Papers

Discriminating between noisy quantum processes is a central primitive for quantum communication, metrology, and computing. While discrimination limits for finite-dimensional channels are well understood, the continuous-variable setting, particularly under experimentally relevant energy constraints, remains significantly less developed. In this work, we establish an energy-constrained chain rule for the Belavkin-Staszewski channel divergence, which yields a fundamental upper bound on the error exponents achievable by fully adaptive, energy-constrained quantum channel discrimination protocols. We then derive efficiently computable bounds on asymmetric error exponents for energy-constrained discrimination of bosonic dephasing and loss-dephasing channels. Specifically, we show that three operationally relevant quantities – the measured relative entropy, the Umegaki relative entropy, and the geometric Renyi divergence – admit semidefinite program (SDP) formulations when the input energy is bounded and the Hilbert space is suitably truncated. Applying these tools, we demonstrate that optimal probes for these channels under energy constraints are Fock-diagonal, and we also enable numerically precise evaluation of bounds on achievable error exponents across discrimination strategies ranging from separable to fully adaptive. The resulting SDPs provide practical benchmarks for quantum-limited sensing in low-energy bosonic platforms.

Solid-spin defects in diamond provide long coherence times and room-temperature optical initialization and readout, making them an attractive platform for compact solid-state quantum gyroscopes. A central challenge for NV-based gyroscopes is that the rotation-induced signal is weak, while near-resonant operation, although enhancing the response, can induce nonadiabatic transitions that degrade the accumulated geometric phase and readout fidelity. Here we investigate a levitated diamond under three-dimensional rotation, in which intrinsic ${}^{14}\mathrm{N}$ nuclear spins associated with NV centers act as sensing qubits. We show that the rotation is encoded in a geometric (Berry) phase and identify a near-resonant regime with strongly enhanced phase response. To suppress the resulting nonadiabatic leakage, we introduce a counter-diabatic protocol derived from the Kato gauge potential. This enables robust geometric-phase accumulation and improves the sensitivity by four orders of magnitude relative to the conventional detuned protocol. We further evaluate the achievable sensitivity and the dominant experimental limitations, including decoherence and protocol overhead, thereby establishing a realistic route toward high-performance NV-based solid-state quantum gyroscopes.

A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum linear programming bounds. However, floating-point inaccuracies prevent the extraction of rigorous non-existence proofs from the numerical methods. Here, we address this by providing rational infeasibility certificates for a range of quantum codes. Using a clustered low-rank solver with heuristic rounding to algebraic expressions, we can improve upon $18$ upper bounds on the maximum size of $n$-qubit codes with $6 \leq n \leq 19$. Our work highlights the practicality and scalability of semidefinite programming for quantum coding bounds.

The counterintuitive Mpemba effect, wherein a hotter system cools faster, critically lacks a general macroscopic theory. Here, starting from linear irreversible thermodynamics, we formulate a generalized Newton's cooling law, $\mathrm{d}T/\mathrm{d}t = -[\gamma_0 + \mathcal{M}Q(t)](T-T_r)$, for a system at temperature $T$ relaxing in a thermal reservoir at $T_r$, where the bare relaxation rate $\gamma_0$ is modified by an initial-state memory term, $Q(t) \propto T(0)-T_r$. Arising from the interplay between heat flux and structural evolution, the coefficient $\mathcal{M}$ governs anomalous relaxation behaviors, where $\mathcal{M} > 0$ ($\mathcal{M} < 0$) induces the (inverse) Mpemba effect. This universal thermodynamic framework maps out phase diagram to provide general criteria for the Mpemba effect in complex systems, offering a macroscopic picture that bridges disparate microscopic approaches.

We propose a framework to explore the internal charge distribution of mesoscopic quasiparticles by inelastic x-ray scattering, while also accounting for the conventional scattering from electrons. Specifically, we investigate a new contribution of intrinsic and optically pumped excitons (bound electron-hole pairs) to the x-ray scattering spectrum of transition metal dichalcogenides (TMDCs). The optical excitation leads to the creation of Wannier exciton populations, adding new quasi-elastic processes beyond the conventional electronic features to the x-ray scattering spectra. Differential spectra (with and without optical pumping) can be used to isolate and identify the internal charge distribution of the optically pumped excitons in the scattering response, potentially offering insights into many-body interactions and quasi-particle dynamics in 2D systems.

Hybrid bosonic codes combining bosonic codes with photon states offer a promising pathway for fault-tolerant quantum computation. However, the efficient generation of such states in optical setups remains technically challenging due to the requirement for complex non-Gaussian resources. In this paper, we propose a novel scheme to efficiently generate hybrid entangled states between a GKP qubit and a photon-number state using small-amplitude cat states as the primary resource. We apply a breeding process using small-amplitude cat states to increase the non-Gaussianity of the input states. This method requires only linear optical elements and homodyne measurements. Furthermore, we demonstrate that this protocol can be extended to generate hybrid qudit states. This scheme has the potential to provide a resource-efficient and experimentally attractive route toward implementing hybrid quantum error correction.

We develop a framework for Matrix Product Quantum Channels (MPQCs), a one-dimensional tensor-network description of completely positive, trace-preserving maps. We focus on translation-invariant channels, generated by a single repeated tensor, that admit a local purification. We show that their purifying isometry can always be implemented by a constant-depth brickwork quantum circuit, implying that such channels generate only short-range correlations when applied on product states. In contrast to the unitary setting, where one-dimensional quantum cellular automata (in one-to-one correspondence with matrix product unitaries) carry a nontrivial index, we prove that all locally purified channels belong to a single phase, that is, they can be continuously deformed into one another. We then extend the framework to a broader class of translation-invariant channels capable of generating long-range entanglement and show that these remain deterministically implementable in constant depth using two rounds of measurements and feedforward.

The generation of exciton valley coherence typically requires linearly polarized (LP) light as an external coherent drive, whereas circularly polarized (CP) light fails to induce coherence. Here, we develop a unified, microscopically-grounded open-quantum-system framework within a five-level model incorporating bright-dark exciton interactions in monolayer WSe2, and demonstrate that the polarization ellipticity of the excitation field provides selective control over distinct exciton species contributing to valley coherence. Specifically, LP and CP excitations generate bright and dark coherence, respectively, with continuous ellipticity tuning enabling controlled transitions between these states. We further reveal dual magnetic advantages for manipulating dark coherence even in the absence of initial coherence: (i) an out-of-plane magnetic field suppresses coherence decay and (ii) an in-plane field enables its optical readout, with quantitatively realistic field strengths. These findings provide a powerful mechanism for accessing hidden dark states via ellipticity-driven coherence transfer, and establish a new pathway for harnessing bright-dark valley-coherence transitions in future quantum control.

Constrained by the complexity of theoretical calculations, current research on genuine tripartite nonlocality (GTN) within the relativistic framework concentrates mainly on Greenberger-Horne-Zeilinger-like states, with few studies addressing W states or even general tripartite states. In this paper, we apply numerical methods to investigate how environmental decoherence and spacetime dilaton influence GTN and genuine tripartite entanglement (GTE) of W states. Our results show that GTN in the physically accessible region displays a “sudden death phenomenon” and that sufficiently strong decoherence completely destroys GTN. By contrast, GTE in the physically accessible region initially remains unchanged and then decays only when the dilaton parameter becomes large. Notably, the GTN and GTE in the physically accessible region can be enhanced by adjusting the decoherence parameter. Furthermore, we also find that the GTN in the physically inaccessible region cannot be generated, whereas the GTE will be produced there. This implies that GTE can cross the event horizon of a black hole and realize the redistribution of quantum entanglement. Finally, we further discuss whether the GTN can be transferred to the bipartite subsystem of the system.

The $t$-model represents the Hubbard model in the limit $U \to \infty$ and is one of the basic models of strongly correlated electrons. On a one-dimensional chain, the model is integrable, and the charge dynamics corresponds to that of free spinless fermions. However, the sequence of spins is frozen, leading to the Hilbert space fragmentation and nontrivial spin dynamics. We consider integrable and perturbed models with perturbations that break integrability while preserving fragmentation, and show that they exhibit various types of spin dynamics, from ballistic transport to anomalous diffusion in the integrable case, and from diffusion to subdiffusion in the perturbed case. Due to fragmentation, in all cases considered, spin transport is mediated by charge transport, with a particular magnetization dependence, most notably leading to subdiffusion in the grandcanonical average of the perturbed model, with a mechanism distinct from subdiffusion in disordered or dipole-conserving models.

Quantum systems promise to revolutionize information processing science and technology [1-3]. The preservation of quantum coherence, the defining property of qubits, fundamentally constrains the performance of quantum information processing with quantum memories [4]. While trapped atomic ions theoretically support million-year coherence based on spontaneous emission [5-7], experimental demonstrations have reached far less, only about an hour [8-13]. Here we combine clock-state qubits with decoherence-free subspace (DFS) encoding to achieve coherence exceeding ten hours. Using correlation-based phase tracking in 171Yb+ ion pairs sympathetically cooled by 138Ba+ ion, we demonstrate this without magnetic shielding or enhanced microwave phase stabilization that previously limited coherence times. DFS encoding references the qubit phase to the inter-ion energy difference to reject microwave phase noise and common-mode magnetic fluctuations, while clock states provide environmental insensitivity. Throughout measurements extended to 1600 seconds, we observe minimal coherence decay, with exponential fits yielding a coherence time of (3.77 +/- 1.09) x 10^4 seconds. Our results establish DFS encoding as a form of passive error correction that eliminates technical noise constraints, unlocking the million-year coherence potential of atomic ions for scalable quantum information processing.

Self-testing is a phenomenon where the use of specific quantum states or measurements can be inferred solely from the correlations they generate. We introduce a universal method for conducting robustness analysis in the self-testing of various quantum resources. Unlike previous numerical approaches, which rely on selecting specific isometries, our method optimizes over equivalence transformations, thereby leading to tighter robustness bounds. This optimization employs the well-established technique of semidefinite programming relaxations for non-commuting polynomial optimization. Our method can be universally applied to diverse self-testing settings, including steerable assemblages in the Bell scenario, constellations of quantum states in the prepare-and-measure scenario, and entangled states in the steering scenario. We demonstrate the method's capability to surpass previously reported robustness bounds across a range of concrete examples.

We introduce a stabilizer formalism for EAQECCs with noise ebits, using special subgroups of product groups of two Pauli groups. This formalism includes the two coding schemes,given by Lai and Brun (C.Y. Lai and T. A. Brun, PHYSICAL REVIEW A 86, 032319 (2012)), for EAQECCs with imperfect ebits as special cases. Then two equivalent formalisms of the formalism are derived in nomenclature of sympletic geometry and additive codes. We apply this theory to construct some EAQECCs with noise ebits, and analyze their performance.

We construct a three-dimensional Calderbank-Shor-Steane (CSS) stabilizer code on the Face-Centered Cubic (FCC) lattice. Physical qubits reside on the edges of the lattice (coordination $K=12$); X-stabilizers act on octahedral voids and Z-stabilizers on vertices, both with uniform weight 12. Computational verification confirms CSS validity ($H_{X}H_{Z}^{T}=0$ over GF(2)) and reveals $k=2L^{3}+2$ logical qubits: $k=130$ at $L=4$ and $k=434$ at $L=6$, yielding encoding rates of 67.7% and 67.0% respectively. The minimum distance $d=3$ is proven exactly by exhaustive elimination of all weight-$\le 2$ candidates combined with constructive weight-3 non-stabilizer codewords. The code parameters are [[192, 130, 3]] at $L=4$ and [[648, 434, 3]] at $L=6$. This rate is 24x higher than the cubic 3D toric code (2.8% at $d=4$), though at a lower distance ($d=3$ vs. $d=4$); the comparison is across different distances. The high rate originates in a structural surplus: the FCC lattice has $3L^{3}$ edges but only $L^{3}-2$ independent stabilizer constraints, leaving $k=2L^{3}+2$ logical degrees of freedom. We provide a minimum-weight perfect matching (MWPM) decoder adapted to the FCC geometry, demonstrate a 10x coding gain at $p=0.001$ (and 63x at $p=0.0005$), and discuss implications for fault-tolerant quantum computing on neutral-atom and photonic platforms.

Decoding a quantum error correction code is generally NP-hard, but corrections must be applied at a high frequency to suppress noise successfully. Matchable codes, like the surface code, exhibit a special structure that makes it possible to efficiently, approximately solve the decoding problem through minimum-weight perfect matching (MWPM). However, this efficiency-enabling property can be lost when constructing implementations for fault-tolerant gadgets such as syndrome-extraction circuits or logical operations. In this work, we take a circuit-centric perspective to formalise how the decoding problem changes when applying ZX rewrites to a ZX diagram with a given detector basis. We demonstrate a set of rewrites that preserve MWPM-decodability of circuits and show that these matchability-preserving rewrites can be used to fault-tolerantly extract quantum circuits from phase-free ZX diagrams. In particular, this allows us to build efficiently decodable, fault-tolerant syndrome-extraction circuits for matchable codes.

In this paper, we examine the properties of spin-polarized interfaces consisting of single-molecule magnet bis(cyclopentadienyl)cobalt(II) (cobaltocene) and two-dimensional magnetic materials, semiconducting CrI$_3$ and metallic Fe$_3$GeTe$_2$, using first-principles density functional theory based calculations. Our calculated adsorption energies indicate the stability of these hetero-interfaces with the observation of hybridization of electronic states across the interface. Magnetic exchange interaction parameters have been obtained from both total energy differences and the Liechtenstein-Katsnelson-Antropov-Gubanov (LKAG) formalism in the basis of maximally localized Wannier functions (MLWFs). Analysis of these parameters shows a strong directional anisotropy in the magnetic substrate-molecule interaction in agreement with the nature of orbital hybridization. Additionally, possible exchange mechanisms are proposed based on orbital-resolved exchange and hopping parameters. We also show that the molecular adsorption may enhance the intralayer exchange interactions, with some exchange parameters reaching up to a 3-fold increase in magnitude compared to the freestanding case. Finally, we observe a 100 % spin polarization at the Fermi level in the cobaltocene/CrI$_3$ interface, which makes it particularly promising for spin-transport applications.

A double-heralding technique is presented for producing heralded entangled photon pairs from spontaneous parametric down-conversion (SPDC). Compared to the swap-heralded schemes studied in previous cascaded SPDC and zero-added-loss multiplexing (ZALM) proposals, this double-heralding technique is found to yield the most resource-efficient implementation in terms of minimizing the total number of sources and detectors required to achieve a specified rate and fidelity. This is achieved by reducing the number of modes and mode-sorting optics needed on the heralding path. Specifically, by immediately detecting any two signal photons from an array of down-converters, the corresponding idler photons can be projected onto an anti-correlated pair state which is shown to be unitarily equivalent to the state produced by swap-heralded sources, and hence can be used directly for long-range entanglement distribution in a ZALM architecture. Quasi-deterministic operation through two distinct multiplexing techniques is analyzed. The analysis derives expressions for the heralded pair probability and fidelity assuming realistic detectors with losses, dark counts, and partial photon number resolution (PNR), providing a framework for implementation of the source on a photonic integrated circuit (PIC).

We develop tools for characterizing vertices of fiber products of polytopes and apply them to simplicial distribution polytopes, a class of probability polytopes arising in quantum foundations and quantum information. In the theory of simplicial distributions, a pair of simplicial sets encoding measurement and outcome spaces determines a convex polytope of compatible probability assignments. Our first results give geometric criteria for detecting vertices of fiber products in terms of support data. These results are obtained in the more general framework of inverse limits of diagrams of polytopes in standard form, and they translate to corresponding criteria for simplicial distributions on arbitrary colimits of measurement spaces. We then focus on one-dimensional measurement spaces, where simplicial distributions recover and generalize local marginal polytopes in graphical models. In this setting, our sharpest results concern dipole graphs, for which we obtain a complete characterization of vertices and refine it to a graph-theoretic criterion. These characterizations are reminiscent of the classical support-graph criteria for transportation polytopes, but they arise in a richer class of polytopes in which vertex structure depends not only on support acyclicity but also on additional geometric compatibility data. Using the collapsing method from simplicial topology, we transfer the dipole characterization to rose graphs and obtain analogous results there. Finally, we apply collapsing to complete bipartite graphs, which encode physically relevant bipartite Bell scenarios, and more generally to arbitrary connected graphs, yielding lower bounds on the number of vertices.

The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of circumventing this limitation using "virtual" implementations of non-physical processes using measurement and data-processing on statistical samples of the unknown input. However, the statistical fluctuations of this data degrades the virtual copies so much that the protocol effectively depletes, rather than proliferate, the sample size – thereby rendering it worse than the "naive" approach of splitting the given sample and sending a subsample to each receiver. In this work, we circumvent this flaw by allowing a small amount of systematic bias in the broadcast data, resulting in approximate virtual copies. We provide efficient semidefinite programs (SDP's) to determine the minimum sample size required to keep the approximation error below a desired threshold and vice versa. For reasonably small error values, we find approximate virtual broadcasting to be viable with sample sizes smaller than naive sample-splitting would demand. Along the way, we prove several symmetry-based simplifications to the problem, allowing optimal approximate broadcasting to be characterized in terms of the simple class of depolarizing channels.

In this letter, we fill a hole in the existing literature about disordered quantum spin systems generated by a random local interaction $\{\mathfrak{h}(Z)\}_{Z\Subset \mathbb{Z}^\nu}$ satisfying a statistical version of translation invariance. We show such systems always have disordered ground states in the thermodynamic limit with the same symmetry. A key tool we use is a disordered version of the Lieb-Robinson bounds, which hold almost surely under mild conditions on $\mathfrak{h}$. Along the way, we formalize the notion of a random state on a $C^*$-algebra and prove a weak-$\ast$ version of the Riesz-Markov-Kakutani theorem, which seems not to have been recorded in the vector measures literature. As a consequence of the existence of the aforementioned disordered ground states, we show that the spectrum of the GNS Hamiltonain associated to the bulk dynamics is deterministic with respect to the disorder.

Energy renormalizations of resident carriers and excitons are studied theoretically, and compared with recent experiments of electrostatically-doped WSe$_2$ monolayers. The calculated energy renormalization of resident carriers, subjected to strong out-of-plane magnetic field, reveals the importance of dynamical screening in transition metal dichalcogenides. The energy renormalization of tightly bound excitons is analyzed through the exchange interaction between the electron (or hole) component of the exciton and resident carriers that share the same spin and valley quantum numbers. Our theory explains the weak energy shift of excitonic resonances despite the strong energy renormalization of resident carriers. We identify the dependence of the energy renormalization on the envelope function of a tightly-bound exciton, showing that unlike free electron-hole pairs, this energy renormalization is not the added renormalizations of a resident electron and resident hole.

Pulsed Dynamic Nuclear Polarization (DNP) is currently receiving substantial interest as a means to enhance the sensitivity of nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) by orders of magnitude. It has also received much attention as a central ingredient in many modalities of electron spin-involved quantum sensing. Relative to spin engineering associated with NMR, the design of efficient pulsed DNP experiments with a broad experimental scope are challenged by large electron-nuclear spin systems, large electron spin-involved interactions, and instrumental non-idealities and limitations. All of this may challenge traditional NMR-like theoretical and numerical pulse sequence engineering. Exploiting state-of-the-art instrumentation and taking advantage of the high sensitivity of DNP relative to NMR, we here demonstrate the use of combinations of Bayesian machine learning methods and constrained random walk procedures to design pulse sequences in situ, by experiments, directly on the spin systems responding to spectrometer instructions. For trityl and nitroxide samples, it is demonstrated that efficient broadband DNP pulse sequences can be designed in situ with experimental protocols benchmarked against in silico analogs.

Ultrastrong light-matter coupling (USC) gives access to exotic quantum phenomena and promises faster quantum gates, yet coherent time-domain control in this regime remains largely unexplored. Here, we realize USC in a hybrid system consisting of an InAs nanowire-based gatemon qubit coupled to a superconducting resonator. Spectroscopy reveals an avoided crossing that cannot be captured by the Jaynes-Cummings (JC) model, as well as photon-number-dependent transitions whose energies deviate markedly from the JC ladder expected in the strong coupling regime. Beyond demonstrating USC, we achieve time-resolved coherent control of the qubit and measure coherence times comparable to gatemons operating outside the USC regime. These results establish that hybrid semiconductor-superconductor qubits can retain coherent control in USC and provide a platform for exploring quantum dynamics and device concepts in this regime.

In July 1976, Metcalfe and Boggs published their foundational paper on Ethernet in Communications of the ACM. Their efficiency model – E = (P/C)/(P/C + W*T) – measures the fraction of Ether time carrying good forward packets under contention. For fifty years this model has framed how the community thinks about Ethernet performance. We argue it is silent on the question that matters for modern intra-rack interconnect: bilateral transaction efficiency – the fraction of link time that produces committed agreements between sender and receiver. Metcalfe and Boggs themselves planted the seed in their EFTP "end-dally" protocol (Section 7.2.2), and the deeper anchor is older still: Abramson's Alohanet carried positive acknowledgments at the link layer – a bilateral mechanism Metcalfe consciously removed in 1973 to obtain Ethernet's simple, ACK-free packet format. The result is a fifty-year bilateral zigzag: Aloha (bilateral) to Ethernet (unilateral) to the EFTP end-dally (bilateral) to TCP (unilateral-with-bilateral-above). We formalize bilateral efficiency, connect it to the back-to-back Shannon channel with Perfect Information Feedback, and – scoping the claim explicitly to intra-rack distances of one meter or less – describe how the Open Aethernet link recovers mutual knowledge at the link layer. The correction to Table 1 is not a different set of numbers. It is a different question.

For decades, it has been known that local hidden variable theories cannot be disproved by collider experiments involving decaying particles. However, if these theories satisfy a small set of mild assumptions, they become testable. In particular, they can be disproved using Bell-like inequalities for $\mu^+ \mu^-$ and $\tau^+ \tau^-$ pairs.

Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant types of constraints. Here, we propose a semidefinite relaxation methodology that can incorporate a breadth of constraints needed in various quantum correlation problems, thereby generalising the seminal Navascués-Pironio-Acín hierarchy. It yields useful results at reasonable computational cost. We showcase the methodology and its features by using it to address five different quantum information problems. These are (i) entanglement witnessing from imperfect measurement devices, (ii) certifying measurements from fidelity-constrained sources, (iii) computing dimensionality in genuine multi-particle entangled states, (iv) benchmarking dimensionality for state preparation devices, and (v) finding uncertainty relations for nearly anti-commuting observables. These applications reflect both the usefulness and versatility of the methodology, as well as its potential for broader relevance in the field.

Modulated symmetries are internal symmetries that act in a spatially non-uniform manner. Consequently, when a modulated symmetry $G_{\text{int}}$ is combined with a spatial symmetry $G_{\text{sp}}$, the total symmetry group takes the form of a semidirect product $G=G_{\text{int}}\rtimes G_{\text{sp}}$. Using matrix product states, we classify topological phases protected by modulated symmetries together with spatial symmetries in one spatial dimension. We show that these modulated symmetry-protected topological (SPT) phases are classified by $H^{2}(G,U(1)_s)$, in agreement with the crystalline equivalence principle, which states that SPT phases protected by symmetries involving spatial elements are in one-to-one correspondence with internal SPT phases protected by the same symmetries, viewed as acting internally. Furthermore, we provide a matrix product state derivation of the Lyndon-Hochschild-Serre spectral sequence for the corresponding internal SPT phases, which enables us to construct an explicit correspondence between modulated SPT phases and internal SPT phases. As applications of this classification, we prove a Lieb-Schultz-Mattis (LSM) theorem for modulated symmetries that forbids the existence of symmetric short-ranged entangled ground state, as well as an SPT-LSM constraint that enforces nontrivial entanglement in the SPT ground state. Finally, we use the classification to establish a similar LSM-type constraints for non-invertible Kramers-Wannier reflection symmetries.

Spatiotemporally correlated errors are widespread in quantum devices and are particularly adversarial to error correcting schemes. To characterize these errors, we propose and validate a nonparametric quantum noise spectroscopy (QNS) protocol to estimate both spectra and static errors associated with spatiotemporally correlated dephasing noise and fluctuating quantum crosstalk on two qubits. Our scheme reconstructs the real and imaginary components of the two-qubit cross-spectrum by using fixed total time pulse sequences and single qubit and joint two-qubit measurements to separately resolve spatially correlated noise processes. We benchmark our protocol by reconstructing the spectra of spatiotemporally correlated noise processes engineered via the Schrödinger Wave Autoregressive Moving Average technique, emulating dephasing errors. Furthermore, we show that the protocol can outperform existing comb-based QNS protocols. Our results demonstrate the utility of our protocol in characterizing spatiotemporally correlated noise and quantum crosstalk in a multi-qubit device for potential use in noise-adapted control or error protection schemes.

We study a so-called semi-ergodic brickwork dual-unitary circuits where, in the infinite volume limit, the two-point correlation functions of single-site operators exhibit ergodic behavior along one light ray and non-ergodic behavior along the other light ray. Here, however, we study intermediate and long-time dynamics of a system in a finite, large volume. Under such dynamics, the Heisenberg evolution of a single traceless single-site operator lies within a restricted subspace, and this time evolution can be mapped to a simpler problem of a single qutrit scattering with a bunch of qubits sequentially. Despite the model being non-integrable and free from any quenched disorder, the operator entanglement grows at most logarithmic in time, contrary to prior expectations. The auto-correlation function can be written in terms of a sum of products of $SO(3)$ matrices, allowing for a random matrix prediction for the auto-correlation function at late times. The operator size distribution also becomes bimodal at certain times, displaying intermediate behavior between chaotic and free systems.

We propose and test logarithmic Krylov (logK) complexity, an operator growth measure akin to Krylov complexity defined through a replica approach, as a viable probe of early-time operator scrambling without false positives. In finite-dimensional quantum systems, such as the Lipkin–Meshkov–Glick (LMG) model and the mixed-field Ising model at the chaotic point, we provide numerical evidence that logK-complexity discriminates between genuine and saddle-dominated scrambling at early times, correctly avoiding the exponential contribution coming from the unstable saddle in the former case, and closely tracking the conventional Krylov complexity in the latter. In integrable quantum systems admitting infinite-dimensional Krylov subspaces, such as the SYK$_{2}$ model and the quantum inverted harmonic oscillator, we show that by modifying the Krylov spreading operator, obtained through generalizing the analytic continuation procedure in the replica trick, the logK complexity can be refined to capture the integrable properties of the theories. We supplement these analyses by extending the Krylov formalism in classical dynamical systems and defining classical versions of these operator growth measures, showing that the false positives arising from unstable saddles in classical phase space are non-existent.