Papers

Qubits are powerful computational resources because each additional qubit doubles the size of the accessible state space. This expressive power comes at a cost: adding qubits also increases circuit size, constraint overhead, and exposure to hardware noise. These limitations are especially critical for near-term quantum computers, making the number of qubits required to formulate a problem a central practical concern. In this work, we present a method for efficiently mapping logistics and routing problems onto qubits through structure-aware encoding reduction. We demonstrate the method on a benchmark problem of latency-resilient routing under dual-link failures. For this benchmark, the reduced formulation substantially lowers both the qubit count and the compiled circuit complexity while preserving the original optimization task. By running the reduced model on the same trapped-ion quantum computer as the benchmark, we obtain a 100X improvement in the success probability. This finding shows how careful problem formulation can make current quantum hardware substantially more effective for practical optimization.

Experimental detection of multipartite Bell nonlocality faces many challenges. The increase in the size of the system demands a higher fidelity of state preparation, a higher detection efficiency, and a larger number of correlators that need to be estimated. These issues are even more pronounced if one wishes to detect a more restrictive variant of Bell nonlocality called genuine multipartite nonlocality (GMNL). In this work, we introduce two classes of multipartite Bell inequalities that are capable of detecting GMNL correlations and address different experimental hurdles in GMNL detection. The first class consists of the number of correlators that scales linearly with the number of parties. The second class increases the number of correlators and, in return, provides higher noise robustness of GMNL detection. Both classes of inequalities are constructed to detect GMNL in graph states, and in fact both can be used for self-testing of graph states and the performed measurements.

Quantum entanglement is a fundamental resource in quantum information science, commonly consumed to perform tasks like quantum teleportation and quantum key distribution. Entanglement concentration converts partially entangled pure states into nearly perfect Bell pairs. While its efficiency is well understood in the asymptotic limit, practical protocols must operate with finite systems. In this finite regime, and at the low error levels relevant in practice, performance is penalized by corrections that reduce the achievable yield. We investigate whether this fundamental finite-size penalty can be mitigated by an entanglement catalyst: an auxiliary state that aids the transformation but is returned exactly and uncorrupted. Although such a catalyst cannot increase the leading-order asymptotic yield, we show that it fundamentally alters the finite-size scaling. For every bipartite pure state with nonuniform Schmidt coefficients, we exactly determine the optimal second-order correction to the yield and show that catalysis completely overcomes this finite-size penalty.

Practical fault-tolerant quantum computing requires qubit-efficient quantum error correction (QEC). Clifford deformations (CDs) modify the stabilizers of a QEC code to lower its logical error rate at no additional resource cost. However, the number of possible CDs grows exponentially with the number of qubits, making exhaustive search infeasible beyond small codes. In this work, we further show that under circuit level noise the optimal CD depends strongly on both the noise model and decoder. To make systematic CD optimization possible, we introduce Evolution-Based Best-arm Identification (EBBI), a shot-efficient search algorithm that treats the circuit, noise model and decoder as a black box. We benchmark EBBI's performance on the rotated surface code, under two strongly $Z$-biased circuit-level noise models with the PyMatching decoder. At distance 3, EBBI finds the optimal CD using up to $\sim 1100\times$ fewer shots than random search. At distance 5, when run at the target error rate, the median EBBI run converges to the CDs we believe to be optimal, while random search never converges. Under a $Z$-biased SI1000-like noise model, EBBI discovers a new CD, the B-XZZX code, which we generalized to larger distances. It differs from XZZX on only a fraction $\mathcal{O}(d^{-1})$ of the qubits at code distance $d$, yet its relative advantage grows from $\approx 5\%$ at $d = 3$ to $\approx 12\%$ at $d = 11$. We thus show that the B-XZZX pattern found by EBBI can be systematically scaled to larger code distances. Our work represents a first step towards scalable CD optimization for general QEC codes.

We study correlation-based entanglement evaluation in rank-2 mixed states of two- and multi-qubit systems. The relevant two-dimensional subspace is treated as a logical qubit embedded in the physical Hilbert space, and factorizable realizations of its logical Pauli operators are classified. For two qubits, this yields nontrivial canonical encodings related by local Clifford transformations. The relation between logical and physical Bloch vectors admits a geometric interpretation as a transversely deformed Bloch sphere, leading to closed-form expressions for two-qubit concurrence and generalized concurrence across $N$-qubit bipartitions. The entanglement scaling factor is obtained directly from complementary-subsystem correlations, without prior calibration of state-preparation parameters. Noisy simulations using the IBM Quantum FakeKingston backend model, with readout-error mitigation and zero-noise extrapolation, confirm the analytical results up to $N=10$ qubits. The protocol therefore enables entanglement estimation from only a small number of measurement settings for this class of rank-2 logical states.

We investigate holographic Krylov complexity in bottom-up holographic QCD models describing the confined phase, using the recently proposed correspondence between the growth rate of Krylov complexity and the proper radial momentum of probes, such as particles and strings, falling in the bulk spacetime. As representative confining backgrounds, we consider two horizonless geometries, namely the dilaton-deformed AdS-soliton and the deformed thermal-AdS spacetime, both arising as solutions of an Einstein-dilaton gravity system. We find that the Krylov complexity associated with a massive particle exhibits qualitatively distinct behavior in these two backgrounds when analyzed in the Einstein frame. In the deformed AdS-soliton geometry, the complexity undergoes periodic oscillations, with both the oscillation period and amplitude depending on the parameters of the model. In contrast, in the deformed thermal-AdS geometry, the complexity grows exponentially at late times and does not display oscillatory behavior. We then investigate string dynamics in the string frame and find that the Krylov complexity exhibits oscillatory behavior in both confining backgrounds. This behavior is traced to the emergence of an additional turning point in the deep infrared of the string-frame geometry. Motivated by this observation, we further analyze massive-particle dynamics in the string frame, where we find qualitatively similar behavior in the two confining backgrounds. Our results demonstrate that the Krylov complexity of confined holographic systems depends sensitively on the choice of probe and frame, while also revealing a closer correspondence between the two confining geometries in the string-frame description.

The recently developed concept of germ graphs (P. Kurasov et al., Phys. Rev. Research 7, L022071 (2025)) is employed to construct families of isocattering, non-isospectral graphs that exhibit dissipation. More specifically, a new pair of isoscattering non-isospectral graphs is constructed by connecting the existing isoscattering non-isospectral graphs, so called attachments, to the different contact vertices of the germ graph. The existing isoscattering non-isospectral graphs contained a two-loop graph labelled $\Gamma_{A2}$ and a three-loop graph labelled $\Gamma_{A3}$. These graphs have an equal total metric length, but different topologies. The resulting graphs $\Gamma_3$ and $\Gamma_4$ are verified as non-isospectral using their Euler characteristics, while their isoscattering properties are investigated by calculating the one-port scattering matrices numerically.

A useful thermodynamic model predicts what a device will do without tracking its full microscopic state. For a finite quantum working medium, the difficult question is which quantities should actually be measured. We develop a task-based method that keeps exact energy accounting separate from calibrated macroscopic prediction. Operator geometry identifies what a measured record determines and bounds what remains uncertain. We then compare direct measurements of dynamical observables with earlier measurements of the same coarse record, selecting the representation together with its measurement cost. A Bose–Hubbard example yields a compact response table tested over a continuous operating region and on unseen microscopic trajectories. A driven Ising chain shows why history is not always the cheaper choice. The result is a way to turn detailed quantum dynamics into a small, reusable, and explicitly qualified thermodynamic description.

We derive approximation rates for Sobolev functions defined on the complex unit sphere and complex projective space, representing quantum states, and on the special and projective unitary groups, representing quantum unitary operations. By using harmonic analysis on compact groups and compact homogeneous spaces, we characterize the corresponding Peter–Weyl decompositions and Sobolev spaces via irreducible representations and the Laplace–Beltrami operator. Combining spectral truncation with finite-depth quantum-circuit approximation, invoking the Solovay–Kitaev theorem, we establish quantitative rates that separate the spectral truncation error from the circuit approximation error.

Josephson junctions are the central nonlinear element of superconducting qubits, yet their standard description is reached through a chain of approximations. We propose a purely quantum-mechanical model of the junction, formulated directly in Hilbert space: a charged particle moves on a one-dimensional loop, and the junction is a point at which the wave function obeys self-adjoint boundary conditions, labelled by a coupling strength $\lambda$, which controls the transparency of the junction, and a phase jump $\delta$, which plays the role of the superconducting phase difference. For a loop with a single junction we solve the spectral problem and show that the ground-state momentum expectation, identified with the supercurrent, factorises exactly as $\langle\hat{p}_0\rangle = I_c(\delta,\lambda)\sin\delta$. For opaque junctions $I_c$ becomes independent of $\delta$ and the first Josephson relation $I=I_c\sin\delta$ is recovered; for strongly attractive coupling, where the ground state is bound to the junction, the $\sin\delta$ law is also recovered, but with an exponentially suppressed amplitude. For more transparent junctions, however, the model predicts deviations from the pure $\sin\delta$ law: $I_c$ acquires a dependence on $\delta$ already at order $\lambda^{-2}$, compatible with the higher Josephson harmonics recently found necessary to describe superconducting qubit spectra, and a fully transparent contact yields a current linear in $\delta$. When the phase varies in time, a gauge transformation shows that the voltage drop across the junction is proportional to $\dot\delta$, so that the second Josephson relation emerges without being imposed. The boundary-condition approach thus reproduces both Josephson relations from first principles and predicts corrections to them, offering a route towards higher-fidelity models of superconducting qubits.

Quantum reservoir computing and its special case, quantum extreme learning, are powerful tools for predicting classical discrete time-series with quantum devices. Forecasting continuous signals, however, requires careful discretization as oversampling artificially boosts short-term accuracy but fails over realistic intervals, while undersampling captures too few features and yields poor predictions. Here, we experimentally generate four continuous time-series signals from a chaotic electronic circuit for forecasting with quantum extreme learning. Since simplified circuit models do not fully capture real behaviour, it is unclear whether algorithms that predict simulated time-series also work for experimental signals. We address discretization via two approaches: (i) sampling local peaks/troughs; and (ii) uniform sampling at the autocorrelation timescale. The former captures resonant behaviour, while the latter fully captures chaotic features as well as allowing the reconstruction of chaotic attractors. Our algorithm achieves high forecasting accuracy for both simulated and experimental signals, demonstrating its power for continuous signal processing on near-term quantum simulators, and remains robust against moderate decoherence.

The nitrogen-vacancy (NV) color center in diamond has found applications in magnetometry across various geometrical scales. In particular, vector magnetometry using hand-held devices with low power consumption is of interest for mobile and geological applications. However, such a device requires efficient driving of the four different orientations of the NV center, thus placing demands on a broadband microwave resonator that provides a uniform and highly insensitive microwave magnetic field at the resonance frequencies of the NV centers. Here, we propose a unique planar resonator design that enables efficient driving of all four orientations of NV color centers over a 100 MHz range with only 0.5 W of microwave input power and 250 mW of laser power, allowing vector magnetic field measurements. Using the planar resonator to drive NV centers in diamond, a compact vector magnetometer was fabricated and experimentally studied. The sensitivity of the device is about \[{1.2\text{ nT}}/{\sqrt{\text{Hz}}}\;\]. While this is not a record sensitivity for diamond-based magnetometers, this device occupies its own niche as a compact hand-held magnetometer.

Deploying QKD-based secure communication at scale requires reducing duplicated optical hardware while preserving the rate of protected user data. Earlier studies established the physical feasibility of carrying CV-QKD and classical signals over shared infrastructure, motivating a quantitative comparison between optical hardware savings and the OTP-encrypted rate. We perform this comparison by defining the secure communication rate (SCR) as the rate jointly supported by secret-key generation and classical transport, and using it to optimize a shared discrete-modulation CV-QKD link. The model combines a binomial 64-QAM security bound with a trusted receiver, protocol traffic, spectral leakage - optical power leaking into the quantum receive band - and Raman scattering. At 25 km, the asymptotic model gives an optimized SCR of 12.079 Mbps, compared with 12.095 Mbps for a separated-link reference, while reducing the transmitter and fiber counts from two to one each in the modeled direction. Increasing channel separation suppresses spectral leakage, but the resulting SCR gain diminishes once receiver bandwidth limits the rate. Under the adopted receiver-noise law, increasing the bandwidth budget from 350 to 750 MHz raises the projected 25-km SCR to 24.535 Mbps despite higher trusted electronic noise. For the studied metropolitan link, sharing saves optical resources with little rate loss, while receiver-bandwidth improvements provide greater benefit than further spectral separation. Together, these results suggest an integration path: share the transmitter and fiber, limit unwanted classical power in the quantum receive band, and increase usable receiver bandwidth where the noise budget permits.

We characterize compactness of the Hilbert-Schmidt semigroups induced by finite-mode Gaussian quantum Markov semigroups with a faithful normal invariant state. A unitary second-quantization representation for every $ s $-embedding shows that compactness at one positive time, compact resolvent, drift stability, and uniqueness of the normal invariant state are equivalent. These conditions imply immediate trace-class membership for all embeddings. We derive exact trace-norm and Hilbert–Schmidt norm formulas, an embedding-independent trace identity, and the generator spectrum with algebraic multiplicities. Examples show that compactness does not require the existence of a spectral gap and that a spectral gap need not imply compactness when the invariant state is not unique.

The present paper sets out a general method for extending the isoscattering, non-isospectral quantum graphs. The methodology is illustrated by considering two graphs, denoted by $\Gamma_1$ and $\Gamma_2$, which have the same total metric length but different topologies. It is demonstrated that, despite the fact that their scattering matrices are identical, their eigenvalues, denoted by $k_n$, and Euler characteristics differ from one another. The next step in the process is to extend both graphs by affixing the same star graph to each of them. Utilising the Titchmarsh-Weyl M-function formalism, it is proven that the newly constructed, extended graphs are also isoscattering and non-isospectral.

Solving combinatorial optimization problems on near-term quantum computers mainly relies on their quadratic unconstrained binary formulation. Lately, binary polynomial formulations start to take the center stage, having a better scaling with respect to the number of used qubits. However, while quadratic forms are straightforward to implement on quantum circuits, polynomial forms of degree $d$ incur in circuit depth overheads, due to the lack of $d$-qubit gates, for $d\geq 3$, on current hardware. In this paper, we study the problem of designing the shallowest quantum circuit for a given polynomial form. We formulate it as a classical binary linear problem and we prove the NP-completeness of a variant of it. On the algorithmic side, we offer a scalable and performant heuristic method to tackle it, Tempura, as well as faster binary linear problem formulations, which offer computational feasibility while sacrificing optimality. Our performance evaluation shows that the algorithms yield far shorter circuits than the state-of-the-art approaches, and Tempura is mostly comparable with them in terms of runtime.

The Zak phase provides a fundamental geometric characterization of one-dimensional band structures and, when quantized by symmetry, serves as a bulk indicator of polarization and boundary phenomena. Conventionally, its exact quantization is tied to a global symmetry of the Bloch Hamiltonian, such as inversion or reflection symmetry. Here, we demonstrate a distinct mechanism by which the Zak phase remains exactly quantized even when the corresponding protecting symmetry is explicitly broken at the level of the full Hamiltonian. The mechanism is based on local support symmetry and destructive interference: symmetry-breaking degrees of freedom are coupled to a topological parent system in such a way that the relevant Bloch states cannot leak into them. The preserved states therefore retain their parent wave functions and inherit their quantized Zak phase exactly, despite the absence of the protecting global symmetry. We establish this mechanism for general one-dimensional insulators and demonstrate it in an inversion-broken minimal model and a reflection-broken armchair nanoribbon, where a quantized $\pi$ Zak phase and associated boundary-localized states persist. We further show that perturbations violating the exact destructive-interference condition continuously dequantize the Zak phase, while a finite regime with a near-$\pi$ Zak phase and boundary response can survive. Our results establish wave-function support, rather than global symmetry alone, as a mechanism for protecting quantized quantum geometry in one-dimensional systems.

Excitons are bound electron-hole pairs in semiconductors whose interactions influence optical properties and determine their collective behavior and emergent correlated phases. Despite the theoretical and experimental significance of these phenomena, a microscopic theory of exciton-exciton interactions that takes into account the full composite nature of these quasiparticles is lacking. Here, we present a general theory of exciton-exciton interactions that builds upon our previous publication [Physical Review B 113, 155440 (2026)], which applied only to conventional semiconductors with weak band hybridization. By contrast, the theory presented here is valid in virtually any crystalline semiconducting system and can be applied to the study of biexciton formation and correlated excitonic phases in systems where band topology, quantum geometry, and moiré effects play a significant role. In addition to the analytical theory, we also present results in simple systems with flat bands with a nontrivial quantum metric and show that the biexcitonic spectrum differs strongly from that in the case without quantum geometry. Our theory paves the way for accurate quantitative calculations of biexciton spectra and excitonic many-body phases in modern condensed-matter systems.

We study how a neural network reorganizes its learned function as training proceeds and as previously unseen parity data accumulate. The trained model is itself a Boolean function on binary strings of finite length. We then evaluate it on all data, inside and outside the training set, and read off its complete sign table. Its $\pm1$ entries are the amplitudes of a normalized state, dubbed the function-state, whose inverse subsystem purity $K_f=1/\textrm{Tr}(\rho_A^2)$ is an effective Schmidt rank. We find that small data additions broaden the Schmidt spectrum, whereas larger additions reconcentrate it in the target mode. The former is called differentiation because the model distinguishes inputs more sharply. The latter is called target-selective recoherence, where the model settles on the single rule shared by the added data. As the dataset grows, the connectivity of the constraint graph defined by the training set increases monotonically, whereas the learned inverse purity changes nonmonotonically. On a fixed connected dataset, as learning proceeds, the Schmidt spectrum begins to reorganize, followed by gains in target alignment and later by improvement in predictive accuracy. This ordering distinguishes three aspects of learning: constraint identifiability, function-state organization, and predictive accuracy. At fixed data size, a function that has already been learned can re-differentiate, an event we call retreat, without changing graph connectivity. Recovery reconcentrates the Schmidt spectrum in a similar target-selective pattern, without exact recurrence of the Boolean state. Thus the percolation of data constraints fixes the identifiable support, while the reduced state produced by training continues to reorganize even after that support stops changing.

We present an explicit quantum circuit that constructs a block encoding of a generator-representable semiseparable (one-pair) matrix directly from its two generators. For an $N\times N$ semiseparable matrix with $N=2^{n}$, the circuit uses $2n+2$ ancilla qubits and has $O({\rm polylog} N)$ depth, and it realizes a $(2\sqrt{N},\,2n+2,\,2 \sqrt{2}\ \varepsilon)$-block encoding, where $\varepsilon$ is controlled by the accuracy of the state-preparation routines that load the generators. The building blocks of the circuit are cyclic shifts, swaps, and Hadamard gates, each admitting an efficient implementation through the binary decomposition of the relevant indices.

Generative machine learning has shown remarkable results across a wide range of interdisciplinary tasks, motivating significant efforts toward Quantum Generative Models as a path to beyond-classical performance, given their capability of generating classically intractable distributions. However, comparatively little attention has been paid to securely delegating such computations to a powerful remote quantum server. In this work, we propose a blind and verifiable protocol for sampling that can be used for the inference phase of such quantum models. Such a protocol inherits blindness from Universal Blind Quantum Computing and achieves verifiability by exploiting known approaches based on trapification schemes. Alongside, to delegate the training phase, we discuss an extension of the previously proposed verifiable end-to-end Delegated Variational Quantum Algorithms (Inajetovic et al., Phys. Rev. Research, 2026). Beyond the usual Accept/Abort outcome characterizing verification protocols, the sampling protocol for inference also provides, even against a malicious server, an estimation of the amount of corrupted generated samples, i.e., a fine-grained feature describing the quality of the outcome connecting verification protocols and application-level benchmarking.

Matter-based two-level quantum systems are fundamental building blocks of quantum technologies, underpinning applications in quantum computing, simulation, communication, and sensing. Today, most of these two-level quantum systems, including Rydberg atoms, trapped ions, superconducting circuits, molecules, and quantum dots, involve transition frequencies in microwave or optical domains. However, extending their transition frequency to the THz spectral range could provide numerous benefits, leveraging the unique properties of THz radiation. Here, we show that an hBN-encapsulated graphene double quantum dot realizes a two-level system with a transition frequency in the THz spectral range. Using low-temperature transport spectroscopy in the dark combined with modeling based on nonequilibrium Green's function formalism, we demonstrate the formation of an artificial molecule, featuring bonding and antibonding states separated by an energy of up to 0.6 meV, corresponding to a resonance frequency of 0.145 THz. This approach provides direct access to important parameters of open double quantum dot systems, including tunneling rates, offering a practical alternative to conventional techniques such as photon-assisted tunneling, which are challenging to implement at THz frequencies. The realized 2D-material-based THz two-level system, compatible with direct on-chip integration, could serve as a key building block for future THz quantum technologies. Furthermore, by involving a single-electron transition, coupling these devices to a THz resonator could enable the exploration of ultra-strong light-matter interactions at the fundamental limit of a single transition coupled to a single cavity, beyond the reach of existing THz quantum systems based on collective transitions.

We investigate restrictions on the dimensions and coordinate fields of real Weyl-Heisenberg fiducial vectors. Our main result is that such vectors can exist only in dimensions $d\equiv 3\pmod{4}$. This result is motivated by evidence showing that real Weyl-Heisenberg fiducial vectors can exist only in dimensions $d = 4m^2 + 3, m \in \mathbb{Z}_{\geq 0}$. We further restrict the possible dimensions when the coordinate field is a totally real number field, an even or odd degree extension of $\mathbb{Q}$, a real quadratic field, or a maximal real subfield of a cyclotomic field. Lastly, we establish non-existence over odd-degree number fields under either positivity of all non-trivial cyclic-shift overlaps or a conjectural containment of a distinguished quadratic field in the SIC field.

Nitrogen-vacancy (NV) centers in diamond are promising quantum sensors for AC magnetic fields. However, conventional dynamical-decoupling-based magnetometry becomes technically demanding at high frequencies because of the requirement for increasingly short and high-power microwave pulses. This paper describes an AC magnetometry technique based on continuous-wave optically detected magnetic resonance (CW-ODMR) measurements, which enables the detection of signals in the hundred-MHz range. By applying a strong static magnetic field transverse to the NV axis, the energy separation between the relevant electron-spin states was tuned and resonantly coupled with the target radiofrequency (RF) magnetic field, thereby forming RF-dressed states. Unlike pulsed dynamical-decoupling schemes, this approach does not require high-power microwave pulse sequences. The key feature of our method is that the detectable frequency can be tuned by controlling the bias magnetic field strength. Using this methodology, we have experimentally achieved the frequency-tunable detection of AC magnetic fields from 14.4-632 MHz. The sensitivity was 0.558 uT/Hz^(0.5) at 14.4 MHz and 24.4 uT/Hz^(0.5) at 632 MHz. We characterized the field-dependent ODMR contrast and linewidth, and found that their degradation at large transverse fields is a important factor limiting the high-frequency sensitivity. These results establish a simple CW-ODMR approach for widely tunable RF magnetic-field sensing without high-power pulsed spin control.

The entanglement-breaking index of a channel is the number of self-compositions after which all entanglement with a reference system is destroyed. In a thermal qubit collision loop whose round is affine in the bath polarisation p, some circuits have thermal valleys: on an interior window of p the index falls below its infinite-temperature value. Rounds at different p compose exactly, so every schedule of polarisations defines a composite channel whose entanglement-breaking status can be certified in ball arithmetic. A gated search of 33 million random circuits finds no valley with contrast above about 3e-3, with an interior maximum near index 90, and yields six certified targets. At the reference target, held inside its window for 88 rounds, a centred excursion to p = 0.05 restores entanglement at exactly eight rounds: every shorter centred pulse certifiably fails, and so do the same eight rounds at the start. A 53-round pulse certifiably beats the static protocol, a depth-three valley is walked down its staircase by pulse duration, and a 1.2 per cent coherent tilt of the ancilla opens the switch at fixed population. Closing the switch costs 21 to 35 rounds. The asymmetry is not one of local rates, which agree to within about two per cent at matched circuit positions (certified). It is one of distance and response: closing must remove an entanglement margin 2.2 times larger, and while hot rounds added to a window hold act almost independently, window rounds added to a hot hold act collectively. Near the crossing, the lever of the log-margin is that of a linear approach to the entanglement-breaking boundary, with no free parameter. At the reference target, depolarising noise of about $4\nu/n$ per round kills a signature of size $\nu$ read after $n$ rounds: 1.3e-4 for the static signal, 6.5e-6 for the eight-round switch.

The uncontrolled endpoint channel can conceal how well a quantum process can protect a logical task under time-resolved control. We formulate a fixed-task resource theory of continuous process tensors with physical access interfaces, entrance-erasing free objects, and budgeted free conversions. Complete-record total-variation error measures performance; the calibrated capability is monotone under conversions that preserve a common free baseline. For unknown-state transmission the baseline is exactly $1-d^{-2}$. Two qubit processes with the same endpoint channel have optimal errors $0$ and $p=\sin^2(2gh)$ at the same finite pulse budget in an ideal-transparent system-only window architecture, forcing any endpoint-only predictor to err by at least $p/2$ on one of them. An exactly solvable family shows how the allocation of a fixed interaction phase around a control window sets the attainable error, and a nontrivial perfect echo requires and attains total control action $\pi$ in that architecture. The separation extends directly to every qubit unitary target at a budget that includes its boundary gate, while unitary tasks in any dimension have baseline $1-d^{-2}$ whenever a budget-feasible free realization gives the depolarizing output. Complete-record implementation bounds quantify coherent and dissipative control imperfections. Continuous-process randomized compilation supplies physical instrument pullbacks; compatible completion conditions extend their action, and certified dynamical bounds yield achievable task-error and capability guarantees. The resulting theory identifies temporal structure and control investment that endpoint characterization alone cannot resolve.

Continuous-variable quantum key distribution utilizes advanced digital signal processing techniques to mitigate channel impairments, driving the progress of high-performance quantum secure communications. Specifically, digital heterodyne receivers are commonly implemented using down-conversion algorithms to detect both components simultaneously where the signal is modulated onto an intermediate frequency to avoid low-frequency noise and bypass stringent optical phase-locking requirements. However, a rigorous analysis of the quantum security implications of the digital down-conversion algorithm remains absent. In this paper, we investigate the algorithm process from the perspective of quantum operator evolution, revealing that the frequency folding effect inherent in down-conversion inevitably mixes the image-frequency information into the baseband signal. To address this issue, we propose a novel operator reconstruction detection scheme based on dual-path digital heterodyne receiver. By performing a non-equal weighted combination of the output operators along two optical paths in the digital domain, this scheme perfectly cancels out the image-frequency operator physically. The robust receiver architecture preserves the baseband noise-suppression advantages, inherently achieves perfect mode balancing for asymmetric optical detection losses, and fundamentally closes the image-frequency crosstalk. Practical experiments have validated the feasibility of the proposed architecture and its effective suppression of image-frequency noise, achieving a performance of 11.4 Mbps @ 42 km. This work lays a solid theoretical and algorithmic foundation for future high-performance, highly secure digital continuous-variable quantum key distribution systems.

Chiral anomaly in topological materials manifests as negative longitudinal magnetoresistance, yet the tunability and evolution of this effect remain elusive. Here we show that doped tellurium serves as a versatile platform to realize a giant negative longitudinal magnetoresistance that is highly tunable via the Fermi level and magnetic field. By moving the Fermi level towards the Weyl point, we observe a pronounced enhancement of negative magnetoresistance, which arises from chiral anomaly and robustly persists up to ambient temperature. Beyond the quantum limit, the system exhibits positive linear magnetoconductance, serving as a compelling transport signature of the chiral anomaly in the lowest Landau level. Notably, in the extreme quantum limit at cryogenic temperatures, the magnetoresistance undergoes a dramatic reversal from negative to positive. This reversal points to a potential field-induced phase transition into a collective electronic state driven by enhanced electron-electron interactions. Our findings provide valuable insights into the unconventional chiral transport and emergent correlated quantum states under extreme magnetic fields.

The resolution of spectroscopic measurements is fundamentally limited by the convolution between a system's intrinsic response and the instrument response function, creating an ill-posed inverse problem. While entangled photons can theoretically bypass these limits, low photon flux has hindered their experimental realization. Here, we propose quantum cross-correlation spectroscopy (QCCS), utilizing macroscopic twin beams (signal and idler beams) to physically circumvent this convolution limit in coherent anti-Stokes Raman scattering. Employing the signal beam as a broadband probe, QCCS achieves all-optical deconvolution through a correlation-enhanced sum-frequency generation channel between the convoluted anti-Stokes and idler beams. By subtracting the uncorrelated background using a 500-femtosecond temporal window, we successfully retrieve narrow Raman bands (8 cm^{-1} and 15 cm^{-1}) completely obscured by a 75 cm^{-1} probe bandwidth without numerical deconvolution or prior knowledge. Our results establish macroscopic quantum correlations as a robust resource for high-fidelity spectroscopy, paving the way for ultrashort-pulse-free operando studies under natural, incoherent excitation conditions.

The indirect-control paradigm offers a scalable approach to quantum computation by restricting external operations to a small subset of qubits, whereas the entire system evolves under its intrinsic many-body Hamiltonian. This framework reduces hardware complexity and limits the noise introduced through control channels. Recently, Anan et al. proposed an implementation of the variational quantum eigensolver (VQE) within this indirect-control architecture. However, the impact and integration of quantum error mitigation techniques in such a setting remain largely unexplored. In particular, zero-noise extrapolation (ZNE), a widely used error mitigation strategy, has not yet been systematically adapted to indirect-control VQE. A key requirement of ZNE is the controlled amplification of noise, which is commonly achieved through circuit-level techniques such as unitary folding. In the indirect-control framework, however, quantum operations are largely governed by continuous time-evolution under the system Hamiltonian, making the construction of physically realizable inverse operations non-trivial. In this study, we investigate the feasibility of implementing ZNE within the indirect-controlVQEframework.We address the challenges associated with unitary folding in the presence of time-evolution operators and, with a minimal relaxation of the indirect-control constraint, we propose a ZNE-based error-mitigation strategy that exploits the symmetry of the one-dimensional XY spin chain.