Papers

Pinsker's inequality sets a lower bound on the Umegaki divergence of two quantum states in terms of their trace distance. In this work, we formulate corresponding estimates for a variety of quantum and classical divergences including $f$-divergences like Hellinger and $\chi^2$-divergences as well as Rényi divergences and special cases thereof like the Umegaki divergence, collision divergence, max divergence. We further provide a strategy on how to adapt these bounds to smoothed divergences.

High-Q bosonic memories are central to hardware-efficient quantum error correction, but their isolation makes fast, high-fidelity reset a persistent bottleneck. Existing approaches either rely on weak intermode cross-Kerr conversion or on measurement-based sequences with substantial latency. Here we demonstrate a hardware-efficient Rabi-Driven Reset (RDR) that implements continuous, measurement-free cooling of a superconducting cavity mode. A strong resonant Rabi drive on a transmon, together with sideband drives on the memory and readout modes detuned by the Rabi frequency, converts the dispersive interaction into an effective Jaynes-Cummings coupling between the qubit dressed states and each mode. This realizes a tunable dissipation channel from the memory to the cold readout bath. Crucially, the engineered coupling scales with the qubit-mode dispersive interaction and the drive amplitude, rather than with the intermode cross-Kerr, enabling fast cooling even in very weakly coupled architectures that deliberately suppress direct mode-mode coupling. We demonstrate RDR of a single photon with a decay time of $1.2 \mu s$, more than two orders of magnitude faster than the intrinsic lifetime. Furthermore, we reset about 30 thermal photons in about $80 \mu s$ to a steady-state average photon number of $\bar{n} = 0.045 \pm 0.025$.

Learning the Hamiltonian governing a quantum system is a central task in quantum metrology, sensing, and device characterization. Existing Heisenberg-limited Hamiltonian learning protocols either require multi-qubit operations that are prone to noise, or single-qubit operations whose frequency or strength increases with the desired precision. These two requirements limit the applicability of Hamiltonian learning on near-term quantum platforms. We present a protocol that learns a quantum Hamiltonian with the optimal Heisenberg-limited scaling using only single-qubit control in the form of static fields with strengths that are independent of the target precision. Our protocol is robust against the state preparation and measurement (SPAM) error. By overcoming these limitations, our protocol provides new tools for device characterization and quantum sensing. We demonstrate that our method achieves the Heisenberg-limited scaling through rigorous mathematical proof and numerical experiments. We also prove an information-theoretic lower bound showing that a non-vanishing static field strength is necessary for achieving the Heisenberg limit unless one employs an extensive number of discrete control operations.

We investigate the experimental prospects for testing a relativistic local quantum measurement inequality that quantifies the trade-off between vacuum insensitivity and responsiveness to excitations for finite-size detectors. Building on the Reeh–Schlieder approximation for coherent states, we derive an explicit and practically applicable bound for arbitrary coherent states. To connect with realistic photodetection scenarios, we model the detection region as a square prism operating over a finite time window and consider a normally incident single-mode coherent state. Numerical results exhibit the expected qualitative behavior: suppressing dark counts necessarily tightens the achievable click probability.

The manipulation of distinct degrees of freedom of photons plays a critical role in both classical and quantum information processing. While the principles of wave optics provide elegant and scalable control over classical light in spatial and temporal domains, engineering quantum states in Fock space has been largely restricted to few-photon regimes, hindered by the computational and experimental challenges of large Hilbert spaces. Here, we introduce “Fock-space optics", establishing a conceptual framework of wave propagation in the quantum domain by treating photon number as a synthetic dimension. Using a superconducting microwave resonator, we experimentally demonstrate Fock-space analogues of optical propagation, refraction, lensing, dispersion, and interference with up to 180 photons. These results establish a fundamental correspondence between Schrödinger evolution in a single bosonic mode and classical paraxial wave propagation. By mapping intuitive optical concepts onto high-dimensional quantum state engineering, our work opens a path toward scalable control of large-scale quantum systems with thousands of photons and advanced bosonic information processing.

This paper presents a theoretical study of the light-induced shift of the coherent population trapping resonance. An analytical model is proposed that describes the interaction of two radiation components with an atomic system using a ${\Lambda}$ scheme and takes into account an additional level of excited state. Both weak and strong coupling regimes with off-resonant transitions are considered. It is shown that, in addition to the conventional dynamic Stark shift, an extra shift arises due to the distortion of the resonance line shape when bichromatic laser radiation interacts with off-resonant atomic transitions. An analytical expression for this additional shift is derived in the weak-coupling limit, and its significant impact on the resonance shape and sensitivity to the intensities of the laser field components is demonstrated. It is found that under strong coupling conditions, the additional shift can deviate substantially from a linear dependence on light intensity, suggesting new opportunities for controlling light shifts in precision atomic devices such as quantum frequency standards.

A relativistic equation for a neutral complex field as a probability amplitude is proposed. The continuity equation for the probability density is obtained. It is shown that there are two types of excitations of this field, which describe particles with positive energy and different dispersion laws. Based on the Lagrangian formalism, conservation laws are obtained. The transition to secondary quantization is considered.

Several photonic quantum technologies rely on the ability to generate multiple indistinguishable photons. Benchmarking the level of indistinguishability of these photons is essential for scalability. The Hong-Ou-Mandel dip provides a benchmark for the indistinguishability between two photons, and extending this test to the multi-photon setting has so far resulted in a protocol that computes the genuine n-photon indistinguishability (GI). However, this protocol has a sample complexity that increases exponentially with the number of input photons for an estimation of GI up to a given additive error. To address this problem, we introduce new theorems that strengthen our understanding of the relationship between distinguishability and the suppression laws of the quantum Fourier transform interferometer (QFT). Building on this, we propose a protocol using the QFT for benchmarking GI that achieves constant sample complexity for the estimation of GI up to a given additive error for prime photon numbers, and sub-polynomial scaling otherwise, representing an exponential improvement over the state of the art. We prove the optimality of our protocol in many relevant scenarios and validate our approach experimentally on Quandela's reconfigurable photonic quantum processor, where we observe a clear advantage in runtime and precision over the state of the art. We therefore establish the first scalable method for computing multi-photon indistinguishability, which applies naturally to current and near-term photonic quantum hardware.

We investigate the open-system dynamics of a micromaser quantum battery in the ultrastrong-coupling (USC) regime. The battery consists of a quantized harmonic mode sequentially interacting, via the Rabi Hamiltonian, with a stream of qubits acting as chargers. USC enhances the charging speed but also induces unbounded energy growth and highly mixed cavity states. Dissipation suppresses this behavior, driving the system to a steady state with finite energy and ergotropy. Using optimal control theory, we show that the interplay between USC and dissipation enhances both charging performance and long-term stability against losses.

This paper presents a systematic study of adversarial hypothesis testing for both quantum-quantum (QQ) and classical-quantum (CQ) channels. Unlike conventional channel discrimination, we consider a framework where the sender, Alice, selects the channel input adversarially to minimize Bob's distinguishability. We analyze this problem across four settings based on whether Alice employs i.i.d. or general inputs and whether the receiver, Bob, is informed of the specific input choice (allowing his measurement to depend on the input). We characterize the Stein exponents for each setting and reveal a striking distinction in behavior: for QQ channels with i.i.d. inputs, Bob's knowledge of the input significantly enhances distinguishability, yet this advantage vanishes when general inputs are permitted. In contrast, for CQ channels, Bob being informed provides a consistent advantage over the corresponding entanglement-breaking channels for both i.i.d. and general inputs. These results demonstrate a unique phenomenon in adversarial hypothesis testing where the CQ channel does not merely behave as a special case of the QQ channel.

Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently narrow energy window, their statistical properties can be described by an unitarily invariant ensemble, and testable criteria have been introduced, which are based on the scaling behavior of free cumulants. In this paper, we investigate the conjecture numerically in translationally invariant Heisenberg spin chains with spin quantum number $S =\frac{1}{2},1,\frac{3}{2}$. Combining a quantum-typicality-based numerical method with the exploitation of the system's symmetries, we study the spin current operator and find clear evidence of consistency with the proposed criteria in chaotic cases. Our findings further support the conjecture of the existence of RMT universality as manifest in the observable properties in quantum chaotic systems.

In the thermodynamic limit, the Dicke-Ising chain maps exactly onto an effective self-consistent matter Hamiltonian with the photon field acting solely as a self-consistent effective field. As a consequence, no quantum correlations between photons and spins are needed to understand the quantum phase diagram. This enables us to determine the quantum phase diagram in the thermodynamic limit using numerical linked-cluster expansions combined with density matrix renormalization group calculations (NLCE+DMRG) to solve the resulting self-consistent matter Hamiltonian. This includes magnetically ordered phases with significantly improved accuracy compared to previous estimates. For ferromagnetic Ising couplings, we refine the location of the multicritical point governing the change in the order of the superradiant phase transition, reaching a relative accuracy of $10^{-4}$. For antiferromagnetic Ising couplings, we confirm the existence of the narrow antiferromagnetic superradiant phase in the thermodynamic limit. The effective matter Hamiltonian framework identifies the antiferromagnetic superradiant phase as the many-body ground state of an antiferromagnetic transverse-field Ising model with longitudinal field. This phase emerges through continuous Dicke-type polariton condensation from the antiferromagnetic normal phase, followed by a first-order transition to the paramagnetic superradiant phase. Thus, NLCE+DMRG provides a precise determination of the Dicke-Ising phase diagram in one dimension by solving the self-consistent effective matter Hamiltonian.

We investigate the coherence properties of parity-protected $\cos(2\varphi)$ qubits based on interferences between two Josephson elements in a superconducting loop. We show that qubit implementations of a $\cos(2\varphi)$ potential using a single loop, such as those employing semiconducting junctions, rhombus circuits, flowermon and KITE structures, can be described by the same Hamiltonian as two multi-harmonic Josephson junctions in a SQUID geometry. We find that, despite the parity protection arising from the suppression of single Cooper pair tunneling, there exists a fundamental trade-off between charge and flux noise dephasing channels. Using numerical simulations, we examine how relaxation and dephasing rates depend on external flux and circuit parameters, and we identify the best compromise for maximum coherence. With currently existing circuit parameters, the qubit lifetime $T_1$ can exceed milliseconds while the dephasing time $T_\varphi$ remains limited to only a few microseconds due to either flux or charge noise. Our findings establish practical limits on the coherence of this class of qubits and raise questions about the long-term potential of this approach.

We analyze quantum state preservation in open quantum systems using quantum error-correcting (QEC) codes explicitly embedded in microscopic system-bath models. Rather than assuming abstract quantum channels, we consider multi-qubit registers coupled to bosonic thermal environments, derive a second-order master equation for the reduced dynamics, and use it to benchmark the five-qubit, Steane, and toric codes under local and collective noise. We compute state fidelities as functions of system-bath coupling strength, bath temperatures, and the number of correction cycles. In the low-temperature regime, repeated error correction with the five-qubit code significantly suppresses decoherence and relaxation for weak-to-moderate couplings. In the high-temperature regime, thermal excitations reduce the effectiveness of all codes, although within the parameter range studied, the five-qubit code still yields the highest fidelities among the three codes. For two-qubit Werner states, we identify a critical evolution time associated with an early-time crossover, before which the overhead of QEC does not compensate for the noise-induced degradation; this critical time increases with entanglement, reflecting the greater fragility of strongly entangled states. Overall, our results provide a microscopic master-equation-based framework for benchmarking QEC performance in realistic open-system environments and for assessing code behavior in near-term noisy quantum architectures.

Pre-execution calibration is a major bottleneck for operating superconducting quantum processors, and qubit frequency allocation is especially challenging due to crosstalk-coupled objectives. We establish that the widely-used Snake optimizer is mathematically equivalent to Block Coordinate Descent (BCD), providing a rigorous theoretical foundation for this strategy for qubit frequency allocation. Building on this formalization, we present a topology-aware block ordering obtained by casting order selection as a Sequence-Dependent Traveling Salesman Problem (SD-TSP) and solving it efficiently with a nearest-neighbor heuristic. The SD-TSP cost reflects how a given block choice expands the reduced-circuit footprint required to evaluate the block-local objective, enabling orders that minimize per-epoch evaluation time. Under local crosstalk/bounded-degree assumptions, the method achieves linear complexity in qubit count per epoch, while maintaining comparable optimization performance. We formalize the calibration objective, clarify when reduced experiments are equivalent or approximate to the full objective, and analyze convergence of the resulting inexact BCD with noisy measurements. Simulations based on a physics-motivated error simulator show that the proposed BCD-NNA ordering attains the same optimization accuracy at markedly lower runtime than graph-based heuristics (BFS, DFS) and random orders, while also achieving optimization quality comparable to a genetic-algorithm baseline. This method is robust to noisy objective-function evaluations and tolerant to moderate non-local crosstalk mismatch. These results provide a scalable, implementation-ready workflow for frequency calibration in near-term superconducting processors and, more broadly, for locality-structured calibration tasks in future scalable architectures.

Studying the complexity of states sampled from various ensembles is a central component of quantum information theory. In this work we establish the average-case hardness of learning, in the statistical query model, the Born distributions of states sampled uniformly from the compact symmetric spaces of type AI, AII, and DIII. These ensembles correspond in various senses to the so called circular and (fermionic) Gaussian ensembles. This finding complements analogous recent results for states sampled from the classical compact groups. On the technical side, we employ a somewhat unconventional approach to integrating over the compact groups which may be of some independent interest. For example, our approach allows us to exactly evaluate the total variation distances between the output distributions of Haar random unitary and orthogonal circuits and the constant distribution, which were previously known only approximately.

We demonstrate that large language model (LLM) agents can autonomously perform tensor network simulations of quantum many-body systems, achieving approximately 90% success rate across representative benchmark tasks. Tensor network methods are powerful tools for quantum simulation, but their effective use requires expertise typically acquired through years of graduate training. By combining in-context learning with curated documentation and multi-agent decomposition, we create autonomous AI agents that can be trained in specialized computational domains within minutes. We benchmark three configurations (baseline, single-agent with in-context learning, and multi-agent with in-context learning) on problems spanning quantum phase transitions, open quantum system dynamics, and photochemical reactions. Systematic evaluation using DeepSeek-V3.2, Gemini 2.5 Pro, and Claude Opus 4.5 demonstrates that both in-context learning and multi-agent architecture are essential. Analysis of failure modes reveals characteristic patterns across models, with the multi-agent configuration substantially reducing implementation errors and hallucinations compared to simpler architectures.

Historically, entanglement and coherence distillation focused on the distillable rate under full knowledge of the initial state. In this paper, we develop a unified finite-blocklength and asymptotic theory for universal distillation from convex compact sequences of possible states stable under tensor products. We first resolve an open question by showing that two regularized variants of the generalized quantum Hoeffding divergence need not coincide, and establish fundamental properties of the Hoeffding divergence and anti-divergence. For universal entanglement distillation, we connect finite-blocklength performance under non-entangling, PPT-preserving, and dually free operations to composite correlated hypothesis testing, yielding reliability functions for non-entangling and PPT-preserving operations characterized by regularized quantum Hoeffding divergences and strong converse bounds via the anti-divergence. We recover the entanglement concentration error exponent, zero-rate exponents under a continuity condition, and distillable entanglements, and characterize the dually free cases by regularized relative entropies under restricted measurements. Additionally, five concrete noise models justify the black-box assumptions for both resources. For coherence distillation under maximally incoherent and dephasing-covariant incoherent operations, we extend the one-shot semidefinite program characterization to universal inputs; relating a relaxed optimization to hypothesis testing yields the high-rate reliability function. A coherent-seed approach extends the single-state formula to the entire direct regime when the zero-error rate is positive. Finally, we completely characterize the states with positive zero-error coherence distillation rate, show that the rate equals the order-zero Petz Rényi relative entropy of coherence, and derive dimension-independent one-shot bounds ......

Quantum algorithms are gaining attention in Computational Fluid Dynamics (CFD) for their favorable scaling, as encoding physical fields into quantum probability amplitudes enables representation of two to the power of n spatial points with only n qubits. A key challenge in Quantum CFD is the efficient readout of simulation results, a topic that has received limited attention in literature. This work presents methods to extract statistical properties of spatial velocity fields, such as central moments and structure functions, directly from parameterized ansatz circuits, avoiding full quantum state tomography. As a proof of concept, we implement our approach for 1D velocity fields, encoding 16 spatial points with 4 qubits, and analyze both a sine wave signal and four snapshots from Burgers' equation evolution. Using Qedma's error mitigation software QESEM, we demonstrate that such computations achieve high accuracy on current quantum devices, specifically IBMQ's Heron2 system ibm_fez.

Recent studies have extensively explored chaotic dynamics in quantum optical systems through the mean-field approximation, which corresponds to an ideal, fluctuation-free scenario. However, the inherent sensitivity of chaos to initial conditions implies that even minute fluctuations can be amplified, thereby questioning the applicability of this approximation. Here, we analyze these chaotic effects using stochastic Langevin equations or the Lindblad master equation. For systems operating at frequencies of $10^5$ to $10^7$ Hz, we demonstrate that room-temperature thermal fluctuations are sufficient to suppress chaos at the level of expectation values, even under weak nonlinearity. Furthermore, nonlinearity induces deviations from Gaussian phase-space distributions of the quantum state, revealing attractor-like features in the Wigner function. With increasing nonlinearity, the noise threshold for chaos suppression decreases, approaching the scale of vacuum fluctuations. These results provide a bidirectional validation of the quantum mechanical suppression of chaos.

The transition to the fault-tolerant era exposes the limitations of homogeneous quantum systems, where no single qubit modality simultaneously offers optimal operation speed, connectivity, and scalability. In this work, we propose a strategic approach to Heterogeneous Quantum Architectures (HQA) that synthesizes the distinct advantages of the superconducting (SC) and neutral atom (NA) platforms. We explore two architectural role assignment strategies based on hardware characteristics: (1) We offload the latency-critical Magic State Factory (MSF) to fast SC devices while performing computation on scalable NA arrays, a design we term MagicAcc, which effectively mitigates the resource-preparation bottleneck. (2) We explore a Memory-Compute Separation (MCSep) paradigm that utilizes NA arrays for high-density qLDPC memory storage and SC devices for fast surface-code processing. Our evaluation, based on a comprehensive end-to-end cost model, demonstrates that principled heterogeneity yields significant performance gains. Specifically, our designs achieve $752\times$ speedup over NA-only baselines on average and reduce the physical qubit footprint by over $10\times$ compared to SC-only systems. These results chart a clear pathway for leveraging cross-modality interconnects to optimize the space-time efficiency of future fault-tolerant quantum computers.

Broadband optical response governs light-matter interactions across photonics, plasmonics, thermal radiation, and quantum fluctuation electrodynamics, yet determining a continuous dielectric function over many decades in frequency typically requires combining multiple spectroscopies, extrapolations, and material models. Here we show that quantum-fluctuation forces provide a route to broadband optical characterization. Casimir interactions depend on the dielectric response of materials across the electromagnetic spectrum, but this information is encoded through Lifshitz theory in a spectrally weighted and nontrivial way. By training physics-constrained supervised learning models on synthetic dielectric spectra and their corresponding Casimir force curves, we invert this relationship and constrain the complex permittivity of materials over more than seven orders of magnitude in frequency and provide an estimate of their values from force-distance data. The reconstruction reveals a direct separation-frequency correspondence: large separations constrain the free-carrier response, whereas shorter separations encode higher-frequency resonant structure. Applying the method to measured force gradients identifies the current experimental limits imposed by measurement noise, restricted separation range, and model complexity. These results establish fluctuation-induced forces as a spectrally weighted route to broadband optical characterization and define the experimental and physical limits that govern what spectral information is accessible from near-field quantum electromagnetic measurements.

Magic states are essential for universal quantum computation and are widely viewed as a key source of quantum advantage, yet in realistic devices they are inevitably noisy. In this work, we characterize how noise on injected magic resources changes the classical simulability of quantum circuits and when it induces a transition from classically intractable behavior to efficient classical simulation. We adopt a resource-centric noise model in which only the injected magic components are noisy, while the baseline states, operations, and measurements belong to an efficiently simulable family. Within this setting, we develop an approximate classical sampling algorithm with controlled error and prove explicit noise-dependent conditions under which the algorithm runs in polynomial time. Our framework applies to both qubit circuits with Clifford baselines and fermionic circuits with matchgate baselines, covering representative noise channels such as dephasing and particle loss. We complement the analysis with numerical estimates of the simulation cost, providing concrete thresholds and runtime scaling across practically relevant parameter regimes.

We study the Fano effect in dissipative cavity quantum electrodynamics (QED), which originates from the interference between the emitter's direct radiation and that mediated by a cavity mode. Starting from a two-level system coupled to a structured reservoir, we show that a quantum master equation previously derived within the Born-Markov approximation can be rederived by introducing a single auxiliary mode through the pseudomode approach. We identify the corresponding spectral function of the system–environment interaction and show that it consists of a constant contribution and a non-Lorentzian contribution, whose interplay gives rise to a spectral profile of the Fano form. The constant contribution represents a Markovian background and is essential for obtaining a Lindblad master equation. Furthermore, by applying Fano diagonalization to an atom–cavity system coupled to common and independent reservoirs, we independently derive the same spectral function and clarify its physical origin. Our results provide a unified description of the Fano effect in single-mode cavity QED systems and reveal its non-Markovian origin encoded in the spectral function of the structured reservoir.

Static phase detuning fundamentally constrains coherent state transfer in asymmetric classical and quantum systems. We introduce a Bloch-sphere formulation for piecewise-coherent modulation that recasts coupled-mode dynamics as geometric trajectories, transforming algebraic control into path optimization. The approach reveals a cone of inaccessibility at the target pole and yields exact geodesic criteria for complete mode conversion in detuned systems. Leveraging this framework, we break time-reversal symmetry to realize a magnet-free optical isolator with near-unity contrast. Furthermore, for detuning larger than coupling between modes, we develop a recursive multi-step protocol enabling deterministic transfer for arbitrary detunings and derive a universal geometric lower bound on the required number of coupling-switching events.

We study SU(3) gauge theory on small lattices in the minimal (qutrit) electric field truncation retaining only the ${\bf 1}, {\bf 3}, {\bf \overline{3}}$ representations for the link variables. Explicit expressions are given for the Kogut-Susskind Hamiltonian for the square plaquette chain and the two-dimensional honeycomb lattice. Our formalism can be easily extended to the minimally truncated general SU($N_c$) gauge theory. The addition of (static) quarks is discussed. We present results for the energy spectrum of the gauge field on these lattices by exact diagonalization of the Hamiltonian and analyze its statistical properties. We also compute the SU(3) string tension and discuss how it is modified by vacuum fluctuations. Finally, we calculate the potential energies of a static quark-antiquark pair and three static quarks and study their screening at finite temperature.

Quantum state tomography is essential for characterizing quantum systems, but it becomes infeasible for large systems due to exponential resource scaling. Overlapping tomography addresses this challenge by reconstructing all $k$-body marginals using few measurement settings, enabling the efficient extraction of key information for many quantum tasks. While optimal schemes are known for qubits, the extension to higher-dimensional qudit systems remains largely unexplored. Here, we investigate optimal qudit overlapping tomography, constructing local measurement settings from generalized Gell-Mann matrices. By establishing a correspondence with combinatorial covering arrays, we present two explicit constructions of optimal measurement schemes. For $n$-qutrit systems, we prove that pairwise tomography requires at most $8 + 56\left\lceil \log_{8} n \right\rceil$ measurement settings, and provide an explicit scheme achieving this bound. Furthermore, we develop an efficient algorithm to determine the optimal order of these measurement settings, minimizing the experimental overhead associated with switching configurations. Compared to the worst-case ordering, our optimized schedule reduces switching costs by approximately 50%. These results provide a practical pathway for efficient characterization of qudit systems, facilitating their application in quantum communication and computation.

Quasiperiodic systems host exotic transport regimes that are distinct from those found in periodic or disordered lattices. In this work, we study quantum transport in the Aubry-André-Harper lattice in a two-terminal setup coupled to zero-temperature reservoirs, where the conductance is evaluated via the nonequilibrium Green's function method. In the extended phase, we uncover a universal subdiffusive transport when the bath chemical potential aligns with the band edges. Specifically, the typical conductance displays a scaling of $\mathcal{G}_{\text{typ}}\sim L^{-2}$ with system size $L$. We attribute this behavior to the emergence of an exceptional point (Jordan normal form) in the transfer matrix in the thermodynamic limit. In the localized phase, the conductance shows exponential decay governed by the Lyapunov exponent. Intriguingly, in the critical phase, we identify pronounced log-periodic oscillations of the conductance as a function of system size, arising from the discrete scale invariance inherent to the singular-continuous spectrum. We further extend our analysis to the generalized Aubry-André-Harper model and provide numerical evidence suggesting that the exact mobility edge resides within a finite spectral gap. This results in a counter-intuitive exponential suppression of conductance precisely at the mobility edge. Our work highlights the distinct transport behaviors in quasiperiodic systems and elucidates how they are rigorously dictated by the underlying local spectral structure.

The high overhead of fault-tolerant measurement sequences (FTMSs) poses a major challenge for implementing quantum stabilizer codes. Here, we address this problem by constructing efficient FTMSs for the class of quantum Hamming codes $[\![2^r-1, 2^r-1-2r, 3]\!]$ with $r=3k+1$ ($k \in \mathbb{Z}^+$). Our key result demonstrates that the sequence length can be reduced to exactly $2r+1$-only one additional measurement beyond the original non-fault-tolerant sequence, establishing a tight lower bound. The proposed method leverages cyclic matrix transformations to systematically combine rows of the initial stabilizer matrix and preserving a self-dual CSS-like symmetry analogous to that of the original quantum Hamming codes. This induced symmetry enables hardware-efficient circuit reuse: the measurement circuits for the first $r$ stabilizers are transformed into circuits for the remaining $r$ stabilizers simply by toggling boundary Hadamard gates, eliminating redundant hardware. For distance-3 fault-tolerant error correction, our approach simultaneously reduces the time overhead via shorting the FTMS length and the hardware overhead through symmetry-enabled circuit multiplexing. These results provide an important advance towards the important open problem regarding the design of minimal FTMSs for quantum Hamming codes and may shed light on similar challenges in other quantum stabilizer codes.

What connects minimal decision-making to contextual probability? We address this question through the Tug-of-War (TOW) principle, a resource-coupled mechanism for multi-armed bandit decision-making. Starting from classical probability, we show that when reward-learning functionality and specified information requirements are fixed, minimizing the necessary relaxation of common event semantics can lead to nonclassical probability. We derive the exact minimum semantic repair and identify the conditions under which information efficiency, calibration, and compositional consistency select contextual statistics. We then construct a single quantum Tug-of-War (QTOW) instrument in which the same decision–reward process both improves stationary decision performance and drives the unconditional learned state beyond the Klyachko–Can–Binicioğlu–Shumovsky (KCBS) noncontextuality bound. A finite diagnostic based on the instrument's recovery operations also yields a corrected contextuality witness. These results connect minimal decision-making, operational economy, and the emergence of contextual probability.