Papers

Using established probabilistic measurement-reversal theory, we study recovery placement in encoded-qutrit teleportation under monitored decay. We characterize the success advantage of reversing a no-jump map only on the encoded support and compare two receiver capabilities. The restricted-map construction applies to general finite-dimensional supports; explicit timing results are obtained for a coherent V-type sender, a $\Lambda$-type receiver, and $S=\{0,2\}$, within a prescribed family of maximal exact sender reversals. With one outcome-independent full-space receiver filter, we maximize success probability at fixed total time subject to a minimum success-weighted conditional fidelity. A single preassigned recovery time yields up to three duration-dependent regimes: no sender reversal, the earliest feasible intermediate reversal, and final-time reversal. If recovery times may be randomized independently of the input and only the pooled successful ensemble must meet the fidelity requirement, the optimum over all such timing distributions mixes the two endpoints for $\Gamma T \ge (\ln 3)/2$. With Bell-outcome-dependent nonunitary receiver recovery, each accepted full-column-rank transfer branch can instead be reversed exactly. For the same model and sender-operation family, omitting sender reversal uniquely maximizes the exact-teleportation success probability for every finite $T>0$ at positive decay rate. Partial pathway coherence further distinguishes relative support gain from absolute recovery success: the long-time dark-state plateau survives only for fully coherent decay. These results show how receiver control capabilities and the meaning of the fidelity constraint determine whether intermediate sender recovery is useful.

We perform a detailed mathematical study of the effective Hamiltonian describing a non-stationary electromagnetic cavity field, introduced by C.~K.~Law, in the presence of uniform linear motion. We find that the corresponding dynamical equations admit a unitary diagonalization and that the normalized velocity of motion satisfies the two-sided bound $\lvert v/c \rvert \lesssim 10.1716$. Although this result is mathematically consistent, the interval obtained is an order of magnitude larger than the physically admissible range $\lvert v/c \rvert < 1$. To address this limitation, we propose a reinterpretation of bosonic coupling terms as generators of the symplectic algebra $\mathrm{Sp}(4,\mathbb{R})$, identifying them with transformations that can be implemented through linear optical elements. Within this photonic approach, the coupling parameters are not restricted to small values, allowing us to explore regimes of strong effective interactions. In this case, we demonstrate the generation of two-mode squeezed states and derive analytical expressions for the average photon number in each mode. Furthermore, we analyze statistical properties that characterize mixedness and entanglement, including intermode correlations, the Mandel parameter, and the linear entropy. The corresponding Wigner function provides a phase-space visualization of the system's behavior, illustrating the connection between cavity motion, mode coupling, and nonclassical field correlations via the underlying symplectic algebra.

Rydberg atomic quantum receivers (RAQR) exhibit exceptional sensitivity to radio-frequency (RF) signals, positioning them as promising candidates for next-generation wireless systems. Extending their capabilities to orthogonal frequency-division multiplexing (OFDM), however, requires atomic responses that go beyond broadband reception and are tailored to the structured interference of multicarrier signals. To bridge this gap, we develop an atomic-comb Rydberg receiver based on six-wave mixing (SWM) transduction. In particular, injecting a multi-tone local oscillator (LO) into the RAQR generates frequency-shifted replicas of the intrinsic SWM response. By subtly tuning the amplitude and phase of each LO tone, constructive and destructive interference can be selectively induced to preserve desired response components while attenuating harmful frequency offsets. Furthermore, we harness the response-reshaping capability of the proposed atomic comb to proactively mitigate OFDM interference. More explicitly, by exploiting the discrete difference-frequency structure of both carrier-frequency-offset (CFO)-induced and phase-noise (PN)-induced inter-carrier interference (ICI), we optimize the atomic-comb response to suppress dominant ICI components directly. We further reveal an intrinsic coupling between spectral shaping and the time-domain effective channel memory, motivating a joint optimization of both ICI and inter-symbol interference (ISI), which simultaneously suppresses inter-carrier leakage and post-cyclic-prefix (CP) tail energy. Extensive simulation results validate our atomic-comb design, unveiling that the proposed atomic comb can effectively reshape the receiver response over the OFDM, while mitigating ICI, shortening the effective channel memory, and substantially lowering CP overhead.

We study the entanglement structure of gravitons in quasicrystalline inflation. Both parity-even and parity-odd interactions generate graviton pairs with nonzero total momentum. For opposite-helicity pairs with identical momenta, the parity-even contribution can be nonzero, whereas the parity-odd contribution vanishes. The transition from inflation to radiation domination produces additional conventional two-mode squeezing. We derive the resulting normal and anomalous covariances. The initially nonzero reciprocal blocks of the full field-momentum covariance remain nonzero under homogeneous evolution, although individual components can vanish. We show that this homogeneous, helicity-preserving evolution acts unitarily within each helicity sector and therefore preserves the entanglement between the complete right- and left-helicity sectors. Nevertheless, it can eliminate entanglement in the reduced state of a co-propagating pair. We illustrate this distinction using a solvable four-mode model.

In this work, we study a theoretical scheme to investigate the monogamy of quantum steering in a hybrid exciton–cavity optomechanical (EOM) system. Within the Gaussian-state formalism, we quantify the steerability among the exciton, photon, and mechanical modes in both the steady-state and dynamical regimes. We establish and verify CKW-type monogamy inequalities for Gaussian steering and demonstrate that the distribution of bipartite steering among the three modes can be controlled through the system parameters. We further examine the influence of thermal noise and temporal evolution on the steering properties and the corresponding monogamy relations. Our results show that increasing the temperature generally suppresses the strength of Gaussian steering and modifies the degree of steering sharing imposed by the CKW-type monogamy relations. In contrast, in the dynamical regime, the steerability can increase with evolution time over suitable temporal windows, indicating that the transient dynamics can be exploited to enhance quantum correlations. These results highlight the potential of hybrid exciton–optomechanical platforms for controllable quantum correlations and provide a promising route toward the generation and manipulation of multipartite quantum resources.

Quantum computation offers a promising alternative to classical Monte Carlo methods by naturally avoiding sign problems through unitary evolution. A common misconception follows from this: because quantum simulation sidesteps the sign problem, it is often assumed to be an essentially perfect substitute for classical sampling. This is false—quantum measurements are intrinsically stochastic, and estimating observables often requires a number of samples that grows exponentially with system size, time separation, or inverse temperature, exactly as in the classical signal-to-noise problem. In this work, we analyze the origin and structure of signal-to-noise problems in quantum computation, drawing parallels with classical Monte Carlo, and demonstrate that such noise persists even in sign-problem-free regimes. We discuss strategies to mitigate it, in particular a quantum generalization of Stein control variates construction, in which unbiased estimators are built from operator commutators $[X,A]$ and their discrete diagonal counterparts, and validate the approach with exactly solvable numerical examples that quantify the achievable variance reduction. Our results underscore that variance reduction, not merely sign-problem avoidance, is required to make quantum algorithms practically viable for many-body physics.

Area laws express the expectation that entanglement in gapped quantum ground states scales with a boundary rather than a volume. In one dimension this holds for every Rényi entropy, and the Rényi area-law conjecture asserts the same in higher dimensions for each fixed $0<\alpha<1$. Here we disprove this conjecture in every spatial dimension two and higher. We construct finite-range Hamiltonians with fixed local dimension, bounded interaction strength, unique ground states and a uniform spectral gap, whose ground states exhibit volume-law Rényi entanglement while obeying a von Neumann area law and remaining connected to product states through uniformly gapped local paths. The mechanism is error-space complexity: locally identifiable components of arbitrarily small weight can encode states with high entanglement complexity. We also establish the worst-case rank-error trade-off for approximate ground-state projectors, a key tool in one-dimensional area-law proofs. At fixed gap, the optimal Schmidt rank at projection error $\epsilon$ across a planar cut of cross-section $A$ scales as $\exp[\tilde{\Theta}((A\log\epsilon^{-1})^{2/3})]$ when $\log\epsilon^{-1}\gtrsim A$. Thus $\alpha=1$ is the sharp threshold for a universal Rényi area law within this adiabatically connected class.

Cancer detection using AI methods and image databases faces several challenges, including limited and imbalanced image datasets, long algorithm training times, and high-complexity feature generation. In particular, many cancer image datasets contain very few malignant examples compared to benign ones, limiting the amount of minority-class data available for training. Although classical AI and especially deep learning methods have had some success in providing cancer diagnostics, Quantum Machine Learning (QML) methods may offer advantages through high-dimensional feature representations, generative data augmentation, and the exploitation of feature correlations through quantum properties such as entanglement. In this paper, we propose using a generative QML method on the compressed breast ultrasound image dataset (BUSI) to generate synthetic images and hence augmented datasets for classifier training. In particular, we train a convolutional neural network with real, synthetic, and a combination of real and synthetic images. We test the algorithm on real images and provide comparative results for all three training cases. Our results show that the classifier trained entirely on synthetic images achieved an AUC-ROC of 0.802 (80.2%), compared with 0.760 (76.0%) for the real-data baseline.

Quantum generative models face growing qubit requirements and concentrated loss landscapes when learning long time series. Here we introduce holographic quantum circuit sampling (HQCS), which combines mid-circuit measurements, qubit reuse and independently parameterized temporal blocks to generate trajectories with a fixed number of qubits. For Haar-random HQCS and a normalized exponential kernel, we prove inverse-polynomial bounds on maximum mean discrepancy loss variance, contrasting with exponential concentration in global Haar-random generators. For generic members of a family of nonstationary Markov processes, temporal parameterization reduces exact-generation gate counts from quadratic to linear in sequence length relative to a specified class of repeated shared-block generators. Simulations demonstrate learning of Gaussian autoregressive processes and historical Volatility Index (VIX) trajectories, with the latter achieving over tenfold lower maximum mean discrepancy than the tested classical benchmarks. These results establish a framework for quantum time-series generation with fixed qubit requirements and provable avoidance of exponential loss concentration as sequence length grows.

Quantum science and engineering increasingly target the exploitation and control of large-scale dynamical systems. As system size grows, novel phenomena and quantum advantages emerge, but the resulting many-body dynamics become correspondingly harder to monitor and characterize. In particular, the underlying Hamiltonian often lacks symmetries, and the induced many-body dynamics quickly become hard to track. Focusing on one of the most important quantum features—entanglement—we demonstrate that, for a broad class of common Hamiltonian models, one can design effective witnesses that detect both the presence and structure of entanglement over relatively long evolution times. Inspired by stabilizer-based simulation, we track the evolution of generalized stabilizers of the underlying state and use them to construct linear entanglement witnesses. Through numerical experiments on Heisenberg-type Hamiltonians with up to twelve qubits, we show that the required number of measurement settings can be kept at a modest scale as the system size increases, and entanglement detection remains effective over evolution times that significantly exceed those accessible to naive approaches. The corresponding calculations can be carried out largely symbolically. Furthermore, unlike accurate state simulation, the stabilizer-based design of entanglement witnesses can be performed in a much more coarse-grained, digitized manner. We hope these results will stimulate further exploration of the quantum control of large systems.

Weak measurement has proven useful for metrology, for probing quantum paradoxes, and for the direct measurement of quantum states. Weak measurements of polarization qubits with temporal pointers provide a direct route to weak-value characterization, including in regimes where the pointer is only partially coherent. We derive a closed-form expression for the post-selected temporal shift that interpolates between the incoherent and coherent (ideal) weak-measurement limits through a single parameter $\nu$, the pointer visibility. The expression is experimentally tested for a range of polarization states spanning three trajectories corresponding to rotations about the principal axes of the Poincaré sphere. Two of the trajectories provide parameter-free benchmarks, with the real part of the weak value following $\cos^2\theta$ and $1/2$. In contrast, the weak value along the third trajectory is sensitive to incoherence and is well described by the single-parameter partial-coherence model, from which a reduced pointer visibility is obtained. Time shifts are extracted from the smoothed derivative of the pulse leading edge with internal calibration, reaching few-picosecond precision on 10 ns optical pulses using commercial components. The same apparatus also gives qualitative access to the imaginary quadrature through the frequency centroid, showing that temporal weak measurements remain accessible and quantitative in partially coherent pulsed systems.

In this work, we study operator controllability of finite-dimensional closed quantum systems driven by a single coherent control. Two general Lie-algebraic results on controllability of such systems are proved. The first gives sufficient conditions under which controllability of the system is preserved when controlled energy-level shifts are added. The second gives a sufficient basis-element condition under which the dynamical Lie algebra contains $\mathfrak{su}(N)$ and the system is therefore operator controllable. These results, together with known controllability conditions, are applied to obtain a complete classification of operator controllability of all three-level quantum systems in terms of their free and interaction Hamiltonian matrix elements. This classification covers all combinations of energy-level and level-spacing degeneracies, two or three allowed transitions, as well as the presence or absence of controlled energy-level shifts, and gives necessary and sufficient conditions for operator controllability in each case.

This work explores the edge state conduction properties of twinned and spiraled, 2D Sb2Te3 topological insulator crystals. We show the structure supports spatially continuous edge states within two spiral and knotted edge conduction channels. The channels are connected through a topological defect. This geometry introduces boundary conditions into the 2D crystal that modifies the edge state dispersion. Using a combination of low loss Electron Energy Loss Spectroscopy, Magnetic Force Microscopy and traditional carrier transport measurements we identify a distinct excitation at 0.155 eV in the spiral that seems to be related to two isolated states within the gap. This state is localized to the crystal edges. The modification of edge state bands using manipulation of a systems quantum geometry may open new avenues for the use of 2D topological systems.

Superradiance is a collective optical effect where emitters cooperatively radiate with a maximal intensity scaling proportional to the square of the number of emitters. Despite the superradiant cascade transitioning through highly entangled states, it has been shown that, for dynamics along the Dicke ladder, superradiance need not generate entanglement between the emitters. By contrast, we show how introducing incoherent local processes – normally considered detrimental to both entanglement and superradiance – can generate high levels of inter-emitter entanglement. We develop a general framework, using degenerate non-Hermitian perturbation theory, for the study of superradiant Liouvillian steady-state degeneracy breaking by these local operations from a few emitters up into the thermodynamic limit. From this, we are able to show that entanglement becomes ubiquitous in this regime and demonstrate its robustness against other forms of symmetric environmental noise. In the regime where pumping dominates, we find that population accumulates towards the maximally entangled minimal pseudo-spin states, corresponding to multi-emitter singlet states. This provides a deeper insight into many-body entanglement and the curious connection between local operations and entanglement generation.

Free classical communication can yield an unbounded single-shot saving in quantum compression, even though it leaves the asymptotic rate of an i.i.d. source unchanged. At every fixed error in $(0,1)$, we exhibit sources whose unassisted compression cost is arbitrarily large, yet a single qubit suffices with classical communication and no preshared entanglement. We establish this separation by determining the exact optimal source fidelity for compression through an $m$-dimensional noiseless quantum channel, with and without free classical communication, while preserving correlations with an inaccessible reference. Without classical assistance, the optimal fidelity is exactly the Ky Fan norm $\|\rho\|_{(m)}$, the sum of the $m$ largest eigenvalues of the source state. With classical assistance, we obtain an explicit spectral threshold formula and a protocol attaining it. Classical communication strictly improves fidelity whenever $m$ is smaller than the source rank. The corresponding compression costs are two smoothed versions of the log-rank entropy, also called max-entropy: trace-distance smoothing under local operations and quadratic smoothing under LOCC. For i.i.d. copies of a fixed source with positive entropy variance, however, the two costs have identical first-, second-, and third-order asymptotic terms. For nonlattice spectra, we determine the constant-order advantage: classical communication saves $\log_2(e)-1$ bits per block asymptotically, and the ratio of assisted to unassisted minimum communication dimensions converges to $2/e$.

When implementing scalable fault-tolerant quantum computing using superconducting quantum processors, one of the critical challenges to overcome is the presence of defective qubits arising from fabrication and calibration imperfections. A defect on a specific qubit severely restricts the connectivity between adjacent qubits, disrupts stabilizer measurements, induces frequent detection events, and consequently inflates the logical error rate. To mitigate this issue, various strategies have been proposed, such as syndrome extraction circuits based on stabilizer folding and the construction of super-stabilizers via gauge operators. However, these methods have primarily been developed for architectures with relatively high connectivity of 3 to 4. Furthermore, experimental demonstrations showing an actual reduction in logical error rates in the presence of physical hardware defects have been lacking. In this work, we propose a defect-avoidance scheme tailored for the heavy-hexagon architecture, which features a lower connectivity of 2 to 3. While previous approaches required four measurement cycles to measure all gauge operators comprising a super-stabilizer, our proposed scheme completes all gauge measurements within only two cycles. We experimentally validate this approach on IBM quantum hardware by identifying physical defects and implementing the defect-avoidance circuits. As a result, avoiding the defect yields an approximately 10% reduction in the logical error rate per cycle for both logical $X$ and $Z$ errors. These findings demonstrate that defects in superconducting hardware can be successfully handled even under the constrained connectivity of heavy-hexagon lattices, and that defect avoidance substantially reduces logical errors on real quantum hardware.

We give an explicit treatment of the third tensor power of the Clifford representation on $n$ qutrits, for $n\geq2$. This representation has five pairwise inequivalent irreducible constituents, with multiplicities $1,1,1,1,2$. The decomposition reduces the Clifford twirl of a tensor cube to four real parameters. Two of them are spectral moments of the input. The other two are cubic invariants expressed as sums of cubes of the Weyl characteristic function and the discrete Wigner function. On trace-one Hermitian matrices, the invariant polynomials of degree at most three are spanned by the constant function and four algebraically independent functions. These functions do not separate Clifford orbits. For pure inputs a single parameter suffices. We recover its range and the characterization of its maximum by stabilizer states. We bound the stabilizer fidelity, determine full separability across the three copies in the symmetric family, and recover the criterion for a complex projective $3$-design. We classify the jointly invariant quantum Boolean functions. For stabilizer testing and for testing unknown observables we give explicit bounds on copies and queries. We also give character formulas for the finite projective Clifford groups and record the complete character table for two qutrits.

Generative AI can be a powerful tool for supporting the design and implementation of quantum applications, whereas the burden of checking whether generated circuits realize the intended computation increases. In this study, we regard this burden of human understanding, checking, and judgment as “trust cost,” and propose a development methodology that integrates AI and formal verification to reduce it. In the proposed development methodology, the implementation is divided into three components: a target mathematical specification, a quantum circuit, and a correspondence theorem and its proof that prove the agreement between the two. This division separates the specifications and theorem statements checked by humans from the theorem proofs entrusted to mechanical checking. As a concrete development example of this proposal, we describe an implementation for the time evolution of a stochastic particle system and its results.

Linear-optical platforms provide a promising route to demonstrate quantum computational advantage, particularly through the boson sampling problem. While a boson sampling system should be large enough to show the quantum advantage, the size of the boson sampling problem is often restricted by experimental constraints. In particular, as a boson sampling system is scaled up, experimental constraints can limit its effective problem size to permit efficient classical simulation. In this paper, we investigate the theoretical scalability bounds for boson sampling systems under practical experimental conditions, including photon loss, mode mismatch, and input state error. We employ non-negativity conditions for phase-space quasiprobability distribution functions to analyze these effects. In addition, we introduce two device-level metrics, the boson sampling score which measures the usable capacity of a given device and the boson sampling volume which provides a common hardware-level benchmark for comparing different platforms and assessing their access to an advantage-relevant problem size regime. Our results provide fundamental insights into the performance of boson sampling systems under realistic experimental conditions and offer practical guidelines for scaling up boson sampling systems.

We investigate dynamical quantum phase transitions (DQPTs) generated by a two-step linear quench with a finite waiting time at the equilibrium critical point. The waiting stage leads to the accumulation of a dynamical phase that depends on the waiting time and directly reflects the critical spectral structure. In the transverse Ising chain, this accumulated phase modifies the critical structure of DQPTs from a single-critical-mode (SCM) regime to a multiple-critical-mode (MCM) regime. We analytically and numerically determine the boundary between the two regimes. Along this boundary, the waiting time approaches a constant in the sudden-quench limit, whereas in the slow-quench limit it follows Kibble–Zurek (KZ) scaling with the quench time. In the SCM regime, the rate function exhibits a conventional linear singularity, $r(t)-r(t^{*})\propto |t-t^{*}|^\alpha$, with the critical exponent $\alpha=1$ near the critical time. At the SCM–MCM boundary, this exponent changes to $\alpha=1/2$, leading to a divergent first derivative of the rate function. Additional discrete parameter lines with $\alpha=1/2$ also appear within the MCM regime in the parameter plane spanned by the waiting and quench times. Our findings establish a direct connection between the accumulated dynamical phase and the critical structure of DQPTs, further supported by an extended Su–Schrieffer–Heeger (SSH) model.

Distributed quantum computing distributes workloads that exceed a single processor's capacity across resource-constrained components. Circuit cutting enables this decomposition, but its effectiveness depends on partition choice. We present SACE, a Simulation-Aware Circuit Partitioning framework with Entanglement-Capability-Aware Screening. EP-Cost screens partitions using a parameter-dependent entanglement-capability proxy and native implementation cost. Under reconstruction constraints, finite-bond refinement selects the candidate that minimizes the worst-subcircuit discrepancy between normalized MPS simulations at bond dimensions $\chi$ and $2\chi$. Across 14 exhaustively enumerated small-scale candidate spaces, EP-Cost-guided genetic algorithm selections attain co-optimal native quasiprobability decomposition (QPD) overhead, with a median within-circuit Spearman correlation of 0.9965 between EP-Cost and QPD overhead. At matched cut counts, EP-Cost reduces QPD overhead by $25.20\times$ and $16.89\times$ for 8- and 9-qubit QFT circuits, respectively, and improves sampled reconstruction. On 12-qubit approximate QFT, deterministic reconstruction reduces Pauli-observable mean absolute error in all six low-bond conditions and total-variation distance in five. With five cuts and 7,776 QPD terms, SACE is best on all four reconstruction metrics in four of six conditions. At 24 qubits, SACE improves exact-local QFT accuracy in all 30 instance-bond-dimension conditions against each EP-Cost-only, Kernighan-Lin, and spectral baseline. The 50-qubit QFT comparisons remain favorable as reference convergence improves. Weighted QAOA circuits provide complementary, more bond-sensitive evidence. Refinement benefits persist across three search methods; larger candidate panels improve the optimized proxy without guaranteeing lower exact-local error.

Quantum machine learning offers new approaches to multivariate event classification in high-energy physics, but its performance relative to optimized classical methods remains uncertain under limited training data and restricted quantum resources. We investigate the sample-size scalability and representation sensitivity of a quantum support vector machine and a variational quantum classifier for Higgs-boson signal–background discrimination using simulated events from the ATLAS Higgs Machine Learning Challenge. The models are trained on balanced subsets ranging from 250 to 4000 events and evaluated on held-out samples preserving the original class distribution. Principal component analysis (PCA) and autoencoder (AE) representations are examined to reduce the input dimensionality and quantum-resource requirements. Four optimized classical classifiers are used as benchmarks under a common preprocessing, validation, and evaluation protocol. We assess training-sample scalability in classical and quantum classifiers using a four-component PCA representation and examine representation sensitivity through a secondary matched-event comparison of four- and eight-component PCA representations. Within the evaluated Higgs-boson classification setting, the QSVM showed stronger performance than the VQC at larger training sample sizes, while remaining below the best-performing classical classifiers.

Trapped ion quantum computing based on the quantum charge coupled device (QCCD) architecture uses functional zoning and ion transport to enable high fidelity computation and all to all qubit connectivity. As trapped ion quantum processing units (QPU) scale, 90{\deg} X-junction turns account for an increasing fraction of total transport time. Frequent junction crossings, therefore, make transport speed and final phonon excitation direct determinants of quantum algorithm execution efficiency. However, complex electric fields in X-junctions complicate waveform design, making it difficult to achieve high speed and low final phonon excitation simultaneously. Here, we develop a waveform design method for low-phonon-excitation high-speed X-junction(LHX-T) transport. It integrates low barrier pseudopotential channel design using multiple radio frequency (Multi-RF), multidimensional shortcut to adiabaticity dynamics, and constrained DC voltage optimization over the entire transport sequence. This framework connects waveform design, control, and computational validation, with smooth multichannel waveforms computed rapidly through a Karush-Kuhn-Tucker(KKT) linear system. The resulting waveform transports a single $^{171}Yb^+$ ion through a 90{\deg} turn in $5\mu s$ at an average speed of 14.6 m/s. Over 50 consecutive round trips, the final equivalent coherent phonon number consistently stays below 0.001, with no noticeable accumulation over time. System level evaluations at the QCCD scale show that the median duration of a single execution cycle is reduced by about $30\%$ across various circuit types. The fraction of execution time spent on transport decreases from approximately $70\%$ to $55\%$. This approach offers a means of designing fast ion transport waveforms with low phonon excitation for scalable QCCD based QPUs and provides a technical basis for efficient execution of quantum algorithms.

We consider spin-coupled Grover walks on hypercubes within the framework of quantum Bernoulli noises (QBN). We identify parity-dependent harmonic subspaces generated by the central Hamming layers: in even dimension they give a fixed-point subspace, whereas in odd dimension the walk reduces on the harmonic subspace to an explicit eight-dimensional reduced dynamics. Using symmetric-group representation theory, we characterize the corresponding isotypic structure and determine the reduced spectrum. The harmonic reduction also yields explicit long-time probability behavior and shows that the resulting states may occupy an asymptotically vanishing fraction of the hypercube while still spanning its full Hamming diameter.

We show that a quantum reservoir computer optimized with its quantum Fisher information (QFI) has a quantum advantage over a classical reservoir of equal readout cost, provided by a quantum-information advantage: optimizing the quantum parameters with the QFI metric. On Mackey-Glass forecasting, a driven Jaynes-Cummings reservoir with one to three atoms beats a tuned echo-state network at every size from 4 to 30 trained weights, by 25-69% in held-out error, and is ahead of 99.5% of 10,000 random networks. After grid and Bayesian searches saturate, the QFI-aware stage lowers the error by 29-51% at 12-30 weights, beyond equal-budget black-box search or classical-parameter gradients alone, and at 30 weights turns a loss into a win. We then derive a fundamental QFI bound on the first-order rate of change of the retrained loss and factorize the gap to this bound into five link efficiencies that identify the physical mechanism limiting optimization.

We present the concept of quadrature-detected zero-to-ultralow-field nuclear magnetic resonance (QD ZULF NMR). Two orthogonal sensors, atomic optically pumped magnetometers, are used to separately detect components of oscillating sample magnetization, which are then combined into a quadrature signal. This approach enables the distinction of positive and negative resonance frequencies with respect to the laboratory frame—such that absolute signs of gyromagnetic ratios can be determined. In addition, QD ZULF NMR reduces peak density and overlap compared to ZULF NMR with single-axis detection, while providing richer information about nuclear-spin dynamics. As an illustration, we present experimental $J$-spectra for thermally polarized [$^{13}$C]-formic acid and [$^{13}$C]-methanol, compounds commonly used in ZULF NMR which represent XA and XA$_3$ spin systems, respectively. A theoretical framework describing QD ZULF NMR signals is provided.

Detecting weak magnetic fields at hertz frequencies is central to biomagnetism, geophysical sensing, and searches for new physics, yet it remains challenging because of technical systematics and environmental noise. Here, we realize a continuously operating molecular magnetic amplifier. Signal amplification by reversible exchange (SABRE) parahydrogen-based hyperpolarization maintains non-equilibrium spin order at zero field, turning scalar-coupled nuclear spins in liquid state molecules into an active, frequency-selective gain medium. Measurements of its complex magnetic susceptibility ($\chi$) reveal an intrinsic response of $ | \chi | \approx$ 10. By feeding the collectively generated magnetic field back to the spins below the threshold for self-sustained $J$-oscillation, we extend the effective spin coherence and cooperatively enhance the susceptibility up to $ | \chi | \approx$ 80. Near threshold, this produces approximately fourfold amplification of a weak (20 pT) magnetic field at 3.37 Hz at the sensor location. These results establish hyperpolarized molecules as a tunable active magnetic medium for narrowband quantum sensing and precision measurement.

Sensing time-varying signals is essential for precision measurement and for characterizing fluctuations in physical systems. In this work, we show that quantum entanglement provides an exponential advantage in the acquisition time required to learn the temporal statistics of a stationary classical signal. The task is to estimate the characteristic function of joint displacements on selected bosonic modes within a fixed-duration window, using continuous measurements of one signal realization. We present an entanglement-assisted scheme based on two-mode squeezed probes and local Bell measurements with protected idlers, and bound its acquisition time accounting for readout noise and correlations between signal windows. For a strictly stationary pulse family, it achieves polynomial acquisition time at inverse-polynomial accuracy with logarithmic squeezing and polynomial photon number. On the other hand, we prove that any local idler-free protocols require acquisition time exponential in the number of selected temporal modes per window. This lower bound holds for both sequentially prepared and arbitrarily temporally entangled probes, allowing non-Gaussian inputs and measurements and causal classical feedback, as long as each output is measured destructively within its time bin. These results establish an exponential quantum learning advantage for a single continuously monitored stationary signal, with the sensing cost measured by total acquisition time.

We show that it is possible for three people to win the GHZ game with just the standard real valued misty state formalism, but each party will need to have two balls instead of one. That is, there will be six balls involved, rather than three. In fact, as a general rule, instead of using complex numbers in a quantum computer you can always add a qubit to "tag" complex numbers. But for proofs of non-locality, like the GHZ game, we cannot have a single universal tagging qubit, because all three parties would need access to it and therefore they could potentially transfer information via it. That's where we need to replace the one ball with three that each only need to be accessed locally.

The low autocorrelation binary sequences (LABS) problem, often formulated as a spin-lattice energy-minimization problem, is a combinatorial optimization problem with a very rugged energy landscape. We demonstrate that iterative optimization of very small subsystems of n spins that are decoupled from the rest of the system achieves global optimization of LABS with a time-to-solution scaling that is competitive with heuristics that optimize the global system of N spins directly. Our isolated-subsystem heuristic with n = 4 achieves a time scaling of O(1.333^N ) on the interval N = [27, 60], while the current state-of-the-art classical and quantum scalings are respectively O(1.34^N ) and O(1.21^N ). Our results suggest that specialized optimization hardware with only small numbers of logical spins may be of practical relevance.