Papers

Quantum feedback control requires acting on noisy continuous measurement records without direct access to the underlying quantum state. We propose Kraus-Parameterized Belief Reinforcement Learning, a pipeline in which a recurrent encoder, constrained to the Stiefel manifold, produces density-matrix estimates that are guaranteed positive-semidefinite and trace-normalized by construction, embedding quantum state geometry directly into the learning loop. A Proximal Policy Optimization (PPO) actor then maps these physically valid belief states to continuous control actions. On a simulated continuously monitored qubit, the resulting policy achieves stable feedback control, maintaining a measurement-conditioned belief fidelity of approximately 0.77-0.80 and exhibiting substantially lower return variance than a parameter-matched LSTM-history baseline across both nominal and out-of-distribution conditions. Although gains in raw target fidelity are modest, the geometric constraint guarantees a physically valid, interpretable belief representation and yields markedly more stable control under measurement inefficiency and abrupt dynamics switches. These results indicate that physics-informed neural memory is a practical inductive bias for reliable quantum feedback control.

We introduce Rand-SEMI-QAOA, a finite-budget QRAO–QAOA ensemble for MaxCut based on a $(3,1)$-QRAC relaxation. The method samples labels uniformly without replacement from the product-$X$ family of an implemented Galois stabilizer mutually unbiased basis (MUB) system. Each selected state–mixer pair is optimized independently for relaxed QRAO energy and then evaluated by deterministic Pauli-sign decoding. Exhaustive scans of the implemented noncomputational MUB catalog place the product-$X$ family first in 18 of 20 validated family-mean cells and in every tested cell for $r=5,6,7$. On a complete cohort of $2{,}400$ random connected 3-regular MaxCut instances with $n\in\{18,20,22\}$, the capped matched-cardinality schedule attains a graph-mean decoded best-of-set approximation ratio of $0.9421$ with one QAOA layer, while the $K=r^2$ schedule attains $0.9319$. These statistics are conditional on the disclosed frozen selector pools and do not estimate variability over selector seeds. An exact gauge identity shows that product-family labels generate the orbit of the QRAO Hamiltonian under an $r$-dimensional sign-gauge group. For common angles and relaxed energy, deterministic syndrome analysis proves branchwise dephasing, while an anisotropic Gaussian surrogate controls the coherent label-averaged response on the scale $\beta=b/r$. The theory does not order independently optimized decoded maxima. The results are finite-size and resource-explicit and do not establish quantum advantage.

We investigate the charging of a harmonic-oscillator quantum battery by a propagating two-photon quantum pulse coupled through a two-level-system charger. Excitation-number conservation reduces the dynamics to a sequential response of the first and second excitation sectors, whose effective non-Hermitian generators exhibit two exceptional points separating overdamped, mixed, and underdamped regimes. We derive the exact full-charging amplitude and the response-matched two-photon temporal mode that achieves perfect charging in the ideal resonant single-channel model. For experimentally accessible Gaussian pulses, moderate temporal anticorrelation or a finite photon delay can enhance charging, whereas positive correlations generally suppress it. States with equal Schmidt number can nevertheless show different charging efficiencies, demonstrating that temporal-mode structure and response matching, rather than nonseparability alone, determine charging performance.

Scalable arrays of identical single-photon sources are a central resource for photonic quantum information processing, quantum networks and quantum metrology. Neutral atoms provide intrinsically identical emitters that can be assembled and rearranged in optical tweezers, but a many-channel fiber interface to individually trapped atoms has remained a major technical challenge. Here we demonstrate a chip-interfaced single-photon source array based on 50 individually addressable $^{87}\mathrm{Rb}$ atoms. A glass waveguide fan-out converts the \SI{5}{\micro m} pitch of the optical-tweezer array to the \SI{127}{\micro m} pitch of a commercial fiber array, mapping each atom to its own waveguide, fiber and single-photon detector. We resolve all 50 channels with an average nearest-neighbor cross-talk of $0.4\%$ and a uniform insertion loss of \SI{2.9}{dB}, and verify single-photon emission with $g^{(2)}(0)=0.29$, presently limited by detector dark counts and residual cooling-light scattering. Combining per-channel atom discrimination, rearrangement and reservoir replenishment, we prepare source subarrays of up to 24 atoms with a $93\%$ fill fraction. For small target numbers, atom loss is repaired from the reservoir at the detection-limited rate of \SI{118}{Hz}. We further fabricate a 784-channel waveguide chip, showing that the photonic interface can be extended well beyond the present number. This architecture establishes a fiber-native neutral-atom platform for larger arrays of identical single-photon sources.

Photonic quantum networks require error-correction architectures that remain useful with finite-energy bosonic states, pure-loss fiber transmission, and explicit resource accounting. In this light, we study a concatenated architecture in which each physical rail is a finitely squeezed Gottesman–Kitaev–Preskill (GKP) qubit transmitted through a pure-loss fiber segment, corrected by teleportation-based GKP error correction with finitely squeezed ancillae, and decoded by an outer quantum parity code (QPC). The GKP layer converts continuous homodyne syndromes into effective rail-level Pauli marginals, while the QPC layer suppresses the residual qubit-level errors. For the concatenated code family considered here, we find a finite-squeezing threshold of $5.06\,\mathrm{dB}$ at zero propagation loss. In the memory setting, the QPC layer lowers the squeezing at which repeated error correction becomes beneficial from $6.7\,\mathrm{dB}$ for bare GKP correction to $5.2\,\mathrm{dB}$ for QPC$(3,3)$ and $4.3\,\mathrm{dB}$ for QPC$(5,5)$, and improves the average-fidelity ratio by up to $75$–$90\%$ in the relevant intermediate-noise regime. In the repeater setting, avoiding pre-amplification gives larger secret-key fractions at moderate squeezing, but also produces an optimal squeezing because highly squeezed GKP peaks become sensitive to loss-induced inward displacement. Resource-normalized rates show that QPC concatenation can exceed the repeaterless PLOB benchmark by orders of magnitude and extend the communication reach, at short repeater spacing, to distances of order $10^4$km with $14$dB squeezing. However, QPC concatenation becomes detrimental when each elementary hop is too lossy. These results provide quantitative design rules for finite-squeezing GKP–QPC quantum memories and repeaters.

Machine-learning detectors for power-system cyberattacks are themselves attack surfaces, and quantum machine learning has been proposed for them. We benchmark fidelity-kernel SVMs and variational classifiers against six tuned classical models on public power-system attack data (Mississippi State/ORNL), across white-box, transfer, decision-based black-box, and poisoning attacks. Our headline finding is methodological: the benchmark's answers are set by the evaluator's choices before the models. Eight choices – six in the evaluation protocol, two in the tuning the benchmark itself runs – each reversed or moved a conclusion at fixed models. The largest is the split: the row-level protocol scores 0.905 macro-F1 where holding whole source files out leaves 0.594, and in the capped matched-dimensionality regime the quantum arm sits within noise of chance with the classical arm 0.024 above it. A fidelity kernel looks most robust until attacked directly (retention 0.886 to 0.064); a mis-fitted surrogate manufactures a 10x asymmetry; an unseeded black-box attack moves 75% between restarts. A positive control explains the accuracy null: the labels, not the pipeline. We give the control that catches each choice and release the seeded benchmark.

Photonic quantum gates are fundamental building blocks for a wide range of optical quantum information processing tasks. We propose an efficient linear-optical scheme for implementing a post-selected three-qubit fan-out gate (also known as a controlled-NOT-NOT gate) using only two ancillary single photons and linear optical elements. The scheme can be generalized to an $n$-qubit fan-out gate, requiring $(n-1)$ ancillary single photons and $(3n-3)$ polarizing beam splitters (PBSs), with a success probability of $\left(\frac{1}{4}\right)^{n-1}$. Compared to the standard gate decomposition approach, which requires $(2n-2)$ ancillary single photons, $(5n-5)$ PBSs, and yields a success probability of $\left(\frac{1}{8}\right)^{n-1}$. Our scheme significantly reduces the resource overhead and improves the success probability. We further evaluate the gate performance and demonstrate improved robustness compared to gate decomposition-based methods.

We investigate the thermalization process of two-level probes in de Sitter spacetime from a quantum-metrological perspective. For a static probe separated by a finite distance from a freely falling observer, both the intrinsic Gibbons–Hawking temperature and the position-dependent Unruh temperature are encoded in the probe state. The mutual influence between the encoding rate of the Gibbons–Hawking temperature and that of the Unruh temperature is studied. Results show that the thermalization rate is equal to the sum of the encoding rates of the Gibbons–Hawking temperature and that of the Unruh temperature. Interestingly, a nonzero inherent acceleration induced by the separation between the probe and a freely falling observer does not necessarily suppress the encoding of the Gibbons–Hawking temperature. Instead, there exists an optimal inherent acceleration at which the encoding rate of the Gibbons–Hawking temperature is maximized. Furthermore, the required total probe time of estimating the thermal effect with sufficient precision is shown in relation with the thermalization rate. The required total probe time and the corresponding number of probes remain experimentally feasible when the position-dependent inherent acceleration satisfies $\frac{a}{2\pi\omega_0}\rightarrow0.1$.

In this work, we investigate the influence of colored noise originating from a heat bath on nonlinear Landau-Zener (LZ) tunneling. The nonlinearity might arise intrinsically from many-body mean-field atomic self-interactions or Kerr nonlinearities in optical systems. Contrary to the well-established picture of thermally enhanced quantum tunneling within the linear LZ paradigm, ensemble statistics of our numerical simulations demonstrate that nonlinearity can give rise to thermally suppressed LZ tunneling: the tunneling probability of the nonlinear LZ system decreases as the amplitude of the colored noise increases beyond a critical value. Analytically, the Wiener-Hermite expansion facilitates elucidation of the intrinsic mechanism accounting for the nonmonotonic dependence of tunneling probability on noise amplitude. We compare these behaviors with stochastic resonance responses and clarify that the two phenomena stem from distinct physical mechanisms. In addition, we obtain approximate solutions in the weak- and strong-noise limits and discuss the implications of our theory.

Additional levels in a qudit can serve as more than extra computational capacity and can represent physically relevant correlations when the algorithmic design reflects the underlying physics of the problem. We demonstrate this principle for quantum chemistry simulation using a qutrit-native spatial-orbital encoding, where $|0\rangle$, $|1\rangle$, and $|2\rangle$ denote orbital occupation states. We establish a qutrit simulation framework that combines number-conserving pair-transfer and broken-pair generators with a projected-Hamiltonian energy estimator constructed from qutrit populations and coherences. Benchmarks for H$_2$, LiH, and H$_2$O show that the encoding reproduces the relevant potential-energy curves, while retaining a compact quantum resource structure. Direct comparison with the pair-only restriction confirms that the third level reduces errors by tens of mHa in LiH and by more than 100 mHa in H$_2$O. Despite a partial spin-coupling truncation in the compact H$_2$O encoding, the resulting energy curve deviates from FCI by only a few mHa over the tested range. Compared with a conventional qubit-based UCCSD approach, the qutrit scheme requires half as many quantum units and reduces the scaling of the parameterized ansatz generator count from $O(M^4)$ to $O(M^2)$, where $M$ is the number of spatial orbitals. This work elucidates how a physically motivated qutrit encoding can reduce quantum-resource requirements while retaining controlled electronic-structure accuracy, thereby providing a concrete starting point for broader qudit-native quantum algorithm design.

We bound the error in ground-state expectations of local observables caused by truncating the spatial tails of a gapped quantum lattice Hamiltonian. We show that the error is controlled by the interaction strength discarded near each site, rather than by the extensive norm of the omitted Hamiltonian. If the gap remains open along a path that removes the interaction tail, the resulting bounds are uniform in system size and extend, under suitable assumptions, to thermodynamic-limit ground states. The convergence rate reflects the decay of the interaction tail: it is algebraic for power-law interactions, superpolynomial for superpolynomial interactions, and exponential at any strictly smaller rate for exponentially decaying interactions. For superpolynomial interactions, we also derive a direct infinite-volume estimate using automorphic equivalence. The results extend to isolated low-energy sectors and parity-even fermionic systems. For two-body interactions decaying as $r^{-p}$ in $d$ dimensions, we prove an error bound $O(R^{-(p-d)})$ for $p>2d$, where $R$ is the truncation range. We construct a gapped non-translation-invariant example that saturates this scaling, showing that the bound is optimal for the general class considered. Our results quantify when finite-range truncations faithfully reproduce the local physics of gapped long-range systems.

Quantum advantage is widely expected to require sufficiently deep circuits, where correlations and global computational structure can grow beyond the reach of efficient classical simulation. This expectation is especially stark for constant-depth circuits with local readout: the expectation value of any fixed local observable lies within a bounded backward lightcone and is therefore classically tractable. Here we show that measurement feedback changes this picture. We establish a strict hierarchy of computational power: at fixed coherent depth, increasing the number of feedback outcomes strictly enlarges the class of functions accessible through a local expectation value. The two ends of this hierarchy exhibit distinct computational regimes. With logarithmic feedback, local expectation values for product-state inputs are efficiently classically simulable. Polynomial feedback, by contrast, enables an explicit family of adaptive shallow circuits to encode prime-field discrete logarithm problem~(DLP) into a fixed single-qubit expectation. Assuming the standard worst-case classical hardness of DLP, estimating this expectation value is classically hard. These results reveal a feedback-driven complexity transition, with further implications for resource lower bounds on DLP and the complexity of local-observable estimation under area-law entanglement. Our results open a new route to quantum advantage with shallow quantum circuits.

We propose several zero-point type arguments based on the inevitable zero point(s) of a spectral gap in the quantum spin system phase diagrams in various dimensions. We consider multi-parameter families of Hamiltonian extending the conventional zero-point theorem that includes only one parameter. Analogously to the zero-point theorem, we only impose model-independent transformation relations along the parameter boundary, rather than specifying any low-energy dynamics or response. We further give a series of conjectures, which generalize our statements in a uniform way. Our results give powerful and universal model-independent constraints on the possible relevant operators for critical phenomena in quantum spin models in arbitrary high dimensions.

High-purity and bright single-photon sources are important for quantum information processing and precision measurement. We propose a collectively enhanced universal photon-blockade scheme in a multi-emitter two-photon Tavis–Cummings system. Independent coherent drives of the cavity and collective emitter enable destructive interference between two-photon excitation pathways, while collective coupling supplies level anharmonicity. Full-quantum master-equation simulations, the Holstein–Primakoff approximation, and a non-Hermitian probability-amplitude analysis yield the optimal conditions: cavity resonance together with phase and amplitude matching. Compared with a purely collective blockade, the proposed scheme lowers \(g^{(2)}(0)\), and essentially preserves the single-photon population. As the emitter number \(N\) increases, the optimal point remains at \(\Delta_c=0\), while the minimum correlation follows \(g_{\min}^{(2)}(0)\propto N^{-2}\). By contrast, unconventional photon blockade shifts away from resonance as \(N\) increases, limiting its purity improvement and brightness. In the weak-drive regime, universal blockade obeys \(g^{(2)}(0)\propto\varepsilon_a^2\), owing to a higher-order bypass through the three-excitation manifold. The drive strength therefore provides an additional purity–brightness control, although the interference mechanism makes the scheme more sensitive to dissipation-rate mismatch. Our results establish a scalable route to bright, high-purity, and tunable single-photon emission in multi-emitter cavity-QED systems.

Quantum metrology offers the possibility of quantum enhancements of the precision of various sensing tasks. In this manuscript, we tackle two open problems in the theory of single-shot quantum parameter learning, going beyond the usual setting of local parameter estimation via repeated measurements. The first concerns the construction of global upper bounds on the learning precision. The second concerns rigorous guarantees on the success probability of parameter learning, namely, lower bounds on the probability of learning a parameter with a certain precision, given the constraints on the resources used for the quantum metrology task. We provide rigorous, practical, and global upper bounds and success-probability guarantees for quantum parameter learning. Most importantly, we establish a fidelity-based learning guarantee for generic mixed-state models that can be viewed as the achievability-side analogue of the quantum Cramer-Rao bound. Whereas the latter provides a no-go constraint, based on the local curvature of the fidelities, our bound uses only pairwise fidelities between parameter-encoded states to certify that a prescribed precision is attainable with a guaranteed success probability. We demonstrate the versatility of the new bounds in a Rabi-frequency-learning example involving a driven qubit coupled to a bosonic environment and a collective-spin Hamiltonian learning problem. Together, the new global bounds and success-probability guarantees allow us to rule out unattainable precision and to certify attainable precision beyond what is possible via standard Fisher-information analysis or binary hypothesis testing bounds. They also allow one to tractably characterize the performance of various learning schemes, without the overhead of an explicit simulation.

A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.

Local measurements transform a many body wavefunction into a statistical ensemble of conditional quantum states. In chaotic systems, the higher moments of such ensembles diagnose the emergence of quantum state randomness, but their structure at equilibrium quantum criticality is largely unknown. Here we show that the projected ensemble of a Tomonaga-Luttinger liquid exhibits a universal nonlinear hierarchy of state overlap moments. Remarkably, the leading scaling exponents are independent of the continuously varying Luttinger parameter. Replica boundary conformal field theory reveals a geometric origin: outcome locking combines the active replica swaps into a single collective rotated sector, while intersecting compact replica branes eliminate the leading interaction dependent zero mode contribution. Matrix product state calculations across the interacting XXZ critical phase and direct free fermion calculations independently confirm the interaction independence and nonlinear hierarchy.

Lesniewski and Ruskai conjectured that the contraction coefficient of every monotone Riemannian metric under a unital stochastic map equals the Hilbert–Schmidt contraction on the traceless subspace. We disprove the conjecture with an explicit entanglement-breaking qutrit channel induced by a doubly stochastic $3\times3$ matrix. A faithful diagonal state and a commuting traceless tangent give, simultaneously for every normalized monotone metric, the exact lower bound $\eta^{\mathrm{Riem}}_{\kappa}(\Phi_K)\ge 8896/20007>(62+2\sqrt{61})/225=\Lambda_2(\Phi_K^{\dagger}\Phi_K)$. The counterexample is entirely classical on a maximal abelian subalgebra. A theorem of Hiai and Ruskai establishes the conjectured identity for all unital qubit maps, so dimension three is minimal among full matrix algebras.

An ideal CNOT maps the phase of a coherent qubit onto the coherence between $\ket{00}$ and $\ket{11}$ of a two-qubit state, producing an output that carries both entanglement and estimable phase information. We ask how post-gate noise degrades these two quantities, and find that they are not lost together. For the phase-encoded X states generated by the protocol, the negativity is a thresholded difference of the surviving coherence $z=f\kappa$ and a population penalty $g$, vanishing once $f\kappa\le g$, while the phase quantum Fisher information (QFI) is the smooth ratio $F_\phi=4z^2/(a+b)$, which stays positive for any nonzero coherence. As a result there is an exact region of state space in which the output is separable but still phase-sensitive. We characterize this region, give the residual QFI $F_\phi^\star=4g_\star^2/(1-2g_\star)$ at entanglement death, and show that channels reaching death at the same coordinate share this residual, with global and independent local depolarization forming one such class and $F_\phi^\star=1/6$ at maximal input coherence. Four standard channels appear as trajectories through this common geometry, and asymmetric population transfer adds a third coordinate that changes the entanglement but leaves the QFI unchanged, which marks where the two-coordinate description applies. We identify a measurement that attains the bound and compare with a direct single-qubit probe, which is more precise under matched exposure; the results are therefore reference benchmarks for phase-information retention, not a claim of metrological advantage.

We introduce a $q$-deformed Deng-Fan potential ($q$DFP) model that enables controlled modulation of short-range repulsion and long-range attraction while preserving the equilibrium configuration. The model is solved exactly within the framework of the time-independent Schrödinger equation, yielding closed-form expressions for the energy eigenvalues and wave functions in terms of hypergeometric functions. We show that the deformation parameter $q$ induces non-uniform spectral shifts and a redistribution of bound states. In particular, for $q<1$, the system exhibits spectral compression and enhanced spatial localization. In addition, we investigate the system from an information-theoretic perspective using Shannon entropy, Fisher information, and Fisher–Shannon complexity measures in both position and momentum spaces. The results reveal that the deformation parameter governs the redistribution of quantum information, establishing a direct connection between spatial confinement and momentum delocalization in accordance with the Białynicki-Birula and Mycielski entropic uncertainty principle. Stronger deformation pushes the quantum state further from the minimum-uncertainty configuration, increasing the entropic excess above the BBM bound and reducing the information content about complementary observables, even as position-space localization sharpens. The analysis of entropic and Fisher information densities further shows how the deformation reshapes both the local information content and the structural complexity of the quantum states. We show that in the limit $q\to 1$, the $q$DFP model is reduced to the standard Deng-Fan potential.

Accurate modelling and understanding of quarkonium production in ultrarelativistic heavy ion collisions requires a formalism that preserves the quantum properties of microscopic $\bar{Q}Q$ systems while treating the interaction of such pairs with the quark-gluon plasma (QGP). The open quantum system approach has recently emerged as one of the most fruitful schemes to meet such requirements. However, the quantum master equations obtained so far in this context are derived assuming a strict ordering between the QGP temperature $T$ and the $\bar{Q}Q$ energy gaps ($\Delta E$) of the quarkonia bound states. This limits their predictive power since, as the QGP expands and cools down, the system traverse all regimes between the quantum Brownian motion (QBM) regime for $T\gtrsim \Delta E$ to the quantum optical (QO) regime for $\Delta E\gtrsim T$. In this paper, we derive and present a more general non-abelian quantum master equation of the Lindblad type, which does not suffer from these limitations and thus allows to faithfully describe the quantum evolution of the $Q\bar{Q}$ pairs during the whole QGP-evolution. We also provide some illustration of the key quantities governing this equation.

Super-radiance is a striking phenomenon resulting from the collective interaction of emitters with light, and it is fundamentally related to the appearance of long-range correlations between the dipole moments of the emitters. As such, it represents a distinct phase of dissipative many-body systems compared to the case of independent emitters, similarly to how ferromagnetism stands out in magnetic materials in contrast to paramagnetism. In this work we address the conditions under which the transition to super-radiance can occur in ensembles of emitters subject to dephasing and individual decay – a situation which is particularly relevant to the case of emitters in the solid state. The simplifying assumption of an ensemble of permutationally invariant emitters allows for the efficient solution of both the dissipative dynamics after a pulsed excitation, as well as of the steady state under incoherent pumping. This exact solution allows us to benchmark a truncated cumulant expansion approach, which can give predictions for arbitrarily big system sizes. We show that super-radiance is fundamentally robust to sizable dephasing and non-radiative decay rates, both under a pulsed excitation, as well as under continuous pumping. This robustness is the result of the collective acceleration effect of super-radiant emission with respect to the individual coupling to a local environment. We establish the universal critical scaling laws at the transition between normal radiance and super-radiance; and we show that, in the super-radiant phase, significant finite-size crossovers can be observed before reaching the asymptotic scaling regime. Our results pave the way for future experiments to provide a quantitative characterization of the scaling properties of super-radiance, seen as a distinct non-equilibrium many-body phase in ensembles of incoherently pumped emitters.

The discrete cylinder phase space offers a natural setting for twisted photons, Josephson junctions, and certain bosonic codes. In that context, we build a number-of-zeros hierarchy for the stellar distribution of states on the discrete cylinder phase space, tied to usefulness for quantum computation. The orbital angular momentum (OAM) and phase eigenstate, having no zeros, sits at the bottom of the hierarchy and share mathematical properties with the coherent state on the plane phase space, both sharing zero rank and a positive Wigner distribution. This reveals a structural peculiarity of the cylinder: its coherent state—the wrapped coherent state—is instead the most quantum, carrying infinitely many zeros, so "coherent state" need not signal classicality across different phase-space geometries. We identify the operations that preserve or change the zero count, giving explicit access to every rank of the hierarchy. We then ask whether this hierarchy also governs localization. Using the $L^r$ norm, the inverse participation ratio, and the Wehrl entropy as complementary measures of spread in the Husimi density, we find that the two hierarchies need not track one another: the wrapped coherent state can be more localized than the OAM eigenstate even though it carries infinitely many zeros.

Anomalous weak values and superoscillations allow a pointer to exhibit an effective shift outside the eigenvalue range of the measured observable. We reformulate this effect in a phase-space path-integral language. For each eigenvalue branch $a_j$ of the measured observable, {the interaction couples $a_j$ to the pointer position $\hat{x}_p$ and thereby translates the conjugate pointer momentum by $\gamma a_j$.} After postselection, {the branch-conditioned amplitudes are coherently superposed with coefficients chosen to produce a superoscillatory approximation. When this conditional amplitude acts on an initial pointer momentum wavepacket for which the finite superoscillatory-window condition is satisfied, the resulting momentum wavefunction behaves as if it had been translated by $\gamma A_w$, rather than by any of the eigenvalue-conditioned shifts $\gamma a_j$. This yields an effective path-integral representation of anomalous weak pointer shifts and motivates their interpretation in terms of interference among finite coarse-grained histories.} We discuss how this picture bears on conservation-law questions.

Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence–imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.

Measurement-responsive quantum experiments require control programs that can revise future operations after execution has begun without disturbing events already committed to precise timing. We present Time-Deterministic and Instruction-Dynamic Execution (TIDE), an FPGA quantum-control processor that separates a runtime-revisable future from a hardware-timed committed-event stream. TIDE provides two complementary update paths: Dynamic Instruction Parameter Update (DIPU) applies a one-shot patch to the next matching event before parameter capture, while Dynamic Instruction Stream Overwrite (DISO) performs guarded replacement, logical deletion, and out-of-line insertion in future resident-program regions. Per-channel committed-event FIFOs isolate accepted descriptors from subsequent control-core and update activity. The implemented Xilinx ZCU102 design meets timing at 250 MHz for the control core and 425 MHz for the timing/update domain. With downstream ready, every tested descriptor committed at least one timing-domain cycle before its programmed timestamp was dispatched in the programmed cycle at the registered output interfaces. In separate post-commit tests, committed timestamps and payloads remained unchanged under the applied perturbations. The minimum all-success mapped DIPU margin was four 250 MHz control-domain cycles. Under continuous payload delivery, an L-word contiguous overwrite completed in L+5 update-domain cycles. Within the characterized guard-distance range, rejected DISO requests preserved the resident path, whereas all admitted replacement, deletion, and insertion transactions exercised here executed a complete revised sequence. TIDE therefore enables runtime adaptation of both parameters and instruction structure while preserving deterministic service of committed quantum-control events.

A recent interpolation-based Quantum Signal Processing (QSP) framework by Alase bypasses the phase-finding procedures required in conventional QSP, allowing for a direct encoding of the target polynomial into a quantum circuit. However, this approach assumes access to a diagonal block encoding of function values without providing an explicit circuit construction. In this work, we address this gap by developing an explicit circuit construction method for diagonal block encodings. The resulting algorithm achieves a computational cost of $\mathcal{O}(d\log d)$ for explicitly constructing block encodings of matrix polynomials, improving upon the best-known theoretical bounds of previous methods. Numerical results confirm this scaling, demonstrating that circuit parameters for polynomial degrees up to $10^7$ can be computed in about a minute on a standard CPU.

Atom-light interaction noise can limit thermal-vapor sensing. Existing theories often treat internal-state dynamics, finite-mode atomic motion, and stochastic renewal separately, obscuring their coupled contributions to measured noise. We develop a general stochastic Liouville-transport theory, tested against polarization-resolved resonant Cs D$_2$ spectra. Joint experiment-theory analysis identifies atom-light noise below approximately 100 kHz as transit-dominated. Ballistic motion through the finite Gaussian mode modulates both the coupling-weighted effective atom number and trajectory-dependent Rabi coupling, producing predominantly common-mode noise. Boundary renewal introduces atoms with independently sampled ground-state sublevels, generating differential population fluctuations with opposite effects on the circular channels. Under an applied longitudinal magnetic field, experiment and theory show the same qualitative nonmonotonic change in common-mode suppression, supporting Zeeman redistribution of the channel responses. The framework can analyze noise in other thermal-atom sensors, including Rydberg-atom electric-field measurements.

The theory of quantum channels is traditionally studied either on finite-dimensional state spaces or within the Heisenberg picture as completely positive maps on C^*-algebras. In this paper, we consider quantum channels as completely positive maps on the duals of general von Neumann algebras in the Schrodinger picture. We investigate the construction of such channels through Pettis integrals using representations of topological groups.

Solving the time-dependent Schrödinger equation (TDSE) via traditional numerical methods is computationally intensive. Transformer models offer a compelling alternative, but standard implementations rely on soft constraints that cannot rigorously guarantee probability conservation. Here, we introduce a Transformer architecture that enforces TDSE probability conservation as a hard constraint. The design intrinsically ensures unitarity across temporal evolution without requiring repeated retraining. Our empirical findings show that this hard-constraint approach is not only physically exact but also computationally superior to conventional soft-constraint methods.