Papers

Can AI agents visually comprehend quantum circuit diagrams and generate verified executable code–and at what cost? We present Quantum Circuit Vision, a cost-aware evaluation framework for multimodal AI agents on quantum circuit visual understanding. We construct a 132-circuit benchmark spanning 13 categories ($1$–$10$ qubits) with executable Amazon Braket code and unitary-fidelity verification. Evaluating three frontier Claude-family models at different capability-cost tiers with $n=5$ repeated trials, we find that the mid-tier model (Sonnet 4.6, $1.30\times$ credits) offers the most favorable balance on the cost-accuracy frontier: 91% pass rate on the core subset at 18% of the per-call cost of the strongest model (Opus 4.6), whose accuracy advantage is not statistically significant (paired $t$: $p=0.083$). Logistic regression confirms that circuit depth–not qubit count–is the primary predictor of failure ($p<0.001$). Chain-of-thought prompting shows no statistically significant effect (all $p>0.18$, $n=5$), suggesting that visual pattern recognition outweighs explicit reasoning strategy for structurally coupled diagrams. We propose a cascade routing strategy (cheap $\rightarrow$ expensive models) that achieves 84% accuracy at 38% of single-model cost, demonstrating that model routing dominates prompt engineering as a cost lever. We release QCV-Dataset (132 circuits, 5 modalities, 1,931 files) on Hugging Face Hub as an open evaluation infrastructure with structured metadata for discoverability, interoperability, and responsible AI documentation, and all evaluation code, cost logs, and verification scripts on GitHub for full reproducibility.

Quantum measurement is a key resource for quantum generative learning, providing intrinsic stochasticity for generating diverse quantum samples. However, in measurement-assisted state-ensemble resampling, repeated measurements can also induce overconcentration: under a fixed measurement trajectory, distinct input states progressively converge toward similar output states, suppressing input-dependent diversity. To diagnose this effect, we introduce three complementary metrics: accuracy, generative power, and input sensitivity. For Haar-random monitored circuits, we prove that one-step models retain input sensitivity up to dimension-suppressed corrections, whereas sequential monitored circuits exhibit a depth-dependent loss of input sensitivity. Motivated by this diagnosis, we propose a truncated quantum denoising diffusion probabilistic model (QuDDPM), which restricts the temporal depth of both the forward diffusion and reverse denoising processes. Numerical benchmarks show that truncated QuDDPM preserves stronger input sensitivity while maintaining accuracy and generative power comparable to the original model. These results identify measurement-induced overconcentration as a dynamical limitation of deep monitored quantum generative models and establish temporal depth as a design parameter for balancing measurement-induced randomness with input-dependent diversity.

We develop the mathematical and physical formulation of cognitive cost optimization that underlies the path-integral model of consciousness. The goal-directed cognitive process is modeled as imaginary-time evolution (ITE) under a projector Hamiltonian that rewards configurations consistent with a target concept. We establish three results. First, this ITE coincides with a double-bracket flow and is therefore the Riemannian gradient flow of a Hilbert–Schmidt cost whose unique minimum is the solution. Second, a Wick rotation re-expresses this non-unitary descent as an equivalent unitary evolution on the same Hilbert space, which admits an exact discrete path-integral representation in which the oracle and the initial-state diffusion projector play the roles of potential and kinetic energy. Third, we identify the continuum from unconscious to conscious processing with the strength of the unitary interaction between the cognitive system and a neural-environment probe, recovering the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) decoherence model of Asano et al. in the Markovian weak-coupling limit, and the projective, reportable fixation of an optimized state in the strong-coupling limit, an insight-like “Aha” endpoint. Both regimes share the same ITE and path-integral structure, and only the measurement-interaction strength varies. The Wick rotation is therefore a technique of re-description, not a physical regime change.

The management of cash replenishment in Automated Teller Machine (ATM) networks requires scheduling recharges in order to minimize operational costs while maintaining high service levels and avoiding cash-outs, under uncertain and time-varying withdrawal demand. This work formulates the ATM cash replenishment problem through a Quadratic Unconstrained Binary Optimization (QUBO) model, which naturally captures nonlinear cost interactions, while incorporating operational constraints through penalty terms. The objective function combines fixed and variable replenishment costs with co-location discounts, as well as penalties for a late replenishment that could cause a service interruption. The resulting QUBO instances are solved using MegaQUBO, a GPU-accelerated QUBO solver. An empirical evaluation on a real dataset of 276 ATMs located in Italy, covering four representative months of 2022 (April, May, October, and November), benchmarks the proposed approach against a threshold-based operational policy. Results show consistent cost reductions of approximately 15%-18% while maintaining an excellent average service level (around 99.8%-99.9). Overall, the study demonstrates that QUBO-based optimization, coupled with GPU-based solving, can provide a practically deployable decision-support tool for large-scale ATM cash logistics.

We draw a structural analogy between quantum error correction (QEC) and error handling in neural circuits with respect to their redundant encodings and constraint-based inferences. In QEC, logical information is embedded in a protected codespace within a larger Hilbert space. A set of commuting checks (e.g. stabilizer constraints) is repeatedly evaluated to produce an error syndrome that identifies which constraints were violated without directly revealing the logical state. A decoder then maps the syndrome to a recovery operation that returns the system to the codespace and suppresses logical failure below a threshold. Neural circuits exhibit error-control strategies that can be viewed through a related biological error correction (BEC) pattern: information is distributed across multiple neurons (redundant encoding), yielding reliable collective activity from error-prone unit operations of individual neurons. The structural analogy with QEC raises the question whether collective activity may be constrained on lower-dimensional manifolds (a biological codespace), allowing recurrent circuit dynamics and mismatch signals to function as syndrome-like indicators of constraint violations, driving fast corrective dynamics and slower adaptive updates. Our structural analogy also suggests that new insights into brain-inspired algorithms for collective information processing may inform novel QEC approaches. We perform numerical experiments using simplified models of qubit and neuron dynamics to illustrate the analogy.

We have experimentally realized a parabolic potential barrier for surface gravity water waves. The analogy between the resulting wave equation and the Schrodinger equation for the inverted harmonic oscillator (IHO) enables us to study the propagation of quantum-mechanical wave packets with different average energies in this iconic scattering model. We observe a clear boundary in the phase-space dynamics, namely the separatrix, which distinguishes wave packets with energies below the maximum of the IHO potential from those with energies above it. In the former case, the wave packet is blocked, whereas in the latter case, it is transmitted. We also measure the corresponding variation in momentum during this process.

We study scalar and vector bosons in the Bonnor–Melvin–$\Lambda$ spacetime within the Duffin–Kemmer–Petiau (DKP) formalism. By employing Umezawa's projection operators, we separate the physical spin-0 and spin-1 sectors and derive the corresponding exact second-order equations in the full curved spacetime, without relying on the conical approximation. For the scalar sector, the radial equation reduces to a Schrödinger-like equation with a trigonometric Pöschl–Teller effective potential. In the vector sector, the longitudinal mode is governed by the same effective potential, whereas the transverse polarizations are described by generalized trigonometric Pöschl–Teller potentials. Because the me\-tric function vanishes at a discrete set of radial points, the radial dynamics is naturally formulated as a singular Sturm–Liouville problem on a fundamental interval, with the physical radial domain fixed by the Friedrichs self-adjoint extension of the corresponding singular radial operators. As a result, all physical sectors exhibit purely discrete radial spectra, and their eigenfunctions are obtained in closed form. These results provide a unified exact treatment of scalar and vector bosons in the Bonnor–Melvin–$\Lambda$ spacetime, complement previous analyses based on the conical approximation, and clarify the role of the global geometric structure of the background in shaping confinement and spectral properties.

Hybrid programs combine a quantum circuit with a classical host program that consumes measurement outcomes. In such programs, an outcome may be syntactically read by the host but semantically non-contributory: changing the outcome cannot change the returned value. Such outcomes obscure gates that are dead only relative to the host semantics, and are therefore invisible to circuit-local optimizers. We present a semantics-aware host-side static analysis that identifies non-contributory measurement outcomes by abstract interpretation, and prove its soundness. We implement the analysis and evaluate it on $24$ application-faithful hybrid workloads across quantum chemistry, optimization, quantum machine learning, and quantum finance. Compared with a syntactic liveness baseline, our analysis identifies more than $4\times$ as many non-contributory measurements, and it standalone enables the removal of $37.98\%$ of total gates on average. Even after the state-of-the-art optimizers like Qiskit, t|ket$\rangle$, and PyZX have already optimized the circuits, our analysis still enables removal of more than $30\%$ of the post-optimized gates, showing that the host-semantic opportunities exposed by our analysis are not subsumed by circuit-local optimization. To scale our analysis, we further lower host programs to an SSA-style levelized intermediate representation that exposes level-wise parallelism for GPU execution, and implement a CUDA backend. We prove that this lowering preserves the analysis result, and the evaluation shows speedups of up to $6.53\times$ over a sequential baseline as structural parallelism increases.

While quantum networks have been extensively studied as a natural extension of the standard Bell scenario with a richer correlation structure, general constructions of nonlinear Bell inequalities with self-testing properties are still largely lacking. In this work, we present a general method for constructing such inequalities in the simplest network scenario, in which two independent sources distribute bipartite quantum states to three spatially separated observers. These inequalities allow for arbitrary numbers of binary measurements and are maximally violated by maximally entangled states of the corresponding local dimensions together with sets of pairwise anticommuting Clifford observables. Importantly, their maximal quantum values can be determined analytically, which makes them particularly promising for device-independent applications. In particular, we prove that these Bell inequalities can be used to device-independently certify the underlying quantum network, including both the quantum states produced by the sources and the observables measured by all parties. To the best of our knowledge, this is the first self-testing result for quantum networks that relies solely on the maximal violation of a nonlocality witness.

Training the variational angles of the Quantum Approximate Optimization Algorithm once on a small instance and reusing them on larger ones, known as parameter transfer, is the standard route past the exact-simulation wall. Existing literature explains its success almost entirely through structural similarity. We identify a new, independent axis that governs transfer whenever constraints are encoded as penalties: the trained angles memorize the penalty weight $\lambda$ of their training instance. For any scalarized cost function with an integer-valued violation count, we prove that at arbitrary fixed QAOA angles $(\beta,\gamma)$ of depth $p$, the probability mass $F(\lambda)$ on the feasible subspace is a finite real trigonometric polynomial in $\lambda$ whose angular frequencies lie on an integer lattice generated by the trained $\gamma$'s. Three consequences follow immediately: transfer feasibility is a resonance peaked where the deployment penalty matches the training penalty; the resonance width scales as $1/(v_{max}\sum_k|\gamma_k|)$, so low-$|\gamma|$ angle sets are systematically more transferable; and the curve exhibits revival peaks at spacings $2\pi/\gamma_k$. We confirm all three predictions by exact statevector experiments on a 20-qubit multi-user resource-allocation QUBO. The theorem is independent of how the angles were obtained and applies to any integer-penalty QUBO, recasting a widely reported failure mode of penalty-based QAOA as deterministic, predictable phase interference rather than an energetic tuning problem.

We report a heterodyne detection scheme for position readout of an optomechanical system, in particular an optically levitated particle, implemented via digital In-phase and Quadrature demodulation on a field-programmable gate array. Compared to the standard homodyne approach, the proposed method offers three key advantages: it remains robust in the presence of strong parasitic back-reflected fields that would otherwise prevent stable phase locking; it produces a signal linearly proportional to the particle displacement, eliminating phase-wrapping distortion; and its calibration factor is intrinsically immune to drifts in the optical power of the local oscillator or scattered field. We experimentally demonstrate and quantify all three advantages through simultaneous homodyne and heterodyne measurements on the same trapped particle. The proposed method can be used in any optomechanical system based on phase readout.

We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register. From a Takens embedding and Vietoris–Rips filtration of S&P~500 returns, we extract combinatorial Laplacians and recast null-space counting as a continuous-PCE Rayleigh-quotient minimization with variational deflation, encoding $n_k$ simplex indices into $O(n_k^{1/\kappa})$ qubits with shallow, ancilla-free circuits. Because the resulting loss is rational rather than bilinear in the correlators, the barren-plateau bound of~\cite{Sciorilli25} does not transfer; empirically the gradient variance decays only polynomially, with no exponential barren plateau, over $n=4$–$12$ qubits. The classical stage matches ripser~\cite{bauer2021ripser} on all 190 sliding windows (2007-2009). On the real market Laplacians ($\beta_1=1$–$22$), warm-starting from a classical null-space surrogate allows PCE-VQE to recover $\beta_1$ exactly at every scale, placing the obstacle in the optimisation landscape rather than the encoding. Chronologically split classification gives in-regime ROC AUC $0.818$, but out-of-distribution evaluation on the 2020 COVID shock and 2022 rate cycle (AUC $0.009$, $0.515$) shows the calibration does not generalize across crisis regimes.

Can a small quantum computer forecast a changing signal better than an ordinary classical method? Many studies say yes, but the classical methods they compare against are often left in a basic, untuned state while the quantum model is carefully optimised. We ask what happens when the classical competitor is given exactly the same care: the same size and the same amount of tuning effort. We study two popular reasons a quantum reservoir is thought to help, using exact simulations of small quantum systems (up to eleven qubits) on prediction tasks. In both cases the quantum advantage disappears once the comparison is fair. In the first, extra quantum measurements add nothing that a simple classical formula of the same size does not already provide. In the second, a feedback loop genuinely helps the quantum model, turning a useless setup into a working predictor, yet a well-tuned classical network still predicts slightly more accurately, and the gap is statistically reliable. Our point is not that quantum reservoirs can never win, but that two of their commonly cited advantages do not hold up against fair classical competitors at this scale. We provide these matched comparisons as a simple, reusable checklist for honest benchmarking. All results are fully reproducible from fixed random seeds.

Mitigating recoil events and minimizing optically induced heating are central challenges in the precise control and cooling of macroscopic particles. To overcome this, we propose trapping resonant dielectric particles for applications in ultra-high vacuum (UHV) levitodynamics. Contrary to other approaches, where suppressing the parasitic resonant scattering was achieved in a standing wave geometry, here we propose a single beam geometry in a dark trap regime. As a promising material platform, we focus on a class of transition-metal dichalcogenide (TMD) particles with high polarizability, characterized by refractive indices in the range $3.7$-$4.8$ and densities up to $9.3~\mathrm{g\,cm^{-3}}$. Using full Mie theory, we identify a range of TMD particle radii that support stable axial and radial magnetic quadrupole trapping in a bottle-beam configuration. We predict that for WS$_2$ particles with a mass of $0.5 \times 10^{12}\,\mathrm{amu}$, one can expect suppression of the scattering rate relative to the mechanical frequency down to $\Gamma/\Omega \simeq 0.02$. This corresponds to a coherence time extended by approximately three orders of magnitude compared with silica particles of the same mass trapped in conventional bright optical traps at UHV. Combined with significantly reduced internal heating, remaining well below the melting point of the material, dark trapping of resonant TMD macroscopic particles emerges as a promising platform for exploring quantum physics with large masses.

Sampling from discrete Markov random fields (MRFs) is a hard problem. We study amplitude-encoded i.i.d. sampling for small MRFs where $2^n$ target probabilities are precomputed classically. This removes quantum exponential speedup but allows a clean comparison against classical MCMC based on independent circuit samples ($\tau \approx 1$). Across 60 instances spanning five graph families (1k-step burn-in, 3k retained samples), the mean ESS ratios of Quantum to Single-Site Gibbs, Block Gibbs, Tuned-Block, and Parallel Tempering are $16.35$, $7.29$, $1.82$, and $1.79$, showing modern classical samplers substantially close this gap. Amortizing $O(2^n)$ preprocessing into wall-clock time, exact inverse-CDF sampling yields $17.7$M ESS/s versus $488$K ESS/s for the quantum sampler ($36\times$ mean rate, $153\times$ per-instance), confirming no wall-clock advantage. We characterize MCMC autocorrelation costs and benchmark amplitude-encoded state preparation at $n \in \{8,10,12\}$. An MPS scaling study ($n \le 40$) shows bond dimension $\chi=32$ achieves $F=0.721\pm0.059$ at $n=40$. Finally, a matched-budget VQC vs. MPS comparison at $n \in \{8,10,12\}$ shows VQC fidelities fall far below MPS: $(F_{\mathrm{VQC}}, F_{\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)$ at compressions $10.7\times$, $34.1\times$, and $113.8\times$.

Practitioners increasingly rely on hosted simulation environments, but their performance characteristics remain poorly documented. We present a systematic benchmarking study of GPU-accelerated approximate quantum simulation across two widely used methods: matrix product states (MPS) and Pauli path simulation (PPS), comparing BlueQubit (a hosted tool that handles hardware provisioning, simulator configuration, and job orchestration) against AWS Braket, Quantum Rings, Qiskit pauli-prop, and PauliPropagation (written in Julia). For MPS, we find that GPU runtime yields sub-quadratic scaling with bond dimension, with a growing advantage over CPU at increasing scale. For Pauli path simulation on IBM's 127-qubit kicked Ising benchmark, GPUs deliver up to ${\sim}1{,}700\times$ speedup at fine truncation thresholds ($\delta = 2.5 \times 10^{-5}$, 27.6M Pauli terms), and are the only backends that reach accuracy regimes below $\delta = 10^{-5}$, which remained inaccessible to the commodity CPU-based implementations and self-contained SDKs evaluated here. We also provide a reproducible characterization of these simulators across regimes, including tradeoffs that isolated evaluations do not show. All benchmarking code and configurations are in a public GitHub repository.

Quantum entanglement and magic are complementary resources underlying quantum computational advantage, yet their dynamical relation in many-body systems remains poorly understood. In this Letter, we show that the mechanism of bipartite entanglement growth is encoded in the relative timescale between the entropy-growth-rate peak and the magic barrier, defined as the transient peak of the anti-flatness of the entanglement spectrum. When entanglement is locally built, the same microscopic process increases the entropy and reshapes the Schmidt spectrum, so the magic-barrier peak occurs in the time window of maximal entropy growth. When entanglement is mainly transported or redistributed, entropy can grow before appreciable spectral non-flatness is generated, naturally separating the two peak times. We demonstrate this distinction in the random-field XXZ chain: the two peaks remain strongly correlated in the thermal regime, while their separation grows systematically across the thermal–MBL crossover. We further validate this theoretical framework by employing Bell-pair initial states alongside a tunable SWAP–Haar random circuit. Our results reveal an intrinsic dynamical connection between entanglement and magic, establishing the magic barrier as a powerful spectral diagnostic of how quantum information is generated, transported, and reshaped.

We investigate a finite-time quantum Otto engine within the framework of gauge-invariant quantum thermodynamics, using the Lipkin-Meshkov-Glick model as the working medium. In this formulation, thermodynamic quantities are defined on equivalence classes of thermodynamically indistinguishable states, leading naturally to gauge-invariant notions of work, heat, entropy, and efficiency. We derive explicit expressions for these quantities and show that the usual work performed during the unitary strokes decomposes into an invariant contribution, associated with changes in the instantaneous energy spectrum and populations, and a coherent contribution arising from finite-time quantum coherences. This decomposition induces the corresponding splittings of engine efficiency and entropy production, providing a geometric interpretation of finite-time irreversibility and clarifying the role of coherence in work extraction. By analyzing the cycle's dependence on driving speed and system size, we identify the engine's operating region and investigate the influence of criticality. We show that crossing the critical region substantially reduces the parameter space in which the cycle operates as a heat engine. At the same time, whenever the engine condition remains satisfied, the discrepancy between the conventional and gauge-invariant descriptions becomes strongly suppressed, indicating that the gauge-invariant sector predominantly carries the extracted work. These results establish a direct connection between gauge-invariant thermodynamics, finite-time irreversibility, and work extraction in many-body quantum thermal machines.

We establish a direct connection between quantum thermodynamics and information geometry by introducing an ergotropic decomposition of the Wigner-Fisher information for Gaussian quantum states. We derive an analytical expression for the Wigner-Fisher information in terms of the phase-space covariance matrix and mean vector, and show that it naturally separates into passive and ergotropic contributions. The passive term is shown to be entirely determined by the Wigner entropy rate of the associated passive state. The ergotropic contribution, in turn, quantifies how displacement and squeezing resources modify the statistical velocity and length of the system trajectory in phase space. As an application, we analyze the recently proposed ergotropic Mpemba effect and demonstrate that it can be traced to the anomalous geometric evolution of the passive state associated with squeezed thermal states. Our results reveal how the extractable work stored in a quantum state constrains its information-geometric structure, establishing a framework that links ergotropy, entropy production rate, and statistical geometry in continuous-variable quantum systems.

Strong electromagnetic backgrounds make quantum electrodynamics a real-time nonperturbative problem involving dressed fermions and dynamical photons. We propose a trapped-ion protocol for simulating intense-field QED in $3+1$ dimensions in the Furry picture. The construction encodes photon modes in collective phonons and Volkov-dressed fermion modes in ion spins, combining native spin-phonon couplings with Clifford circuits that compress nonlocal Jordan–Wigner strings. For nonlinear Breit–Wheeler pair production, the protocol has polynomial resource scaling and is benchmarked against exact single-mode dynamics with controlled Trotter errors. With experimentally motivated phonon heating and dephasing, zero-noise extrapolation substantially reduces deviations in photon-survival and pair-production signals. These results provide a hardware-efficient route to intense-field particle-production dynamics beyond perturbative or static-field descriptions.

This article reads two recent tractatus-style texts - Niccolo Covoni and Carlo Rovelli's Tractatus Quanticus (arXiv:2512.06034) and Mikolaj Sienicki and Krzysztof Sienicki's Tractatus de Conscientia (arXiv:2607.05459) - together with Jenann Ismael and Huw Price's interpretive introduction Against Totalitarianism (arXiv:2601.01070), as parts of what may be called a New Tractatus Program. The program is unified by a single pressure point: the demand for a perspective-free description of reality, whether as a final inventory of facts, a world viewed from nowhere, or a self placed outside the physical order. On the relational interpretation of quantum mechanics, Tractatus Quanticus revises Wittgenstein's opening claim by replacing the world as the totality of facts with the world as what is the case from some perspective. Against Totalitarianism then makes the philosophical stakes of this move explicit by challenging the idea of the world as one closed totality. Tractatus de Conscientia carries the same discipline into the theory of consciousness, where conscious experience is treated neither as a mysterious substance nor as mere behavior, but as an integrated, temporally thick, operationally accessible perspective. Read together, these texts point toward a post-classical philosophy of partiality: reality is not abolished, but de-absolutized; consciousness is not mystified, but constrained by access, coupling, memory, and evidence; and the limits of language become inseparable from the limits of perspective. The article does not claim that relational quantum mechanics is the only viable interpretation of quantum theory. It instead develops the philosophical consequences of the relational reading. Its aim is programmatic rather than demonstrative: it does not prove a new ontology, but organizes a family of arguments around disciplined perspective-dependence.

Cavity optomagnomechanics provides a versatile platform to explore macroscopic quantum correlations, particularly nonreciprocal entanglement. In this work, we propose a theoretical scheme to generate switchable bipartite and tripartite entanglement in an optomagnomechanical ring cavity by exploiting phase-controlled magnon squeezing. Indeed, two spatially separated ferrimagnetic YIG microbridges become entangled through their magnetostriction-mediated coupling to mechanical motion and a common cavity field via radiation-pressure interaction. The squeezing process introduces two phase-dependent contributions to the magnon response, namely an effective detuning shift $\Delta_{\theta_j}$ and a quadrature-damping contribution $\kappa_{\theta_j}$, both of which reverse sign upon a $\pi$ phase shift, providing an in situ control to switch the entanglement response. The nonreciprocal entanglement is defined operationally through the asymmetric entanglement response under the phase reversal $\theta_j \to \theta_j + \pi$, quantified by normalized contrast ratios $C_E$ and $C_{\mathcal{R}}$, which measure the relative difference between the entanglement obtained at $\theta_j$ and at the phase-reversed configuration $\theta_j+\pi$. The resulting phase-tuning method provides a flexible and robust route to achieve high-contrast bipartite and tripartite entanglement within stable parameter regions, establishing magnon squeezing as a practical quantum resource for switchable quantum correlations in hybrid platforms.

We investigate Unruh-DeWitt detectors coupled to composite observables of a quantum scalar field, including quadratic coupling to the field momentum and coupling to the local energy density. We develop a distributional framework for evaluating the corresponding detector response functions and apply it to detectors crossing the Rindler firewall. While we recover the finite response of the derivative-coupling model, we show that quadratic momentum coupling leads to products of distributions that do not admit a canonical, regulator-independent definition in the sharp-firewall idealization. The vacuum correspondence between the local energy-density and quadratic momentum responses motivates the conjecture that analogous difficulties may arise for energy-density coupling in the sharp firewall model. Within the sharp, pointlike composite-coupling model considered here, our analysis further suggests that these pathologies originate from the discontinuous severing of correlations across the Rindler horizon.

Achieving valley splittings well in excess of the thermal energy of electrons and avoiding valley excitations is essential for the consistent initialization, operation and readout of gate-defined Si spin qubits. In this work, we present a device-level optimization strategy for pushing valley splittings to between 1 and 5 meV, well beyond values reported in nearly all previous theoretical studies. Using device-scale simulations that incorporate atomistic alloy disorder through a 1D tight-binding theory, we demonstrate that our proposed approach yields large valley splittings with a tight distribution across disorder realizations, a key requirement for reproducible qubit performance at scale. The approach rests on an unorthodox Si/SiGe heterostructure design combining a narrow quantum well, a small Ge spike, and a pure-Ge cap. We corroborate these predictions with targeted atomistic density functional theory calculations. These results offer a clear path forward for scalable Si/SiGe spin qubit devices and, if realized experimentally, effectively eliminate valley splitting as an existential problem for large scale SiGe-based quantum processors.

We propose a novel formulation of master equations for open systems wherein the evolution of a state is determined solely by its local behaviour at any point of time. Specifically, our formulation allows for a local interpretation of the workings of beyond-Markovian dynamics as opposed to the more common conception that non-Markovian state evolution is affected by its cumulative past history. Quite interestingly, local determinacy is found prevalent in quantum dynamics. We illustrate the advantages of our coordinate-free formulation with exact analyses on two physically relevant models.

Extending and refining a preceding work, the free evolution of a quantum wave function, with fixed initial and final modulus, is considered in the general case where nodes are allowed. The method is based on considering a suitable simple functional related to the quadratic optimal transport cost in discrete time. Under reasonable assumptions it is shown that, if nodes are present, the free evolution of the wave function with fixed initial and final modulus is a sort of local minimum. If no nodes are present the minimum is global, suggesting intrinsic instability of the nodes in a free quantum evolution.

Partial differential equations are a promising application area for fault-tolerant quantum algorithms, but the subject lies between two communities with different languages: numerical analysis and quantum computation. These lecture notes provide a numerically grounded introduction for readers entering from either field. Block encoding is the organizing principle: once a discretized differential operator is embedded in a unitary, primitives such as quantum singular value transformation, Hamiltonian simulation, linear combinations of unitaries, amplitude amplification, and measurement can be assembled into algorithms for elliptic, hyperbolic, and parabolic PDEs. Each chapter begins with a standard finite difference or finite element discretization and follows the full pipeline from the continuous PDE to quantum encoding, transformation, and extraction of a quantity of interest. Particular attention is paid to the factors governing end-to-end performance, including discretization error, state preparation, normalization, postselection, and measurement cost. A final chapter introduces nonlinear problems through Carleman and Koopman-von Neumann linearizations. The aim is not a comprehensive survey or a claim of universal quantum advantage, but a mathematically transparent entry point and a shared vocabulary for researchers in both communities.

Tunneling is essential in the initialization, measurement, and control of quantum dot qubits. In silicon, such tunneling connects not only the qubit states but also valley minima in the conduction band on opposite sides of the Brillouin zone, with large consequences for the quantum dot behavior. Here we present a full characterization of the intravalley and intervalley tunnel couplings, including their complex phases – the valley phases. These phases are shown to control measurable parameters, including the ratios of the gaps at anticrossings between quantum states of a double quantum dot. The valley phases themselves evolve as a function of the quantum dot gate voltages and depend on the underlying atomic structure of the quantum well. Knowledge of the valley phases completes the picture and fills a key gap in our understanding of sample-wide variations of valley couplings and the physical parameters that depend on them, including spin-orbit coupling, valley-orbit mixing, and Landé $g$-factors.

Quantum information theory (QIT) characterizes the capabilities and fundamental limits of quantum information processing, underpinning quantum communication, computation, and error correction. Formalizing its coding theorems requires connecting finite-block protocols, analytic inequalities, and asymptotic limits within a unified machine-checked framework. Existing developments, however, lack a reusable operational layer that defines codes, error criteria, achievable rates, and capacities independently of their information-theoretic characterizations. In this work, we present LeanQIT, a Lean 4 library for finite-dimensional QIT. It provides composable, kernel-checked interfaces for quantum states and channels, source and channel codes, finite-block performance criteria, hypothesis testing, one-shot quantities, and asymptotic rate constructions. Using this infrastructure, we formalize Schumacher's quantum source-coding theorem, the Holevo–Schumacher–Westmoreland classical-capacity theorem, and the entanglement-assisted classical-capacity theorem together with its strong converse. By separating operational definitions from analytic characterizations and exposing reusable achievability, converse, and asymptotic components, Lean-QIT provides a machine-readable foundation for formal QIT and a compositional knowledge substrate for emerging AI-assisted formalization, automated proof search, and agentic reasoning in quantum information and computation.

We revisit von Neumann's theory of infinite tensor products of Hilbert spaces. On the set $\Gamma$ of equivalence classes of $C_0$-sequences, which labels the incomplete tensor products inside the complete tensor product, we introduce a natural pseudo-ultrametric $d$: the distance between two classes is the convergence exponent of the series $\sum_j|\langle\varphi_j,\psi_j\rangle-1|$ formed from any pair of representatives. We show that $d$ is well defined on equivalence classes, satisfies the strong triangle inequality, and is complete. Distinct classes may lie at distance zero, so $d$ separates points only after passing to the quotient $\widetilde\Gamma$ of $\Gamma$ by the relation $d=0$; the pair $(\widetilde\Gamma,d)$ is then a complete ultrametric space. As an application, we show that a product unitary $\bigotimes_j U$ whose factor $U$ satisfies $\inf_{\|x\|=1}|\langle x,Ux\rangle-1|>0$ (in particular, a unitary on a finite dimensional space with $1\notin\sigma(U)$) displaces every class to the maximal distance $1$. Guided by the intended application – a caricature of Everettian branching, in which the sectors of the infinite tensor product play the role of worlds – we also develop a gauge-invariant variant $\tilde d$ of the metric, based on von Neumann's weak equivalence and matched to the quasi-equivalence of product states on the quasi-local algebra. The displacement of a class under a product unitary, measured by $\tilde d$, is class dependent and realizes every value in $[0,1]$. We interpret $\tilde d$ as a decoherence exponent: it measures the polynomial rate at which two branches of the universal state vector become operationally distinct as ever larger portions of the environment are monitored.