardware, in light of the allocated shot budget.

We propose a quantum rotation diversity (QRD) scheme for optical quantum communication using binary phase-shift-keying displaced squeezed states and homodyne detection over Gamma-Gamma turbulence channels. Consecutive temporal modes are coupled by a passive orthogonal rotation that redistributes the displacement amplitude between slots, yielding a diversity order of two under independent fading and joint maximum-likelihood detection. Analytical expressions for the symbol-error rate performance, along with asymptotic results for the diversity and coding gains, are derived. The optimal rotation angle and energy allocation between displacement and squeezing are obtained in closed form. Furthermore, we show that when both the displacement amplitude and the squeezing strength scale with the total photon number, an effective diversity order of four is achieved. Numerical results validate the analysis and demonstrate the super-diversity behaviour of the proposed QRD scheme.

Generating quantum data by learning the underlying quantum distribution poses challenges in both theoretical and practical scenarios, yet it is a critical task for understanding quantum systems. A fundamental question in quantum machine learning (QML) is the universality of approximation: whether a parameterized QML model can approximate any quantum distribution. We address this question by proving a universality theorem for the Many-body Projected Ensemble (MPE) framework, a method for quantum state design that uses a single many-body wave function to prepare random states. This demonstrates that MPE can approximate any distribution of pure states within a 1-Wasserstein distance error. This theorem provides a rigorous guarantee of universal expressivity, addressing key theoretical gaps in QML. For practicality, we propose an Incremental MPE variant with layer-wise training to improve the trainability. Numerical experiments on clustered quantum states and quantum chemistry datasets validate MPE's efficacy in learning complex quantum data distributions.

Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high cost of logical error rate evaluation. We propose a Bayesian optimization framework to discover quantum error-correcting codes that improves data efficiency and scalability with respect to previous machine learning approaches to this task. Our main contribution is a multi-view chain-complex neural embedding that allows us to predict the logical error rate of quantum LDPC codes without performing expensive simulations. Using bivariate bicycle codes and code capacity noise as a testbed, our algorithm discovers a high-rate code [[144,36]] that achieves competitive per-qubit error rate compared to the gross code, as well as a low-error code [[144,16]] that outperforms the gross code in terms of error rate per qubit. These results highlight the ability of our pipeline to automatically discover codes balancing rate and noise suppression, while the generality of the framework enables application across diverse code families, decoders, and noise models.

The one-shot zero-error classical capacity of a quantum channel is the maximum amount of classical information that can be transmitted with zero probability of error via a single channel use. This capacity is fundamentally characterized by the logarithm of the independence number of the noncommutative graph induced by the quantum channel. Consequently, the additivity of the one-shot zero-error classical capacity is equivalent to the multiplicativity of the independence number of the associated noncommutative graphs. As the independence number is not multiplicative in general, the specific conditions under which multiplicativity is preserved remain an open question in quantum information theory. Here, we establish some sufficient conditions for the multiplicativity of the independence number and provide explicit examples of quantum channels that satisfy these criteria. Furthermore, we investigate the block form of noncommutative graphs and derive the conditions under which the independence number remains multiplicative within this framework. These results offer new insights into the structural properties of noncommutative graphs and the fundamental limits of zero-error quantum communication.

Bell nonlocality provides a device-independent (DI) way to certify quantum randomness, based on which true random numbers can be extracted from the observed correlations without detail characterizations on devices for quantum state preparation and measurement. However, the efficiency of current strategies for DI randomness certification is still heavily constrained when it comes to non-maximal Bell values, especially for multiple parties. Here, we present a family of multipartite Bell inequalities that allows to certify optimal quantum randomness and self-test GHZ (Greenberger-Horne-Zeilinger) states, which are inspired from the stabilizer group of the GHZ state. Due to the simple representation of stabilizer group for GHZ states, this family of Bell inequalities is of simple structure and can be easily expanded to more parties. Compared with the Mermin-type inequalities, this family of Bell inequality is more efficient in certifying quantum randomness when non-maximal Bell values achieved. Meanwhile, the general analytical upper bound for the Holevo quantity is presented, and achieves better performance compared with the MABK (Mermin-Ardehali-Belinskii-Klyshko) inequality, Parity-CHSH (Clauser-Horne-Shimony-Holt) inequality and Holz inequality at $N=3$, which is of particular interests for experimental researches on DI quantum cryptography in quantum networks.

Various quantum key distribution (QKD) protocols require bright single-photon sources with a very low probability of multiphoton emission. In this work, we investigate single-photon generation from a negatively charged quantum dot embedded in an elliptical pillar microcavity, driven by either resonant excitation or adiabatic rapid passage (ARP). Our results show that ARP excitation significantly suppresses multiphoton emission and improves photon indistinguishability compared to resonant excitation. We further evaluate the secure key rates of both BB84 and twin-field QKD (TF-QKD) using a quantum-dot single-photon source and compare its performance with that of Poisson-distributed sources (PDS), such as weak coherent pulses. The analysis reveals that ARP provides a modest but consistent enhancement in secure key rate relative to resonant excitation. We show that quantum-dot single-photon sources offer improved performance compared to PDS sources at short and intermediate distances within the chosen parameter regime; however, at longer distances, PDS sources slightly surpass them in both decoy-state BB84 and TF-QKD under the same conditions.

Determining the ground and low-lying excited states is critical in numerous scenarios. Recent work has proposed the ancilla-entangled variational quantum eigensolver (AEVQE) that utilizes entanglement between ancilla and physical qubits to simultaneously tagert multiple low-lying energy levels. In this work, we report the experimental implementation of the AEVQE on a superconducting quantum cloud platform, demonstrating the full procedure of solving the low-lying energy levels of the H$_2$ molecule and the transverse-field Ising models (TFIMs). We obtain the potential energy curves of H$_2$ and show an indication of the ferromagnetic to paramagnetic phase transition in the TFIMs from the average absolute magnetization. Moreover, we investigate multiple factors that affect the algorithmic performance and provide a comparison with ancilla-free VQE algorithms. Our work demonstrates the experimental feasibility of the AEVQE algorithm and offers a guidance for the VQE approach in solving realistic problems on publicly-accessible quantum platforms.

Ensembles of atoms interacting via their Rydberg levels, known as "superatoms" for their ability to encode qubits and to emit single photons, attract increasing attention as building blocks for quantum network nodes. Assessing their performance requires an accurate, physically informative and numerically scalable description of interactions in a large and disordered ensemble. We derive such a description from first principles and successfully test it against brute-force numerics and experimental data. This model proves essential to make quantitative predictions about gate fidelities or photon emission efficiencies, and to guide experiments towards large-scale superatom-based systems.

Quantum interference between interacting systems is fundamental to basic science and quantum technology, but it typically requires precise control of the interaction phases of lasers or microwave generators. Can interference be observed if those interaction phases are stable but unknown, usually prohibitive for complex state without active control? Here, we answer this question by experimentally preparing a Schrödinger-cat-like state of an internal qubit and a motional oscillator of a trapped $^{40}$Ca$^{+}$ ion, and its robustness to such uncontrolled phase. By applying alternating red and blue sideband pulses, we enforce a strict qubit-parity correlation and interference inherently insensitive to stable but unknown phases of the driving laser. For this qubit-parity interference, we use a minimal two-pulse interferometric sequence to demonstrate characteristic visibilities of $20\%$ and $40\%$, which approach the theoretical visibility limit, providing a scalable coherence witness without full state tomography for high-dimensional states.

The integration of high-penetration renewable energy introduces significant stochasticity and non-convexity into power system dispatching, challenging the computational limits of classical optimization. While Variational Quantum Algorithms (VQAs) on Noisy Intermediate-Scale Quantum (NISQ) devices offer a promising path for combinatorial acceleration, existing approaches typically treat the power grid as a "black box", suffering from poor scalability (barren plateaus) and frequent violations of physical constraints. Bridging these gaps, this paper proposes a Physics-Informed Hybrid Quantum-Classical Dispatching (PI-HQCD) framework. We construct a topology-aware Hamiltonian that explicitly embeds linearized power flow equations, storage dynamics, and multi-timescale coupling directly into the quantum substrate, significantly reducing the search space dimensionality. We further derive a noise-adaptive regularization mechanism that theoretically bounds the effective Lipschitz constant of the objective function, guaranteeing convergence stability under realistic quantum measurement noise. Numerical experiments on the IEEE 39-bus benchmark and a 118-bus regional grid demonstrate that PI-HQCD achieves superior economic efficiency and higher renewable utilization compared to stochastic dual dynamic programming (SDDP). Theoretical analysis confirms that this topology-aware design leads to an O(1/N) gradient variance scaling, effectively mitigating barren plateaus and ensuring scalability for larger networks. This work establishes a rigorous paradigm for embedding engineering physics into quantum computing, paving the way for practical quantum advantage in next-generation grid operations.

Continuous measurement of quantum systems provides a standard route to quantum trajectories through the successive acquisition of information which further results in measurement back-action. In this work, we harness this back-action as a resource for global $U(1)$ symmetry restoration where continuous measurement is combined with a $U(1)$-preserving unitary evolution. Starting from a $U(1)$ symmetry-broken initial state, we simulate quantum trajectories generated by continuous measurements of both global and local observables. We show that under global monitoring, states containing superpositions of distant charge sectors restore symmetry faster than those involving nearby sectors. We establish the universality of this behavior across different measurement protocols. Finally, we demonstrate that local monitoring can further accelerate symmetry restoration for certain states that relax slowly under global monitoring.

We apply the wavelet formalism of quantum field theory to investigate nonperturbative dynamics within the Hamiltonian framework. In particular, we employ Daubechies wavelets in momentum space, whose basis functions are labeled by resolution and translation indices, providing a natural nonperturbative truncation of both infrared and ultraviolet truncation of quantum field theories. As an application, we compute the energy spectra of a free scalar field theory and the interacting $1+1$-dimensional $\phi^4$ theory. This approach successfully reproduces the well-known strong-coupling phase transition in the $m^2 > 0$ regime. We find that the extracted critical coupling systematically converges toward its established value as the momentum resolution is increased, demonstrating the effectiveness of the wavelet-based Hamiltonian formulation for nonperturbative field-theoretic calculations.

Leveraging the quantum advantages of highly excited atoms, Rydberg atomic receivers (RAREs) represent a paradigm shift in microwave detection with extremely high sensitivity and broadband tunability. However, existing studies often model RAREs as isotropic point receivers and neglect the spatial variation of Rydberg atomic states within vapor cells, which can lead to inaccurate characterization of their reception patterns. To address this issue, we theoretically analyze the spatial response of a local-oscillator (LO) field-dressed RARE. Our results reveal that as the vapor-cell length increases, a receiving beam aligned with the LO field is formed, and its beamwidth is inversely proportional to the cell length. This finding enables atomic beamforming with only a single atomic vapor cell to enhance signal-to-noise ratio. Furthermore, we analyze the maximum beamforming gain of a single vapor cell by balancing the fundamental tradeoff between improved spatial selectivity and increased laser attenuation in the atomic medium as the vapor cell length becomes longer. To mitigate the beamforming-gain loss caused by laser attenuation, we further propose a segmental-vapor-cell architecture. In this architecture, multiple short vapor cells are arranged along the optical propagation path and separated by clear-air gaps. This design effectively expands the reception aperture while keeping the total vapor-cell length, and hence attenuation loss, fixed. As a result, it achieves a narrower beamwidth and higher beamforming gain than a conventional single-vapor-cell receiver, as demonstrated by extensive numerical results.

Emergent cooperation in classical Multi-Agent Reinforcement Learning has gained significant attention, particularly in the context of Sequential Social Dilemmas (SSDs). While classical reinforcement learning approaches have demonstrated capability for emergent cooperation, research on extending these methods to Quantum Multi-Agent Reinforcement Learning remains limited, particularly through communication. In this paper, we apply communication approaches to quantum Q-Learning agents: the Mutual Acknowledgment Token Exchange (MATE) protocol, its extension Mutually Endorsed Distributed Incentive Acknowledgment Token Exchange (MEDIATE), the peer rewarding mechanism Gifting, and Reinforced Inter-Agent Learning (RIAL). We evaluate these approaches in three SSDs: the Iterated Prisoner's Dilemma, Iterated Stag Hunt, and Iterated Game of Chicken. Our experimental results show that approaches using MATE with temporal-difference measure (MATE\textsubscript{TD}), AutoMATE, MEDIATE-I, and MEDIATE-S achieved high cooperation levels across all dilemmas, demonstrating that communication is a viable mechanism for fostering emergent cooperation in Quantum Multi-Agent Reinforcement Learning.

This book arises from the need to provide a clear and up-to-date overview of the impacts of quantum computing on cryptography. The goal is to provide a reference in Portuguese for undergraduate, master's, and doctoral students in the field of data security and cryptography. Throughout the chapters, we present fundamentals, we discuss classical and post-quantum algorithms, evaluate emerging patterns, and point out real-world implementation challenges. The initial objective is to serve as a guide for students, researchers, and professionals who need to understand not only the mathematics involved, but also its practical implications in security systems and policies. For more advanced professionals, the main objective is to present content and ideas so that they can assess the changes and perspectives in the era of quantum cryptographic algorithms. To that end, the text's structure was designed to be progressive: we begin with essential concepts, move on to quantum algorithms and their consequences (with emphasis on Shor's algorithm), present issues focusing on "families" of post-quantum schemes (based on lattices, codes, hash functions, multivariate, isogenies), analyze the state of the art in standardization (highlighting the NIST process), and finally, discuss migration, interoperability, performance, and cryptographic governance. We hope that this work will assist in the formation of critical thinking and informed technical decision-making, fostering secure transition strategies for the post-quantum era.

We present a general framework for applying linear quantum error mitigation (QEM) techniques directly to physical qubits within a logical qubit to suppress logical errors. By exploiting the linearity of quantum error correction (QEC), we demonstrate that any linear QEM method$\unicode{x2014}$including probabilistic error cancellation (PEC), zero-noise extrapolation (ZNE), and symmetry verification$\unicode{x2014}$can be integrated into the physical layer without requiring modifications to the subsequent QEC decoder. Applying this framework to memory experiments using PEC, we analytically prove and numerically verify that the leading-order contribution to the logical error can be removed, increasing the effective code distance by 2. Our simulations on repetition and rotated surface codes show that a distance-3 code with physical-level PEC achieves logical error rates lower than or similar to a distance-5 unmitigated code while using 40% and 64% fewer qubits, respectively. These results establish physical-level QEM as a widely compatible and resource-efficient strategy for enhancing logical performance in early fault-tolerant architectures.

Quantum memories feature a reversible conversion of optical fields into long-lived atomic spin waves, and are therefore ideal for operating as sensitive atomic sensors. However, up to now, atom-light interferometers have lacked an efficient approach to exploit their ultimate atomic sensing performance, since an extra optical delay line is required to compensate for the memory time. Here, we report a new protocol that records the photocurrent via heterodyne mixing with a stable local oscillator. The obtained complex quadrature amplitude that carries information imprinted on its phase by an external magnetic field, is successfully recovered from the interference patterns between the light and the atomic spin wave, without the stringent requirement of having them overlap in time. Our results reveal that the sensitivity scales favorably with the lifetime of the quantum memory. Our work may have important applications in building distributed quantum networks through quantum memory-assisted atom-light interferometers.

Bohr's Complementarity Principle is a core concept of quantum mechanics. In this article, an updated complementarity relation for the wave and ondulatory aspects of a quantum system is presented and discussed. Two interferometric experiments are implemented in one and two qubit circuits and executed on real hardware. The final state density matrices are reconstructed using quantum state tomography and the complementarity relation is tested via direct computation. Results of the executions are presented both graphically and with a mean squared error analysis for a better comprehension.

Efficient entanglement distribution is a cornerstone of the Quantum Internet. However, physical link parameters such as photon loss, memory coherence time, and gate error rates fluctuate dynamically, rendering static purification strategies suboptimal. In this paper, we propose an Adaptive Purification Controller (APC) that automatically optimizes the entanglement distillation sequence to maximize the goodput, i.e., the rate of delivered pairs meeting a strict fidelity threshold. By treating protocol selection as a resource allocation problem, the APC dynamically switches between purification depths and protocols (BBPSSW vs. DEJMPS) to navigate the trade-off between generation rate and state quality. Using a dynamic programming planner with Pareto pruning, simulation results show that our approach mitigates the "fidelity cliffs" inherent in static protocols and reduces resource wastage in high-noise regimes. Furthermore, we extend the controller to heterogeneous scenarios, and evaluate it for both multipartite GHZ state generation and continuous-variable systems using effective noiseless linear amplification models. We benchmark its computational overhead, showing decision latencies in the millisecond range per link in our implementation.

Quantum technology advances crucially depend on the scaling up of essential quantum resources. Their ideal multiplexing offers more significant gains in applications; however, the scaling of the nonidentical, fragile and varying resources is neither theoretically nor experimentally known. For bosonic systems, multimode interference is an essential tool already widely exploited to develop quantum technology. Here, we analyze, predict and compare essential scaling laws for a constructive interference of multiplexed nonclassical Gaussian states carrying information by displacement with weakly fluctuating squeezing in different multimode interference architectures. The signal-to-noise ratio quantifies the increase in displacement relative to the noise. We introduce the gain-to-instability ratio to numerically estimate the effect of unexplored resource instabilities in a large scale interference scheme. The use of the gain-to-instability ratio to quantify the scaling laws opens steps for extensive theoretical investigation of other bosonic resources and follow-up feasible experimental verification necessary for further development of these platforms.

Extending hyperuniformity from classical to quantum fluctuations in electron systems yields a framework that identifies quantum phase transitions and reveals underlying gap structures through the quantum weight. We study long-wavelength fluctuations of many-body ground states through the charge-density structure factor by incorporating intrinsic quantum fluctuations into hyperuniformity. Although charge fluctuations at zero temperature are generally suppressed by particle-number conservation, their long-wavelength scaling reveals distinct universal behaviors that define quantum hyperuniformity classes. By exemplifying the Aubry-Andre model, we find that gapped, gapless, and localized-critical-extended phases are sharply distinguished by the quantum hyperuniformity classes. Notably, at the critical point, multifractal wave functions generate anomalous scaling behavior. We further show that, in quantum-hyperuniform gapped phases, the quantum weight provides a quantitative measure of the gap size through a universal power-law scaling. Along with classical hyperuniformity, quantum hyperuniformity serves a direct fingerprint of quantum criticality and a practical probe of quantum phase transitions in aperiodic electron systems.

Quantum Energy Teleportation (QET) constitutes a paradigm-shifting protocol that permits the activation of local vacuum energy through the consumption of pre-existing entanglement and classical communication. Nevertheless, the implementation of QET is severely impeded by the fundamental locality of gapped many-body systems, where the exponential clustering of ground-state correlations restricts energy extraction to microscopic scales. In this work, we address this scalability crisis within the framework of the one-dimensional anisotropic XY model. We initially provide a rigorous characterization of a monolithic measurement-induced strategy, demonstrating that while bulk projective measurements can theoretically induce long-range couplings, the approach is rendered physically untenable by exponentially diverging thermodynamic costs and vanishing success probabilities. To circumvent this impasse, we propose and analyze a hierarchical quantum repeater architecture adapted for energy teleportation. By orchestrating heralded entanglement generation, iterative entanglement purification, and nested entanglement swapping, our protocol effectively counteracts the fidelity degradation inherent in noisy quantum channels. We establish that this architecture fundamentally alters the operational resource scaling from exponential to polynomial. This proves, for the first time, the physical permissibility and computational tractability of activating vacuum energy at arbitrary distances. The significance lies not in net energy gain, but in establishing long-range QET as a viable protocol for remote quantum control and resource distribution.