Papers

Sharing entanglement among multiple users remains a central challenge for scalable quantum networks. Recent work proposed an on-demand entanglement packet architecture in which a controller uses a Time Division Multiple Access (TDMA) approach to allocate network resources. Quantum nodes are assigned a periodic schedule that probabilistically fulfills application requests for end-to-end entanglements. The schedule is recomputed periodically using well-known algorithms, such as Earliest Deadline First (EDF). However, a static schedule offers limited flexibility when outcomes are stochastic and arrivals are asynchronous. To overcome this limitation, we propose an online scheduler that dynamically schedules, defers, retries, or drops entanglement distribution reservations. In our simulations, the dynamic scheduler achieves lower completion time, higher completion ratio, and higher throughput than the static baseline. Furthermore, when the network is overloaded, the dynamic scheduler continues to construct deadline-feasible schedules and degrades gracefully.

We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary fusion categories (UFCs), as well as anyon condensation. In both cases, the NI-SETO is a relative center of UFCs. All NI-SETOs can be realized in either model, where we can use enriched UFCs to get chiral examples on the boundary of a 3D Walker-Wang model representing the anomaly. We describe several examples of NI-SETOs and compute the qualitative symmetry action on anyons and symmetry defects using tube algebra techniques.

We study a class of quantum error-correcting codes through the geometry of complex abelian varieties. These codes, introduced by Gottesman–Kitaev–Preskill, are built from symplectically integral lattices and therefore naturally define polarized complex abelian varieties. We give a precise mathematical formulation of this relationship and extend it to a dictionary between the main structures of GKP code theory and classical objects in the theory of abelian varieties. For instance, under this dictionary, the finite-dimensional code space becomes the space of theta functions $H^0(X, L)$, logical Pauli gates arise from the theta group, passive logical Clifford gates correspond to automorphisms of the polarized abelian variety, and concatenation with stabilizer codes corresponds to isogeny. We also prove several key results that give precise mathematical formulations of statements about these codes that often appear in heuristic form in the physics literature. In particular, we prove that the encoding is asymptotically isometric, that every logical Clifford gate is realized by a Gaussian unitary, and that, for noise of small variance, the failure probability is governed to first order by the shortest nontrivial displacement in the kernel of the polarization isogeny, a systolic invariant of the underlying polarization. This leads naturally to optimization problems on the moduli space of polarized abelian varieties.

Stokes' theorem turns Abelian Berry phases into curvature fluxes, whereas path ordering precludes such a simple formula for non-Abelian holonomies. We show that a quantitative form of this intuition survives: arbitrary Wilczek–Zee holonomies obey a universal quantum geometric limit~(QGL), in which the holonomy magnitude is bounded by a surface integral of the non-Abelian curvature norm. Recasting holonomic evolution as an effective Stokes–Schrödinger dynamics driven by transported curvature, we identify the QGL as the geometric counterpart of conventional quantum speed limits, with a time-integrated generator norm replaced by a surface-integrated curvature cost. The induced contour–surface variational problem is governed by a non-Abelian Lorentz force, which we address with a brachistochrone ansatz of curvature-weighted geodesics. Applied to an SU(2) tripod dark subspace, near-optimal protocols spontaneously align the transported curvature along a single Lie-algebra direction, effectively taming non-Abelianity.

Variational Quantum Algorithms (VQAs) combine quantum circuits with classical optimization to tackle problems that may benefit from the capabilities of near-term quantum hardware. In knowledge graph embedding, recent proposals based on this approach follow a similar overall architecture but differ in the way they compute the score function and in the number of qubits they require. One design uses $n+1$ qubits and obtains the score through a switch test on an ancillary qubit, while another employs $2n+1$ qubits and applies a swap test between two registers. In both cases, entities and relations are represented in a Hilbert space of dimension $d = 2^n$, with comparable computational cost and the same mean squared error loss. This work introduces a unified framework that captures the two schemes and makes it possible to explore new variants. Within this setting, we propose an alternative that keeps the intuitive meaning of the score function while dispensing with ancillary qubits and entangled measurements. The result is a model better suited to current NISQ devices, reducing hardware demands without sacrificing interpretability.

A set of quantum data can look classical in every local test and still fail to admit a single classical explanation of the whole composite system. We formulate this failure as global contextuality. Here global means global in the physical sense of the whole multipartite system, not the local/global terminology of sheaf theory. Each party's local statistics are noncontextual and each measured multipartite context admits a generalized local hidden-variable description, but the GLHV block descriptions cannot be promoted to a single noncontextual hidden-variable model for the whole system. Three bipartite constructions exhibit this separation. A polarization-path construction gives a direct global obstruction. A qubit-qutrit KCBS construction gives an algebraic scenario-level example, with explicit formulas for the unconditional KCBS operator, the correlation-polytope constraints, and the postselected violation. A flagged qutrit Werner-local state gives a state-level example: the state is entangled and local for all projective measurements, its local qutrit marginals do not violate KCBS, yet postselection rules out a single GNCHV model. We also spell out the classical composition lemma: classical conditional hidden variables can be absorbed into a larger hidden variable, whereas quantum contextual data need not allow such a factorization. Within the general Bell-type framework considered here, with arbitrary parties and arbitrary local compatible contexts, but no cross-party joint measurements, the absence of local contextuality and GLHV-type generalized Bell nonlocality does not imply the existence of a global noncontextual hidden-variable model. Global contextuality is thus a compositional obstruction to classical explanation.

Nonlinear optical light sources enable the generation of photons with polarization states that are intrinsically determined by underlying material dynamics, rather than imposed through external modulation. Here, we investigate the fundamental quantum communication performance achievable using four-wave-mixing signal fields emitted by a representative two-dimensional perovskite system. The experimentally reconstructed signal field is represented by Stokes-vector trajectories on the Poincaré sphere to establish a practical framework for visualizing spin-driven polarization encoding. An empirical nonlinear response model further connects the properties of the signal field to microscopic exciton and biexciton electronic structure, revealing that interference between resonantly enhanced optical transitions governs the accessible polarization states. The model additionally predicts that modest stabilization of the lowest-energy biexciton could substantially improve the polarization-encoding performance and provide a route toward materials optimization. More broadly, these results motivate closer integration of nonlinear spectroscopy, semiconductor materials, and quantum information science in the development of novel light sources for quantum communication.

Many applications in quantum simulation, quantum chemistry, and quantum machine learning require not a single quantum state but an ensemble of states characterizing the heterogeneity of a target system. Preparing such ensembles state-by-state is prohibitive in both variational and fault-tolerant settings, thereby motivating a generative modeling approach. We introduce latent-conditioned parameterized quantum circuits (LPQCs), a hybrid quantum-classical framework in which classical neural networks map a latent variable sampled from a prior distribution to the parameters of a parameterized quantum circuit. We prove that LPQCs are universal approximators for probability measures over density operators in the 1-Wasserstein distance, extending classical universal approximation theorems to the quantum-distribution setting. We additionally introduce a multimodal latent prior and a mixture-of-experts circuit architecture, and show empirically that the latent-conditioned parameterization alleviates the barren plateau problem during optimization, a behavior for which we provide rigorous partial guarantees. Numerical experiments validate the framework on a synthetic multi-cluster ensemble of mixed quantum states and on a QM9-derived ensemble of 3-D molecular structures. In these tasks, LPQC outperforms recent quantum generative baselines and matches the generation quality of a classical neural-network baseline, while requiring an output dimension that grows only linearly with the number of qubits rather than exponentially. By leveraging classical expressivity in the latent space, LPQCs offer a tractable route to quantum generative modeling.

This paper establishes that Krylov complexity contains the entire information about the dynamics of a quantum operator, extending the list of equivalent quantities that can serve this purpose, such as the Lanczos coefficients, the return amplitude, and the spectral density. To demonstrate this equivalence, an explicit recursive algorithm is constructed to calculate Lanczos coefficients from the Taylor expansion of the Krylov complexity around $t=0$. Furthermore, the paper discusses the distinction between Krylov and spread complexity, clarifying why a similar recursive algorithm cannot exist for the latter without additional dynamical input. These results provide a “proof of principle” for using Krylov complexity as a complete characterization of operator evolution in quantum systems.

We run a numerical linked-cluster expansion with a quantum algorithm (NLCE+QA), computing ground-state energies and one quasi-particle dispersions in the thermodynamic limit using a 20-qubit trapped-ion quantum processing unit (QPU). The NLCE+QA framework extracts thermodynamic-limit properties from small-cluster calculations, making it naturally suited for near-term quantum devices. Projector-based block-diagonalization schemes such as projective cluster-additive transformation (PCAT) are essential to NLCE+QA, and they involve matrix inversion and square root operations that amplify measurement noise. A central question is therefore whether current hardware can provide expectation values that are accurate enough to withstand non-linear classical post-processing. We explore this challenge for the transverse-field Ising model (TFIM) in one dimension, on a ladder geometry, as well as in a longitudinal field in one dimension. For the quantum algorithm, we consider adiabatic state preparation (ASP), as well as a variational quantum eigensolver (VQE) trained on a classical device. The final expectation values are obtained from the QPU, using a novel alternative to the Hadamard test that we name the CX-test. We explore the regimes currently attainable on quantum devices and comment on the improvements needed for quantum computers to achieve results beyond classical reach.

Distinct Clifford orbits of magic states can exhibit different stabilizer ranks at small tensor powers. We establish this for qutrits, where the single-qutrit Clifford group has four inequivalent orbits of magic states: Strange, Norrell, Hadamard-eigenstate, and the qutrit T-state, but a nontrivial upper bound on the asymptotic exponent had been pinned down for only the qutrit T-state. For the other three orbits we give explicit stabilizer decompositions, yielding upper bounds on the per-copy asymptotic stabilizer-rank exponent: $\gamma_S \le \log_3(2)/2 \approx 0.316$ for the Strange state, and $\gamma_{H_3}, \gamma_N \le \log_3(4)/3 \approx 0.421$ for the Hadamard-eigenstate and Norrell orbits, all strictly below the prior $\gamma_{T_3} \le 1/2$ baseline. We also prove the first nontrivial $\Omega(m / \log m)$ asymptotic lower bounds for the Hadamard-eigenstate and Norrell orbits, and exhibit two-qutrit Clifford circuits that convert two copies of these states into an injectable phase state with constant success probability, enabling constant-overhead injection of one non-Clifford diagonal gate per orbit. In the case of qubits, we give a closed-form decomposition of the qubit T-type orbit at four copies matching the existing $\gamma_T \le \log_2(3)/4 \approx 0.396$ exponent via a direct algebraic identity rather than an entangled cat-state construction. An open-source library stabrank accompanies the paper, with Lean 4 proof formalizations of all the decompositions.

We construct a detailed microscopic noise model for multi-qubit (MQ) gate operations in the context of trapped ion architecture with all-to-all connectivity. We find that phonon heating and motional dephasing are well captured by effective single- and two-qubit error channels that can, in principle, act between arbitrary pairs of qubits. Nevertheless, the median magnitude of two-qubit errors between uncoupled qubits is substantially smaller than that of errors between gate-coupled qubits. Errors associated with photon scattering are shown to solely propagate to qubits participating in gate operations. Lastly, we combine all noise sources, assigned with experimentally relevant parameters, and explore the scalability of a quantum error correction (QEC) scheme based on the rotated surface code, as a function of error rates and code size. Our analysis bridges device-level physics and QEC performance for MQ gates in trapped-ion architectures.

In this note, we formulate the notions of the direct and inverse problems and contact points for the Feynman diagrams. For the electron-photon interaction case, the solutions of these direct and inverse problems are presented. The interrelations between Feynman diagrams and the classical colored graphs are discussed.

We present a theoretical investigation of coherent control over the orientation of an individual molecule strongly coupled with a cavity using chirped-pulse driving. Specifically, we explore the dynamics of carbonyl sulfide (OCS) molecules under the influence of two chirped pulses with different spectral phases. We compare two pulse configurations: one with equal chirp rates ($\beta_{+} = \beta_{-}$) and another with unequal chirp rates ($\beta_{+} \neq \beta_{-}$). Numerical simulations reveal that chirped pulses enable precise control of the molecular orientation, achieving a maximum orientation degree of 0.5773. By analyzing the distribution of molecular polariton states, we show that chirped pulses can activate multiphoton processes, leading to deviations from the predictions of first-order Magnus expansion methods. Additionally, we demonstrate the robustness of the maximum orientation with respect to chirp amplitude and detuning, providing insights into the role of pulse parameters in optimizing control. This work introduces a new strategy for controlling molecular orientation in cavity-based systems and offers valuable perspectives for future experimental applications.

Matrix product states (MPS) serve as a key tool for studying quantum systems from chemistry and condensed-matter physics, making their preparation on quantum computers an important task in interfacing classical and quantum simulation. Many systems of interest have $U(1)$-symmetries induced by particle number and spin projection conservation, allowing to restrict the MPS tensors to be of block-sparse form, a property widely used in the implementation of classical algorithms such as the density matrix renormalization group. We reduce the cost of fault-tolerantly preparing block-sparse MPS within the standard ancilla-assisted linear-depth approach by implementing row and column permutations that transform the block-sparse matrices into block-diagonal form. These block-diagonal unitaries are then implemented via unitary synthesis, with the cost being determined by the size of the largest block. In this context, we modify the unitary synthesis approach of Berry et al. in order to reduce the Toffoli cost for real-valued unitaries by a factor of $\sqrt{2}$. In numerical benchmarks, we achieve Toffoli cost improvement factors of $10 - 30$ compared to the state-of-the-art for MPS of various molecular systems.

Due to their exceptional isolation from the environment, magnetically levitated particles are explored as extremely sensitive mechanical sensors. For future gravity experiments on quantum superpositions, such systems need to be cooled close to their ground state. To demonstrate the combination of state of the art vibration isolation, milligram levitated high Q mechanical resonators and position detection with low noise, we present linear feedback cooling of a magnetically levitated gravity sensor to below 2 picometer amplitude and below 10 millikelvin mode temperature for two translational modes (the x- and y-mode) simultaneously. The sensor is a levitating permanent magnet in a type I superconducting trap, where its six resonance frequencies are measured with a superconducting coil coupled to a DC SQUID. This signal is measured with a lock-in amplifier and a feedback signal is sent to a piezoelectric actuator, allowing the cooling of resonant modes at 50.6 and 68.0 Hz simultaneously. These two translational modes have Q factors of $3.8 \cdot 10^6$ and $5.5 \cdot 10^6$ respectively. The experiment is mounted inside a dry dilution refrigerator where it is vibrationally attenuated with 110-130 dB at these frequencies. In this work, we discuss future improvements on the setup which may enable quantum ground state cooling on a magnetically levitated particle, that has previously been shown to be a gravitational sensor.

Dynamic circuits use real-time outcomes of mid-circuit measurements, processed by a classical controller, to adapt subsequent operations during circuit execution. This additional flexibility over static circuits comes at a price. Mid-circuit measurements are typically slower and noisier than unitary gates. Furthermore, classical feedforward requires exchanging information between the quantum processor (QPU) and the classical controller, introducing latency that erodes the practical performance of dynamic circuits. We propose a compile-time optimization framework that reduces the use of classical controls in dynamic circuits while preserving their semantics. At its core, the framework uses a static analysis that symbolically executes the circuit by propagating classical information alongside the quantum state. By combining this classical-quantum information with the Probabilistic Circuit Model extended with probabilistic controls that emulate classical feedforward, we obtain an intermediate probabilistic representation of the dynamic circuit. In this representation, mid-circuit measurements and classically controlled operations can be removed or rewritten as purely unitary operations and probabilistic components. Compared to existing compile-time optimizations that target only mid-circuit measurements, our method applies to a broader class of dynamic circuits expressible in modern quantum programming languages. We evaluated our framework on randomly generated dynamic circuits, achieving about 50% classical feedforward reduction and even higher reductions in favorable settings.

Resonances in quantum mechanics are commonly introduced as quasi-bound states embedded in the continuum, a perspective that can be conceptually challenging due to the abstract nature of continuum states. In this work, we discuss an alternative approach that avoids an explicit treatment of the continuum by formulating the problem in terms of discrete quantum states. Our discussion is based on the stabilization method, in which the system is confined to a finite region such that the continuum is replaced by a discrete energy spectrum. Resonances then appear as characteristic features in the energy levels under variation of the confining box size, providing an intuitive interpretation in terms of a two-level system while remaining closely connected to standard quantum mechanics curriculum. We review the method, derive selected results, and discuss practical strategies for extracting resonance parameters from stabilization diagrams. In addition to established fitting procedures, we introduce a novel approach based on the analysis of spatial localization of resonant states, which enables a robust identification of resonance properties. The approach is illustrated using both attractive and repulsive delta-shell potentials, which serve as simple and instructive model systems amenable to analytical treatment.

Genuine multipartite entanglement and full inseparability are two inequivalent quantum resources. Even though all genuinely multipartite entangled states are also fully inseparable, not all fully inseparable states are genuinely multipartite entangled. There exist fully inseparable states that can be prepared as convex mixtures of states separable with respect to different bipartite splits. Here, we are interested in examples of Gaussian states that possess this type of entanglement, so-called fully inseparable biseparable states. We show for several archetypical families of multimode Gaussian states that fully inseparable biseparable candidate states are actually genuinely multipartite entangled. Using projections to finite-dimensional subspaces and fully decomposable witnesses, we observe a shrinking of the regions of potentially fully inseparable biseparable Gaussian states with growing dimension of the projection subspaces. We therefore conjecture that all fully inseparable Gaussian states are genuinely multipartite entangled.

Molecular rectifiers, as prototypical components of molecular electronics, present unique opportunities for pushing device miniaturization to its ultimate limits. Nevertheless, challenges including limited rectification ratios (RR), insufficient robustness, and poor reproducibility impede their practical deployment. To make molecular rectifiers competitive with silicon-based devices, it is important to fully understand the design principles and fabrication methods from both mechanistic and experimental perspectives. By holistically considering the transport mechanisms, modulation strategies, fabrication, characterization techniques, and theoretical simulations, this review provides a comprehensive overview of molecular rectifiers. Representative examples of conceptually significant and high-performance molecular rectifier systems are highlighted to illustrate the relationships between rectification mechanisms, molecular design strategies, and device realization. Building on these discussions, we present an outlook for current bottlenecks and future directions to guide the development of molecular rectifiers. This review aims to serve as both a conceptual framework and a technical reference for researchers working at the intersection of molecular electronics and nanoscale device engineering in the post-CMOS era.

In recent years, light detection and ranging (LIDAR) has seen a steep rise in the sensitivity of measuring the distances of remote objects. Here, we propose to enhance the sensitivity of LIDAR even further by exploiting Dicke's concept of superradiance, i.e., the collective light emission of statistically independent light sources. By using $N$ thermal light sources (TLS) and measuring intensity correlations of order $m \geq 2$ instead of $m=1$, i.e., the intensity, we show that the Cramér-Rao bound on the measurement of the distance of a remote object undercuts that of traditional LIDAR by a factor of $N$, and can be reduced further with increasing correlation order $m$. Our numerical calculations are supported by analytical expressions for the special cases of two and three TLS and a general approximate expression for any number of TLS.

Quantum Cramér–Rao theory is intrinsically local: it bounds precision near a specified parameter value, and its saturating measurement generally depends on that value. Barankin-type bounds use finite parameter displacements, but remain anchored to a chosen reference value. This leaves open a basic global-estimation problem: when the parameter is known only within a broad domain, what precision can be guaranteed by a single estimator and a single measurement strategy fixed before the true value is localized? We answer this question by introducing global score functions tied to a weighted variance over the whole parameter domain. Their correlations generate a hierarchy of precision bounds: global Cramér–Rao and Barankin-type bounds arise as restricted levels, whereas unrestricted score correlations yield a fully global bound for the prescribed weighted variance. The hierarchy recovers local Cramér–Rao theory in the many-repetition limit and reveals genuinely global precision limits for finite data over broad domains. In the quantum setting, the construction identifies when this fully global bound can be realized by a single parameter-independent measurement. The same framework extends to Bayesian estimation, recovering the Van Trees bound in the local limit while yielding stronger finite-width lower bounds on the Bayesian mean-square error beyond this limit.

Parametric Hamiltonians often exhibit point-like spectral degeneracies, called diabolic points (DPs) or conical intersections, which can lead to singularities in the Provost-Vallee metric of eigenstate manifolds. We regularise the metric by a transformation to polar coordinates and develop a formalism in which DPs act as bridges between adjacent eigenstate manifolds, glueing them into a single connected state manifold (CSM). We characterise the topology of this structure and extend the local rules for nodal lines governing the Berry phase to global ones. On the CSM, the class of geodesics can be enlarged by those passing through the DPs. They can be stable with respect to their initial direction, and can be shorter than those constrained to a single eigenstate manifold, providing new geodesic shortcuts. Further, the CSM provides a new mechanism for Berry phase computation along paths traversing the DPs.

We introduce a low-overhead technique for quantum error mitigation based on post-selection using auxiliary qubit measurements. The method exploits the structural property that, in an error-free computation, auxiliary qubits are often expected to return to the zero state after use. By selectively measuring these qubits at carefully chosen points in the circuit, erroneous shots can be identified and discarded, improving result fidelity with minimal hardware overhead. To account for circuit noise, including measurement errors, we analyze the likelihood that a measurement outcome indicates a corrupted shot. This analysis is informed by the measurement's backward light cone, namely the set of circuit operations that could affect the outcome. Shots whose auxiliary measurement outcomes imply a corruption likelihood above a tunable threshold are rejected. Simulations show that the method reduces the false-negative rate by approximately 10% while discarding only approximately 1% of valid shots. The threshold controls the bias-variance tradeoff inherent to post-selection, allowing the method to be adapted to the fidelity and sampling requirements of different applications.

We propose a practical computational framework for detecting structural changes in parameter-dependent topological data. In many applications, such as time-series data analysis, anomaly detection, and monitoring of systems under changing control parameters, persistence diagrams describe the birth and death of topological features at each parameter value, but they do not fully capture how these features are reorganized over time. To address this limitation, we represent homological features by zero modes of the ordinary combinatorial Hodge Laplacian and track the corresponding feature spaces in a common ambient chain space. This allows us to compute curvature and holonomy as descriptors of local reorganization and accumulated memory in evolving topological structures. Curvature highlights parameter regions where homological features mix or change rapidly, while holonomy summarizes the net effect of such changes after a closed cycle. We also establish stability estimates showing that these descriptors are robust under perturbations of the Hodge Laplacian on regular regions. Numerical experiments on controlled time-dependent point-cloud data show that the proposed method detects tracking instability, distinguishes systems with nearly identical persistence diagrams, and captures cycle-level memory invisible to pointwise feature matching. These results suggest that zero-mode transport geometry can serve as a useful computational tool for analyzing dynamic topological data.

Quantum light sources such as squeezed light are essential for quantum information science and technologies, but the scalable production of multiple beams of them remains a challenge. Here,we experimentally demonstrate a novel approach to the generation of a large spatial array of polarization-squeezed light beams via atomic-coherence-enhanced nonlinear optical processes using a single atomic vapor cell. Unlike schemes based on independent squeezing generators, the squeezing dynamics of each channel here are governed by a common collective ground-state atomic coherence, produced by all input beams, homogenized by the thermal motion of the atoms, and protected against wall collisions by a paraffin coating. Consequently, the optical states of all channelsare coupled and regulated by each other via the moving atoms, leading to synchronization behavior.We realized a 30-beam array of polarization squeezed state with 2.03 dB of squeezing, experimentally verified the synchronization, and observed improved purity of the squeezed state as well as the system response to perturbations when the size of the array increases. This work provides a pathway towards scalable high-performance quantum light sources for applications in precision measurement, quantum imaging and quantum information processing.

Levitated mechanical systems are promising candidates for quantum gravimetry, as gravity couples directly to their center-of-mass motion, enabling the large mass of a mesoscopic particle to serve as a sensing resource. In this paper, we propose a mechanical squeezed-Fock qubit gravimeter using a Duffing oscillator that is driven by a detuned two-phonon pump. In the squeezed-Fock basis, the gravitational force couples to the anti-squeezed quadrature, which enhances the gravity-induced transition rate while preserving the direct mass scaling of the mechanical force coupling. We show that sensitivity improves with reduced effective qubit splitting that is controlled by the squeezing parameter and the Duffing nonlinearity. We further analyze mechanical damping and show that squeezing converts ordinary dissipation into anisotropic qubit noise, setting a practical trade-off between signal amplification and decoherence rate. These results identify the mechanical squeezed-Fock qubit as a new platform for quantum-enhanced gravimetry.

Optical control of electron-generation sites has broadly enabled ultrafast nanoscale imaging, spectroscopy, and functional control. Existing approaches achieve nanoscale site selectivity by shaping localised optical fields around nanostructures, thereby limiting independent site selectivity within the same local-field hotspot. Here, using a single-molecule electron emitter, we show that site selectivity can instead be encoded in the electronic excitation pathway, enabling subnanometric control of electron birth sites within a common local-field hotspot. By tuning the photon energy, we selectively access different groups of molecular states whose combined contributions define emission channels with distinct spatial character, thereby reversibly switching the electron birth site within the same emitter. The switching is read out directly in the far-field emission pattern and occurs upon changing the photon energy, but not upon varying the intensity or polarisation. Our results establish optical birth-site selectivity that is not dictated by the local-field distribution, opening a route to electron birth-site control through the electronic excitation pathway.

Heat conduction in low-dimensional systems exhibits strong deviations from Fourier behavior due to anharmonicity and long-lived vibrational correlations, challenging conventional computational approaches. The $\beta$-Fermi–Pasta–Ulam–Tsingou ($\beta$-FPUT) chain provides a minimal nonlinear lattice model for studying anomalous transport, yet its quantum real-time dynamics remain difficult to access with classical methods. We develop a first-quantized digital quantum-simulation framework for the quantum $\beta$-FPUT lattice, targeting fault-tolerant quantum computers. By working directly with discretized lattice displacements rather than truncated phonon occupation spaces, the approach captures anharmonic interactions while avoiding bosonic encoding overheads. We construct Trotterized circuit blocks for real-time evolution and introduce a Hermitian quadrature decomposition of Fourier-mode displacement operators that enables shallow quantum circuits for mode-resolved displacement correlators. We analyze the quantum resources required for the full simulation and measurement workflow, providing qubit counts, gate complexity, circuit-depth and resource estimates as functions of system size and resolution within a fault-tolerant workflow. These results establish a concrete algorithmic blueprint for simulating quantum transport dynamics in nonlinear low-dimensional lattice models on fault-tolerant quantum hardware.

Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We present a general learning-based framework that, given only an encoding circuit, constructs physical implementations of logical operations while enforcing structural properties such as transversality or shallow depth. Our approach is validated by rediscovering known logical operations of standard stabilizer codes. We then extend it to a co-design procedure, dubbed variational early fault-tolerant quantum computing (VarEFTQC), which tailors non-additive encodings to a given noise model and enforces desired logical gate sets, such as transversal IQP-type families or low-depth universal sets. A software library implements the complete learning pipeline, including loss-function variants, ansatz families, and optimization routines. Together, these results position VarEFTQC as a proof-of-concept framework for discovering hardware-adapted logical gadgets for early fault-tolerant quantum computing.