Papers

We investigate how the compactification of some spatial dimensions in Rindler spacetime affects the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a charged scalar field prepared in the Fulling-Rindler vacuum state. A toral compactification is considered with quasi-periodicity conditions on the field operator along the compact dimensions. The phases of these conditions are interpreted in terms of the magnetic flux enclosed by the compact dimensions. For a general number of spatial dimensions, the components of the VEVs are explicitly separated, corresponding to the expectation values in the Minkowski vacuum. As a limiting case, the VEVs are retrieved in Rindler spacetime with trivial topology. We demonstrate that, for non-zero phases in the periodicity conditions, the vacuum energy-momentum tensor exhibits off-diagonal components with indices in the compact subspace. Near the Rindler horizon, the leading terms in the asymptotic expansions of the field squared and the diagonal components of the energy-momentum tensor coincide with the corresponding VEVs in Rindler spacetime with trivial topology. The off-diagonal components of the energy-momentum tensor vanish on the Rindler horizon. For small accelerations, the difference between the VEVs in the Fulling-Rindler and Minkowski vacua is exponentially small. The exception to this is a massless field with zero phases in the periodicity conditions. In this special case, the difference decays according to a power law as a function of acceleration. As an application, we consider the VEVs near the horizon of cylindrical black holes and topological black holes with toroidal horizons.

Quantum low-density parity-check (LDPC) codes are a promising route to fault-tolerant quantum computation, but their use requires efficient preparation of encoded states. Standard encoder constructions generate circuits through fixed algebraic procedures, yet the resulting circuit can contain substantial redundancy. We formulate LDPC encoder preparation as a circuit-resynthesis problem: given the linear-reversible matrix implemented by the encoder's CNOT block, we seek a lower-cost equivalent circuit that can be routed efficiently on the target hardware and which mitigates noise. We propose a novel optimization approach referred as two-sided Hamming descent and a noise-aware optimization pipeline for this task. Across several families of Calderbank-Shor-Steane (CSS) LDPC encoders, including Bivariate Bicycle, hypergraph-product, and entanglement-assisted codes, the proposed pipeline produces substantially smaller and shallower encoder circuits than the standard constructions and the synthesis baselines considered, cutting gate counts by 53.8% in aggregate across the benchmark and by up to 68% on the Bivariate Bicycle family. The gains remain visible after routing, where the two-qubit depth is reduced by up to 71% and translate into higher-fidelity state preparation under circuit-level noise. On the Bivariate Bicycle family, live-range scheduling further reduces routed preparation failure by up to 13.7% without adding two-qubit gates to the selected circuit. These results indicate that encoder-matrix resynthesis, combined with hardware-calibrated selection and scheduling, is an effective compiler-level tool for preparing quantum LDPC code states.

Cavity quantum electrodynamics (QED) with ultracold fermions provides a promising platform for realizing many-body quantum chaos through disordered, photon-mediated long-range interactions. Such setups are inherently open and are therefore subject to dissipation arising from cavity photon loss and atomic spontaneous emission. In this article, we study the driven-dissipative dynamics of a typical cavity QED setting including controllable disorder and long-range interactions. We find that the two dissipation sources have qualitatively different structures. Cavity loss reduces to a single dephasing channel, whereas spontaneous emission in the experimentally relevant regime generates a collection of nonlocal dephasing channels. Cavity-induced dephasing preserves signatures distinguishing integrable from chaotic Hamiltonian dynamics in observables that depend linearly on the density matrix, while spontaneous emission suppresses these signatures. By contrast, quantities that probe the structure of the many-body state, such as the entanglement entropy, are strongly affected by both dissipation mechanisms. Assuming experimentally realistic parameters, we derive quantitative constraints for the observation and control of many-body quantum chaos in cavity-QED platforms.

We investigate the spectral and topological properties of a zigzag Kitaev chain constructed from two diagonally coupled one dimensional Kitaev chains with a zero and finite superconducting pairing phase difference. Using a Bogoliubov-de Gennes formulation, we analyze the energy spectrum, distribution of Majorana zero modes (MZMs), the quasi-particle dispersion, and the winding number, respectively. For a zero phase difference, the resulting energy spectrum shows topological phases with two, four MZMs, and trivial regions. The phases of gap closure determine the topological phase boundaries. In particular, for the phase difference between $\phi=\pi$, the degeneracy of MZMs is partially lifted, leading to modified topological phases compared to the case $\phi=0$. The topological and trivial phase boundaries are further confirmed by evaluating the quasi-particle dispersion and the topological invariant, namely the winding number. We show that the zigzag Kitaev chain contributes independently to the total winding number $\nu = 1$ and $2$, giving rise to distinct topological phases that support two and four MZMs. The $\nu = 0$ gives rise to a trivial region. The energy spectrum of systems corroborates the analytical phase boundaries and reveals characteristics associated with hybridization, enabling us to obtain the complete phase diagram of the zigzag model. Our results establish the zigzag Kitaev chain as a minimal platform for engineering MZM quantum computations, with potential applications in the study of topological phases and Majorana based qubit physics.

Atomic oven generating controllable atomic beam flux plays a fundamental role in quantum gas experiments. Here, we report a new heater design that can heat up an high temperature atomic oven with fast thermal response. The new heater shows a heating rate improved by 7.65 times comparing to that of the conventional resistive heater while the crucible temperature can heated up to 1200K. With this oven, we generated a collimated ytterbium beam with flux exceeding $10^{14} \text{ atoms/s}$ at 823 K. We believe that our design offers a promising solution for shortening experimental dead time and improve the experiment efficiency in cold atom researches.

Quantum batteries (QB), as an energy storage and transfer device, not only show obvious advantages compared to classical electrochemical batteries, but also have important applications in quantum information. Self-discharging is a central obstacle to storing useful work in open QB, especially when the charger itself provides an unavoidable loss channel. Here we show that such charger-induced loss can be converted into a protection mechanism by combining Purcell effect with quantum Zeno effect. We reveal that the virtual photon process and the Purcell effect can induce the strong coupling regime to the quantum Zeno regime, in which the stronger the dissipation of the charger, the weaker the self-discharging effect of the QB. As a result, the dissipation caused by the charger to the QB can be suppressed four orders of magnitude in our scheme. Meanwhile, the quantum Zeno effect induced by the Purcell effect can also avoid the energy backflow between the QB and the charger. Owing to the significantly suppressed dissipation, the stored energy of QB can be charged to a nearly full state and the stored energy is almost converted into extractable work, which greatly improves the energy conversion efficiency.

The supersymmetric properties of the generalized Dirac oscillator allow us to determine the entanglement entropy between the spin and the continuous variable in a purely algebraic manner. The entanglement has a relativistic origin and disappears in the nonrelativistic limit. The entanglement entropy attains its maximal value in the limit of infinite energy.

We analytically determine the ultimate limits of state preparation in two-level open quantum systems driven by coherent control. For a dissipative qubit governed by a GKSL master equation, we give an exact characterization of the reachable set in the Bloch ball. Dissipation excludes a region of states in the Bloch ball which cannot be approached even under arbitrarily strong coherent driving, and we prove that this region has a nontrivial geometry whose boundary is a surface of revolution around the $x$-axis which is analytic except for two conical singularities. We derive a closed-form control protocol for moving on this boundary, and construct an explicit protocol that steers the system arbitrarily close to any prescribed boundary state. These results provide a complete geometric constructive description of reachable qubit states in the standard dissipative environment, establishing fundamental bounds on controllability and state-preparation fidelity for open two-level quantum systems.

To enable sequential sharing of Bell-nonlocality by an unbounded number of copies, each copy must satisfy two requirements. First, the measurements must be incompatible to extract nonlocality. Second, the post-processsed state, obtained as an equal mixture of the two post-measurement states, must remain nonlocal. We show that the incompatibility requirements impose nontrivial constraints on the choice of the initial nonlocal state and the amount of measurement noise required to ensure that the post-processed state remains nonlocal for an unbounded number of copies. We establish this result for two measurement scenarios, namely, when each copy performs unsharp measurements corresponding to a pair of anti-commuting Pauli observables, and when each copy performs probabilistic projective measurements (PPMs) of a pair of anti-commuting Pauli observables. Furthermore, we show that, in the asymptotic limit, the nonlocal post-processed states of all the copies are almost identical, leading to a quantum Zeno-like confinement within the nonlocal region.

The presence of a cosmic string modifies vacuum fluctuations, making the evolution of a two-level polarizable atom position-dependent. Such modifications produce effects on the atomic dynamics analogous to those induced by a reflecting boundary. We show that these quantum boundary effects can be estimated by performing a sequence of $N$ measurements on a single probe atom. For a fixed total probe time, the precision limit is attained by preparing each probe in its optimal initial state, performing the corresponding optimal measurement, and shortening the probe time of each probe. The optimal measurement is uniquely determined by the probe's initial state, and the precision limit obtained with the atom initially in the excited state is four times higher than that for an equal-weight superposition state. The estimation precision displays damped oscillatory behavior as the atom-boundary or atom-string separation increases. In the boundary case, the optimal polarization is always parallel to that boundary. In cosmic-string spacetime, by contrast, the optimal polarization is along the azimuthal direction around the string. The relative advantage of the other polarization directions depends on both the atom-string separation and the deficit angle. For small deficit angles and sufficiently large separations, radial polarization perpendicular to the string becomes less favorable than the other directions.

We establish a strict logical separation between two distinct phenomena in orthogonality hypergraphs: chromatic completeness, the possibility of assigning a single globally consistent nondegenerate spectrum to all contexts, and geometric coordinatizability, the existence of a faithful orthogonal representation by rays. A strong chromatic number larger than the Hilbert-space dimension obstructs only the former. It does not, by itself, obstruct the existence of a faithful orthogonal representation. We make this separation explicit by comparing two three-dimensional examples with the same strong chromatic number. A completed 25-ray version of the Yu-Oh configuration has strong chromatic number four and nevertheless possesses an explicit faithful orthogonal representation in R^3. Conversely, Greechie's G_{32} hypergraph also has strong chromatic number four, and has a separating and unital set of two-valued states, but we give an elementary algebraic proof that it admits no faithful orthogonal representation in C^3. The obstruction in G_{32} is therefore not chromatic but projective-geometric: the incidence relations force two distinct atoms to collapse onto the same ray.

The typical mechanisms of ergodicity breaking in isolated interacting quantum systems, such as many-body localization and quantum many-body scars, originate from the nonthermal nature of the underlying eigenstates. Here, in the absence of nonthermal eigenstates, we identify a mechanism for collective revivals of multiparticle Wannier states (MWSs) associated with nearly linear bands in a spatially modulated Bose-Hubbard lattice. The MWSs, as superpositions of multiparticle Bloch states within individual energy bands, give rise to band-resolved Wannier-sector fragmentation. The key idea is that spatially periodic modulation folds and separates energy bands of a simple lattice into several sub-bands, among which nearly linear sub-bands inherit the linear segments of the original bands. Although multiparticle Bloch states satisfy the eigenstate thermalization hypothesis (ETH), the MWSs in the nearly linear band still exhibit long-lived collective revivals, due to emergent equally spaced energy levels. Our work provides a route to weak ergodicity breaking in which long-lived revivals arise from spectral phase coherence among ETH-satisfying eigenstates rather than from scar-like nonthermal eigenstates.

Universal quantum computers are expected to generate arbitrary complex quantum states of logical qubits encoded in many physical qubits. This capability hinges on a fault-tolerantly implemented universal gate set, which no single quantum error-correction code admits transversally but which becomes accessible by joining complementary codes via lattice surgery. Here we report on the experimental generation and certification of logical genuine multipartite entanglement in a trapped-ion quantum processor using a transversally implemented universal logical gate set. The gate set is accessed via lattice surgery across two different codes and comprises a Hadamard gate on a four-qubit surface code and a doubly controlled Pauli-$Z$ ($\overline{\mathrm{CCZ}}$) gate on an eight-qubit 3D colour code. To showcase this lattice-surgery toolbox, we generate both stabiliser (Greenberger-Horne-Zeilinger) and non-stabiliser ($|\overline{\mathrm{CCZ}}\rangle$) states of three logical qubits and verify their genuine multipartite entanglement–a form of correlation beyond statistical mixtures of bipartite entanglement across any bipartition. We further use these cross-code primitives to demonstrate arbitrary rotations of single logical qubits via a $\overline{\mathrm{CCZ}}$-based resource gadget accessing the full universal gate set through lattice surgery. Together, these demonstrations showcase the core building blocks of an architecture for fault-tolerant quantum computation and its ability to generate complex logical quantum states.

We study continuous-time quantum walks on cycles. We prove two complementary results. Firstly, the cycle $C_9$ does not admit uniform mixing at any time. Using the similar idea and Dickson polynomials, we prove that $C_{15}$ does not admit uniform mixing at any time neither. Secondly, for every prime $p$, we show that the cycle $C_{p^2}$ admits $\epsilon$-uniform mixing.

Cross-click operators, the POVM elements for simultaneous clicks in detectors assigned to different measurement bases, are used in QKD and entanglement-verification analyses with realistic threshold detectors to bound multiphoton contributions. Earlier applications verified the needed growth of the minimum eigenvalue $f^{(n)}$ on the $n$-photon subspace only numerically over finite sectors. This work gives an analytic characterization for passive linear-optical analyzers with arbitrary efficiency mismatch and dark counts. The key observation is that every silence operator is the second quantization $\Gamma(A)$ of an explicit single-photon contraction $A$, whose $n$-photon restriction is $A^{\otimes n}$ on $\mathrm{Sym}^n$. This yields: (i) monotonicity $f^{(n+1)}\ge f^{(n)}$; (ii) two-sided exponential bounds $\max_b \gamma_b|A_b|^n \le 1-f^{(n)} \le \sum_b \gamma_b|A_b|^n$, which determine the exact asymptotic convergence rate from single-photon spectral data; (iii) for ideal detectors and $n\ge1$, the exact formula $f^{(n)}=1-\sum_b p_b^n$; and (iv) an exact factorization $1-f^{(n_A,n_B)}=(1-f_A^{(n_A)})(1-f_B^{(n_B)})$ for the two-party cross-click operator. The results apply to polarization, time-bin, and spatial-mode analyzers within the stated threshold-detector model. As an application, we obtain closed-form photon-number weight bounds used in detection-efficiency-mismatch analyses, replacing finite-sector Fock-space numerics by formulas valid for all photon numbers.

We really design the trimerized circuits for the non-Hermitian one-dimensional Su-Schrieffer-Heeger models. There are three models, the initial one just considers the nearest neighbor coupling, the enhanced one is extended to contain the next-nearest-neighbor coupling, and the final one is reenhanced by introducing the Peierls phase. We investigate the dynamics of the circuit Laplacians with respect to the models, find that the topological states appear in the initial model and the response intervals are substantially affected by the next-nearest-neighbor coupling channels and the Peierls phase. These results are practically demonstrated by numerical simulations and experimental measurements. As a conclusion, the trimerized circuits can provide an adjustable and simple platform to investigate new topological physical states.

Infrared divergences (IRDs) are usually treated as pathologies to be cancelled, regularized, or hidden in dressed asymptotic states. This paper develops a complementary and constructive viewpoint: an IRD is the signature of an itinerant vacuum – a quantum vacuum that wanders continuously through a family of inequivalent states as a classical order parameter evolves. Each value of the order parameter carries its own coherent vacuum, so moving the order parameter means traversing a succession of orthogonal vacua. The IRD is the field-theoretic cost of this wandering, and the $1/f$ noise, gravitational memory, and non-Gaussian fluctuations that emerge from it are its observable classical remnants. The technical core is an exact separation in the real-time closed-time-path (CTP) effective action. The infrared-divergent imaginary part of the influence functional must not be left as a divergent coefficient in a deterministic equation of motion; it is instead converted, by a Hubbard–Stratonovich identity, into a classical stochastic source. This step is an algebraic identity of the generating functional and requires no prior coarse graining or decoherence assumption: the retarded kernel encodes the memory of past vacuum transitions, while the noise kernel encodes the quantum uncertainty of the next one. We apply this construction to four parallel arenas – soft QED, scalar fields in de Sitter space, soft gravitons, and non-equilibrium phase transitions – and show that the same itinerant-vacuum mechanism underlies $1/f$ current noise, the primordial power spectrum, gravitational memory, and order-parameter dynamics. A geometric formulation in terms of a Hilbert-space bundle over the vacuum manifold is outlined as an outlook.

Resource-efficient computation is of central importance in the noisy intermediate-scale quantum (NISQ) era, where decoherence, gate errors, and restricted qubit connectivity severely limit the reliable execution of quantum algorithms. In this work, we demonstrate that incorporating circuit design considerations is crucial for developing resource-efficient variational quantum algorithms. By focusing on the Hadamard test circuit architecture, hardware-aware qubit connectivity, and problem-specific adaptive framework, we analyze how circuit design constraints can systematically reduce the measurement overhead associated with repeated evaluations of the candidate gate pool in adaptive algorithms. Specifically, we demonstrate reductions in the required measurement resources ranging from at least 25% to as high as 50% - 55%. To assess the effectiveness of our approach, we investigate the ground state problem of the nonlinear Schrödinger equation. Overall, our work contributes to resource-friendly strategies for quantum computation and underscores that algorithmic frameworks should systematically integrate circuit design constraints with hardware-aware and problem-specific structures to enhance the practical feasibility of quantum devices in the NISQ era.

We overview similarities and, importantly, differences in computational bottlenecks and accuracy requirements that can be addressed with machine learning (ML) and artificial intelligence (AI) techniques in electronic and nuclear DFT. From these follow different promising methodological and algorithmic choices depending on whether one machine learns the exchange correlation (XC) functional, the kinetic energy functional (KEF), the density or the basis functions. In particular, while the popular deep neural networks remain a potent choice in the context of KS DFT, we highlight their disadvantages when building KEFs and highlight conceptual advantages - yet to be fully realized - of symbolic regression for both electronic and nuclear DFT. We point out promising approaches that can be carried from the more extensively investigated ML-enhanced electronic DFT to nuclear DFT.

Neutral-atom array and cavity quantum electrodynamics offer complementary strengths for quantum science: scalable, reconfigurable qubit architectures and strong coherent light-matter coupling. Combining them in a single platform requires an optical cavity with simultaneously high cooperativity, sufficient mode volume to accommodate atom array, and ample side optical access for atom trapping, imaging, cooling, and rearrangement, a combination that is challenging to achieve. Here we realize an atomic array integrated with a millimeter-scale Fabry–Pérot cavity whose optically-characterized single-atom cooperativity reaches $\eta_{\mathrm{cav}}=125\pm13$. Atom-cavity transmission spectra of trapped atoms yield an effective spectroscopic cooperativity $\eta_{\mathrm{spec}}=106\pm 3$, providing an in-situ verification of strong coupling in the integrated platform. In this integrated system, we achieve a state-measurement fidelity of $99.925^{+15}_{-18}\%$ for a single atom with a 4-$\mu$s readout time. We also demonstrate simultaneous coupling of up to 21 individually trapped atoms to the antinode of the cavity mode. The key technical advance is a two-step mirror-fabrication method combining precision mechanical shaping and carbon-dioxide laser polishing, which produces concave fused-silica mirrors with sub-millimeter radii of curvature and residual roughness below $2~\r{A}$. Our results establish a regime of cavity-integrated atomic array that simultaneously provides high cooperativity, large mode volume, and flexible manipulation of individual atoms, opening opportunities for cavity-assisted quantum state readout and long-range entanglement-engineering in atom-array platforms.

The theory of quantum error correction was established decades ago. Yet limitations in physical noise levels and available physical-qubit counts continue to hinder the development of scalable quantum computing systems. In this paper, we present analytical estimates of logical error rates for advanced QEC codes across leading hardware platforms and distributed quantum computing systems using a simple but unified framework. The analysis captures dominant contributors to logical error, including effective circuit volume and two-qubit gate overhead. The framework provides a fast and conservative estimate of logical error rates and identification of dominating factors in different hardware platforms, such as circuit volume, routing overhead, inter-QPU operations, or asymmetric noise protection. We show that several qualitative trends observed in larger-scale simulations can be reproduced and interpreted analytically within this framework. We further demonstrate that the framework can be used to find the sweet spot design region of distributed QEC, which is critical for the design of distributed quantum computing systems.

Artificial atom-like systems are a promising candidate for next generation quantum processing. Among them, dark excitons exhibit one of the longest lifetimes at high temperatures. Here, we demonstrate coherent control of dark excitonic states in metal-organic chalcogenolates (MOChas) by using an ultrafast pulse shaper at room temperature. These dark exciton states are optically accessed via two-photon absorption and directly read out with a four-wave mixing process. The system is described by a non-perturbative, two-photon Hamiltonian based on well-known atomic physics and applied to a three level system comprised of two dark excitons. Empirical and theoretical state specific optical access is shown via a simple optical pulse shape. The developed Hamiltonian-based description is a first step towards a quantum processing platform using three-level systems and two photon transitions, one example being dark excitons in the MOCha silver benzeneselenolate (mithrene). Simple conditions for gate operations are laid out and described.

In the theoretical study of nonequilibrium non-Hermitian systems, obtaining exact analytical solutions for their nonadiabatic dynamics is highly desirable yet often challenging. In this work, we identify a class of non-Hermitian quantum systems where this difficulty can be substantially reduced. Employing the Wei-Norman approach, we show that for a spin-$S$ subject to a general non-Hermitian time-dependent drive, the matrix elements of the evolution operator can be expressed in closed analytical forms (via Jacobi polynomials) in terms of the corresponding spin-$1/2$ model. This approach is straightforward and accessible to nonspecialists in Lie algebra. As an application, we investigate a specific nonequilibrium non-Hermitian phenomenon known as defect freezing, i.e., the existence of excitations in the adiabatic limit, in spin-$S$ extensions of the $\mathcal{PT}$-symmetric Su-Schrieffer-Heeger model under linear quenches. We derive exact analytical expressions for the momentum-resolved excitation probabilities and the total excitation densities. Our results reveal that defect freezing occurs exclusively in momentum sectors that traverse the $\mathcal{PT}$-symmetry-broken region – and thus pass through a pair of higher-order exceptional points (EPs) – during the quench; notably, the excitation density exhibits a singularity at a critical value of the non-Hermiticity parameter. This work enriches the analytical toolkit for nonadiabatic dynamics in multi-level non-Hermitian systems and provides quantitative, testable predictions for defect freezing across higher-order EPs, possibly accessible on platforms such as electric circuit networks and photonic lattices.

Large language models can generate plausible quantum code, but it is unclear whether they can reliably target the specific software development kit (SDK) version requested by the user. We study this problem as API drift and introduce quantum-api-drift, a benchmark for measuring version fidelity, defined here as execution success on the requested SDK version, cross-version compatibility, failure modes, and documentation-guided repair in LLM-generated quantum SDK code. We instantiate the benchmark with Qiskit, a representative quantum SDK that underwent substantial interface changes across v0.43, v1.3, and v2.0. We evaluate 17 models on 50 tasks with 3 samples per prompt, yielding 450 generated samples and 1,350 executions per model. Sixteen models are tested in a matched REST API setting with a 1024-token output cap, while GPT-5.4 (Codex CLI) is reported separately as a reference configuration. Across the 16 matched REST models, diagonal Pass@1 ranges from 0.02 to 0.85. Claude Opus 4.7 is strongest on v0.43 and v2.0, while Grok 4.20 is strongest on v1.3 at 0.513. Error profiles differ systematically by model strength: weaker models fail mainly with broken imports, while stronger models more often reach deprecation-level failures. Documentation-guided repair succeeds for 0.19 to 0.59 of repair attempts overall and is consistently much more effective for migration to v2.0 than to v1.3. The benchmark artifacts are publicly available at https://github.com/arasyi/quantum-api-drift. These results show that version alignment is a distinct evaluation axis for quantum code generation and that API drift remains only partly recoverable even with migration guidance.

In spread complexity, the growth rate of the average position of a time-evolved state along its Krylov chain recovers the proper radial momentum of an infalling particle in AdS. It is, however, a measure of the first moment only, irrespective of the spread of the wavepacket away from its classical trajectory. The rate of a normalized Krylov-Wigner negativity can be proposed as a diagnostic of the second moment of the boundary state that captures this spreading. Starting with the seed-normalized Krylov-Wigner distribution, that is, the Wigner transform of the descendant cloud with the decaying return amplitude divided out, we obtain an analytic Bessel form in the macroscopic limit and compute its total negativity explicitly. Retaining the Bessel variable all the way through, we find that the negativity goes as $\sinh^{4\Delta}(\pi t/\beta)$. But the raw normalized-state negativity saturates to an $O(1)$ constant, well below the $O(\sqrt{D})$ bound. Using the exact negative binomial statistics of the Krylov chain, the normalized negativity is at late times a fixed power of the second moment of the Krylov wavepacket, $\mathcal{N}(t)\propto[\mathrm{Var}(\hat{N}_{\mathrm{Krylov}})]^{\Delta}$, for every $\Delta>1/2$. The relation linearizes precisely at $\Delta=1$. In this regime via the momentum dictionary of Caputa et al. (arXiv:2410.23334), the rate becomes the product of the proper radial position and momentum, $\mathcal{R}\propto\mathcal{C}\,P_\rho$, which we interpret as the rate of the tidal stretch of nearby geodesics falling into the horizon. We also comment briefly on a speculative direction for future research, in particular the interpretation of the transverse string size operator in terms of the Krylov number operator through the common $\mathrm{SU}(1,1)$ discrete series.

The correspondence between $2\times 2$ Hermitian matrices and Minkowski $4$-vectors recovers Lorentzian symmetries from the internal degrees of freedom of a qubit, with no reference to an external spacetime. Recent work characterises the resulting Lorentz invariants and leaves the mechanism of emergence – what singles out a time direction – as an explicit open question. We give an elementary answer and, in doing so, correct a natural misattribution. The bare spin space $(\mathbb{C}^2,\varepsilon)$ is $SL(2,\mathbb{C})$-symmetric and singles out no axis; so is the null cone it generates. What selects a future-timelike axis is the choice of a Hermitian inner product, equivalently a positive reference form $\sigma^0$: this choice – made in passing from a normed space to a Hilbert space, before any probability is assigned – reduces $SL(2,\mathbb{C})$ to its maximal compact $SU(2)$, the stabiliser of $\sigma^0$. The Born rule enters one level later: $\langle \xi \vert \xi \rangle = \text{tr}(\sigma^0 \, \xi\xi^\dagger)$ is the projection of the state's null vector onto $\sigma^0$, i.e. its energy in that frame, and under a boost it rescales as a Doppler shift. Thus the Hilbert structure selects the axis; the Born rule is where that axis becomes a measurable energy and where the frame-dependence of $\lvert\psi\rvert^2$ becomes empirical. The ingredients are classical; what we add is their identification as the mechanism the recent programme leaves open, with the symmetry-breaking step located precisely. This is a kinematic identification of that step, not a dynamical account of why a particular axis is selected. We close by handing back the many-qubit case, where the datum is a tuple of such choices.

Random circuit sampling of bitstrings from a Haar-random quantum state is widely believed to be classically intractable, and has therefore been implemented as a primary benchmark for demonstrating quantum advantage. Here, we challenge this premise by proposing an efficient classical frozen-tree sampling algorithm that exploits the conditional scale invariance of Haar-random quantum states [Oh, arXiv:2602.19448]. The frozen-tree sampler draws bitstrings of $n$ qubits in $O(n)$ time per sample. Moreover, its output probability $p_F(x)$ is statistically identical to the probability $p_C(x)$ of a random quantum circuit, since both are independent instances of the same Dirichlet distribution. Consequently, no statistical test acting on samples alone can distinguish the classical frozen-tree sampler from a quantum random circuit. The claimed quantum advantage of random circuit sampling therefore does not withstand scrutiny: its hardness lies not in sampling from the Dirichlet distribution, which is classically efficient, but in identifying a specific circuit realization.

We develop a Lie-Jordan geometric formulation of finite-dimensional open quantum dynamics, building on the algebraic framework introduced in our previous work (arXiv:2606.26477). The Hilbert-Schmidt operator space is endowed with an orthonormal Hermitian basis, in which the commutator and anticommutator are encoded by the structure tensors \(C_{\mu\nu}{}^\lambda\) and \(B_{\mu\nu}{}^\lambda\). Within this formulation, the von Neumann and Gorini-Kossakowski-Lindblad-Sudarshan equations admit a direct component representation. Our central result is the identification of a basis-independent universal trilinear dissipative map, \( \mathcal D(X,Y)Z=XZY-\frac12\{YX,Z\}, \) whose components define a universal operator-space tensor depending only on the Lie-Jordan structure tensors. The physical dissipator is obtained by contracting this tensor with the expansion coefficients of the Lindblad operators and the Kossakowski matrix, thereby separating the universal algebraic structure from the model-dependent physical information. We further show that the combinations \((B+C)\) and \((B-C)\) generate internal left and right transports, allowing the elementary dissipative map to be expressed as a left-right bimodule action corrected by an ordered Jordan contribution. The universal map satisfies basis-independent trace and Hermitian-conjugation identities, from which trace preservation, Hermiticity preservation of the complete dissipator, and the reality of its component representation in a Hermitian Hilbert-Schmidt basis follow. We also derive its Hilbert-Schmidt adjoint and illustrate the formalism for a qubit with pure dephasing and amplitude-damping channels. This construction provides a tensorial and affine-geometric interpretation of the universal superoperator structure derived in arXiv:2606.26477 while keeping the algebraic and model-dependent sectors explicitly separated.

Quantum simulations of gauge theories are typically built on spatial lattices, an approach that has enabled major progress at the cost of requiring fixed background geometries and obscuring the treatment of curved and dynamical spacetimes. Large-$N$ matrix models offer an alternative, encoding spacetime geometry and gauge fields in the commutation structure of a set of Hermitian matrices, with the classical continuum emerging smoothly at large matrix dimensions. Here we introduce a Floquet framework that makes these models directly accessible to programmable quantum platforms. We show that Euclidean path integral weights of a Yang-Mills matrix models are reproduced, at leading order in the coupling, by the ensemble-averaged fidelities of Haar-random states evolved under periodic sequences of matrix operators. The observables for the simulated matrix model can then be accessed through established randomized benchmarking protocols in terms of the Loschmidt echo. The encoding requires exponentially fewer qubits than canonically quantized approaches. Numerically, we validate the fidelity-weight correspondence, demonstrate parallelized quantum circuits that sample the path-integral measure, and identify the deconfinement transition of an $SU(2)$ gauge field on both flat and expanding cosmological backgrounds. By avoiding a fixed spacetime lattice, the framework preserves continuous symmetries and unitarity on dynamical geometries, opening quantum simulation to field and spacetime dynamics beyond the reach of conventional lattice methods.

Standard device-independent self-testing uses Naimark dilation to assume projective measurements, masking the operational limitations of realistic non-unitary observables. We establish a robust pure self-test for the singlet and Pauli observables that entirely circumvents dilation of the measurement apparatus. Assuming a pure state to model an untrusted source, we regularize the physical non-projective operators and derive an analytic $\mathcal{O}(\sqrt{\epsilon})$ robustness bound. Our results suggest that device-independent certification of real implementations is significantly more demanding than standard projective models imply.