Papers

In the conventional theory of quantum computation, universality is discussed in terms of properties of unitary gate sets. In many experimental setups, however, we instead have access to a parametrized set of Hamiltonians, which can be exponentiated for any desired time. Accordingly, we formulate a continuous analogue of universality, where adding one expensive Hamiltonian control to a cheap set of local control operators allows for universal computation. We find several concrete sets of 1- or 2-local Pauli generators $S$ and $n$-qubit “magic" Hamiltonians $H$ that together generate the full Lie algebra $\mathfrak{su}(2^n)$, with a special focus on the Ising Hamiltonian $J$. We propose a method to directly implement any unitary by exponentiating these generator sets, and give bounds on the needed time of application of the magic Hamiltonian $H$. We find that the number of applications of $H$ needed to approximate any unitary up to accuracy $\epsilon$ scales exponentially in the number of qubits as expected from the standard application of the Solovay-Kitaev theorem. We also find phase transitions in the size of the generated Lie algebras as the parameters of the Ising Hamiltonian are varied. We find an algorithmic application of the Chow/Rashevskii technique to implement unitaries corresponding to iterated commutators.

Wetterich showed that certain 1+1D probabilistic cellular automata are equivalent to fermionic QFTs and posed the 3D construction as an open problem. We construct one: a layered automaton ("coincube") whose conversion blocks form the real quaternion representation of Cl(0,3), controlled by binary environment fields whose streaming outruns the carrier ("fresh tape") – no bit is consulted twice, and the single-particle ensemble propagator equals the annealed Bloch operator at every time. Exact results: the step operator is unitary for an explicit complex structure; the local Grassmann action is extracted mechanically; the single-carrier excitation is a Weyl fermion with an isotropic leading cone (slope ratios 1 within errors, factorized transport excluded by >=10 error bars); at finite momentum the node carries a parity-odd anisotropy c(q)kx ky kz/|k|, cancelled on the Dirac branch whose gap is 2 arctan[qm/(1-qm)], while off-resonant spectators stay massless; media-mediated interaction obeys Ug = (1-2gq^2) U. Obstructions: ballistic transport admits only finite velocity sets; Abelian sign gauges leave the factorized surface; no protected 2-component node survives an exhaustive search. Finally, a dichotomy for the quaternionic event class: an isotropic cone forces overdamping – Q = w_0/Gamma <= pi/(2 ln 2) at all densities, 0.66 at working density – while in-state unitarity forces factorized transport. Postselected two-boundary amplitudes evade this, exactly unitary at all times under the fresh tape, with induced weight positivity open: the relativistic object here is an amplitude whose probabilistic reading is unsettled.

Bayesian quantum tomography requires efficient inference while preserving a posterior fixed by the prior and Born likelihood. Learned transport provides fast amortized samples, but reward tuning can reshape the generated distribution rather than improve exploration of this fixed target. We introduce GRPO-QPS, a target-preserving framework in which GRPO learns proposal behavior and an exact Metropolis correction preserves the posterior after training. Across the evaluated reconstruction benchmarks, GRPO-QPS improves over BuresTomFlow and Flow-GRPO on thermal, cat, Dicke, and cluster families, and it closely matches an exact two-qubit reference posterior. Tuned conventional MCMC is slightly stronger on several original continuous benchmarks where the available fixed proposals already match the posterior geometry well. To test whether this reflects a fundamental limitation of learned exploration, we evaluate a more challenging multimodal thermal posterior. At six qubits and 800 shots, the learned proposal achieves a minimum effective sample size of 102 per $1{,}000$ likelihood calls, compared with 28 for prior independence, 27 for a tuned fixed mixture, and 20 for Haario adaptive Metropolis. A record-conditioned policy also transfers to unseen 3,000-shot records, matching or exceeding the strongest conventional baseline in all nine held-out seed-record comparisons. These results show that GRPO-QPS combines target-preserving Bayesian inference with broad gains over learned transport baselines and a sampling advantage when efficient exploration requires proposal geometry beyond the evaluated conventional kernels.

An important problem in quantum technologies is the generation of a target evolution of an open quantum system. A core component of this task is the ability to determine whether the actual evolution of the system coincides with the target evolution. For the generation of unitary quantum channels in open quantum systems, it was shown by Goerz, Reich and Koch [New J. Phys. 16 055012 (2014)] that for determining whether the actual evolution coincides with a desired unitary it is sufficient to compare their action on three special density matrices. In this work, we consider controlled generation and unique determination of non-unitary quantum channels in open quantum systems with particular emphasis on rank two single-qubit quantum channels. We prove that to uniquely determine such quantum channels it is sufficient to consider their action on only three suitably chosen density matrices. Based on this theoretical result, we numerically investigate generation of various non-unitary target single-qubit quantum channels in open quantum systems using coherent and incoherent controls.

Spin correlations offer a quantum-information perspective on the partonic final states produced in high-energy scattering. We discuss the spin-density matrix of a heavy quark-antiquark pair in two complementary small-$x$ processes. In coherent diffractive production, color-singlet exchange enforces an unusually strong relation between entanglement and Bell nonlocality: a longitudinal photon creates a maximally entangled pair, whereas for a transverse photon the pair is generically both entangled and Bell nonlocal, with a model-independent point of maximal entanglement. In inclusive back-to-back production, the density matrix factorizes into a hard spin tensor and the unpolarized and linearly polarized Weizsäcker–Williams gluon distributions. The latter generates an azimuthal modulation and can increase the concurrence when the dijet relative momentum and imbalance are approximately orthogonal. Strikingly, in the saturation model considered, nonlinear effects wash out this modulation for $q_\perp\lesssim 3Q_s$, whereas the dilute BFKL limit, in which $G_2/G_0\to1$, yields a maximal modulation independent of the imbalance magnitude. These results connect quantum-information observables with the Pomeron and saturation physics.

We develop a certified finite-horizon quantum optimal-control framework based on fixed-rank Hierarchical Tucker (HT) surrogates. Under a uniform rank-dependent HT truncation-accuracy condition, we establish exponentially decaying trajectory, cost, and value-function errors and near-optimality of surrogate-generated controls. We further derive a logarithmic rank–performance relation, an a posteriori cost certificate from realized truncation perturbations, and guarantees for inexact surrogate optimization and control convergence under additional regularity conditions. Numerical experiments on controlled XXZ spin chains provide finite-sample evidence consistent with the truncation condition and illustrate the trade-off between HT rank, representation size, surrogate accuracy, and control performance.

Computing many instances jointly can reduce communication per instance. We ask whether such savings occur in the simultaneous-message-passing (SMP) model and how they depend on quantum messages and shared resources. For every finite total function $f$ and fixed error $0\le\varepsilon<1$, we prove that the optimal worst-case communication per instance for $f^n$ converges to \[ D^\parallel(f)=\log|\mathrm{Row}(f)|+\log|\mathrm{Col}(f)|, \] where $\mathrm{Row}(f)$ and $\mathrm{Col}(f)$ are the sets of distinct rows and columns of the table $(f(x,y))_{x,y}$. This holds for classical and quantum SMP without shared entanglement, with or without shared randomness. Thus, transmitting row and column indices is asymptotically optimal, even with bounded error, joint computation, and quantum messages. In particular, the exponential advantage of quantum fingerprinting for a single instance of equality without shared randomness disappears in the asymptotic rate. We also prove that the same threshold governs an exponential strong converse: every fixed worst-case communication rate below it forces the probability of computing all $n$ outputs correctly to decay as $2^{-\Omega(n)}$, even on average under a fixed product input distribution. With shared randomness, the optimal expected communication rate is $(1-\varepsilon)D^\parallel(f)$. Entanglement shared between each sender and the referee halves both rates; arbitrary tripartite entanglement gives no further reduction. The results extend to a class of total relations and yield one-way characterizations with $D^\parallel(f)$ replaced by $\log|\mathrm{Row}(f)|$. Our proof reduces SMP to one-way communication and relates successful computation to sampling based on quantum min-entropy; we also give a simpler proof of the key lemma using the pretty-good measurement.

Perturbative quantum gravity is ultraviolet divergent and, as shown by 't Hooft and Veltman, non-renormalizable. A recent object-relative, Lorentz-invariant weighting of internal electromagnetic modes renders selected one-loop contributions of quantum electrodynamics finite without counterterms. Here that weighting is derived rather than postulated: causality defines a mode resonator bounded by the Hubble radius and re-defined in every inertial frame, and the self-gravitation of each mode quantum deforms its spectrum. Applied to linearized gravity, the graviton self-coupling reaches order unity at the Planck wave number, so that the mode content available to a loop is suppressed beyond it. Any suppression exceeding a threshold fixed by the diagram renders the one-loop integrals finite; no cutoff is imposed and no mode structure above the Planck scale need be derived. For pure gravity the same power counting extends to every loop order, and the leading suppression already meets the resulting condition for every topology with more than one vertex; a single class of single-vertex insertions is excluded. The Bianchi identity takes the role of the Ward identity at one loop, and the transformation between the resonators of two inertial frames is unitary. The same finite mode content yields a vacuum energy density of order H^2/G, of the observed sign and magnitude, from the Planck and causal infrared wave numbers alone. A contribution tracking the instantaneous expansion rate is an exact rescaling of the gravitational constant and is excluded by primordial nucleosynthesis, so the mode basis must be frozen in any inertial system; referring it to the stationary de Sitter horizon fixes the remaining coefficient to the geometric value 6/pi and makes a value for the energy density of gravitational vacuum fluctuations possible which can be interpreted as origin of the dark-energy effect.

We investigate thermal rectification and its thermodynamic cost in a three-qubit XXZ spin chain coupled to three thermal reservoirs: two local baths attached to the boundary qubits and a collective bath jointly coupled to the middle and right qubits. This asymmetric dissipative architecture allows the collective environment to actively reshape energy transport. We show that the heat current carried by the collective bath changes sign as its temperature is varied, and that the spin-chain anisotropy provides an effective internal control parameter for suppressing the boundary heat currents. These features yield thermal rectification coefficients of about $3.36\%$ at maximum bias and up to $20.1\%$ in the strongly anisotropic regime, although the latter comes at the cost of severely reduced heat currents. Beyond rectification, we evaluate the steady-state entropy production rate and identify a low-irreversibility operating window near the collective-current reversal, whereas increasing the local boundary couplings monotonically raises the thermodynamic cost. Our results establish collective dissipation as a tunable control mechanism for quantum heat transport and uncover a nontrivial trade-off among rectification, heat-current magnitude, and irreversible losses.

We prove that the quantum monad in dimension $2n$ admits no natural transformation to the polymorphism clone of linear equations modulo $n$. Consequently, for every $n\geq 2$, there exists an unsatisfiable system of linear equations over $\mathbb{Z}_n$ whose constraint system game admits a perfect finite-dimensional quantum strategy. As a corollary, we completely characterise pseudo-telepathic constraint languages in finite dimension. The proof combines a result of Harding, Jager, and Smith on group-valued measures on subspaces of Hilbert spaces with the polymorphism-minion characterisation of quantum pseudo-telepathy.

Quantum computation gives rise to new pseudorandom primitives for states and unitaries, including pseudorandom state generators (PRSGs), pseudorandom function-like state generators (PRFSGs), and pseudorandom unitaries (PRUs). In this paper, we show a full unitary oracle separation between PRFSGs and PRUs. The separation holds between the strongest state notion and the weakest unitary notion: even adaptively secure, quantum-accessible PRFSGs do not imply non-adaptively secure, forward-only PRUs, even when their implementations are allowed to be non-unitary and use an arbitrary number of ancillary qubits. This reveals a fundamental distinction between pseudorandomness for quantum states and for quantum unitaries. Our main technical idea is to view a candidate PRU construction with access to state generation oracles as a map from the underlying oracle states to implemented unitaries, and to study the derivatives of this map. These derivatives are inherently low rank, and we exploit this low-rank structure to distinguish the resulting unitaries from truly random ones. We believe this differential perspective may be useful for studying other structural questions about quantum states and unitaries.

The classical capacity of a quantum channel generally requires regularization because input codewords may be entangled across channel uses. We remove this regularization for generalized amplitude-damping channels (GADCs) and determine their exact strong-converse exponent throughout the full parameter range. The exponent is a single-letter transform of the sandwiched Rényi Holevo information and is attained by product input codewords with collective decoding. The key ingredient is a decomposition of the joint output into positive operators whose triangular factors have identical scalar Gram matrices after norm compression. A sharp triangular Schatten-norm compression inequality then establishes maximum output norm multiplicativity for diagonally sandwiched GADCs tensored with arbitrary completely positive maps. This yields additivity of the sandwiched Rényi Holevo information at every order above one. Consequently, the classical capacity equals the known one-copy Holevo information and admits a scalar optimization. Thus, entangled input codewords improve neither the capacity nor the optimal exponential decay of decoding success above capacity.

Can a classical network not only encode a quantum-like state, but also read out its measurement statistics through its own collective dynamics? Here we introduce a network-native readout scheme for a structured classical network whose community modes form an effective two-qubit state space. Network connectivity selects a dominant collective mode that encodes the state, while a fixed set of ten elementary connectivity perturbations probes its collective response. The resulting shifts of the dominant growth rate form a complete basis of expectation values for the real two-qubit sector, from which joint-outcome probabilities associated with arbitrary real projectors are reconstructed by linear combination. Once these ten spectral responses are measured, the same data generate correlations over a continuous family of measurement settings. As a benchmark, for an encoded Bell state four selected correlations give $|S|=\chsh>2$, whereas a separable product-state reference remains within the Clauser–Horne–Shimony–Holt (CHSH) bound $|S| \leq 2 $. These results establish an informationally complete dynamical readout of effective two-qubit states directly from the spectral response of a classical network.

This text explores the fundamental divide between empirical laboratory data and continuous theoretical physics models, framing the "quantum measurement paradox" as an ontological error, specifically E.T. Jaynes' “mind projection fallacy” where abstract mathematical tools like wavefunctions are mistaken for physical reality. While quantum theory successfully predicts ensemble averages, it remains inherently silent on individual, event-by-event detection statistics. To resolve these conceptual mysteries without resorting to ad-hoc explanations like wavefunction collapse, the text introduces Event-By-Event Simulation (EBES). As a modular, discrete-event simulation framework utilizing causally-driven Deterministic Learning Machines (DLMs), EBES bypasses continuous time and pre-specified probability distributions. Instead, it generates discrete data from the bottom up in a strictly localized, cause-and-effect manner. Ultimately, EBES provides a computationally efficient methodology that mirrors actual laboratory observations, modeling phenomena that lie entirely beyond the reach of standard quantum theory.

Variational quantum algorithms recast state preparation as classical nonconvex optimization, but it is often unclear when multistart local search suffices and when population-based global search justifies its evaluation cost. Using a landscape-first design, controlled QAOA experiments identify two mechanisms making local search unreliable: parameter reuse across circuit layers and competition between 2-local and 3-local cost terms. Increasing QAOA depth alone does not replicate this effect. We test these mechanisms across eight unseen spin glasses, fresh $N=10$ and $N=12$ instances, and standard MaxCut, transverse-field Ising, and Heisenberg models. On all eight unseen spin glasses, adaptive differential evolution (DE) achieves lower median error than both multistart BFGS and multistart Powell on the two difficult constructions, whereas the independent-depth control does not. The parameter-reuse effect transfers to MaxCut at both sizes, while standard VQE models remain favorable to local search. A pre-benchmark landscape score combining random-start local outcomes and 1D parameter slices is fixed from confirmation data before evaluating new optimizers. It predicts whether adaptive DE outperforms multistart BFGS by over one spectral-range percentage point on 50 new quantum objectives with 80–86% condition-level accuracy. The clearest indicator of global-search utility is that local search frequently traps in inferior basins, rather than circuit depth or curvature anisotropy. The findings motivate whether quantum circuit complexity can be traded for harder classical optimization when robust global search is available.

We propose a novel scheme to generate and manipulate bipartite and tripartite entanglement and Bell nonlocality in a closed-loop three-mode optomechanical system, where two optical modes are simultaneously coupled to a mechanical mode via typical optomechanical interactions and also coupled to each other through field transmission. This configuration gives rise to a phase-sensitive coupling, in which the relative phase directly controls the population distribution between two optical modes, enabling coherent redistribution of quantum correlations. By tuning this relative phase, we achieve deterministic switching of bipartite entanglement between two optical-mechanical pairs, as well as tunable genuine tripartite entanglement among three modes. Employing the displaced-parity measurement, we construct both the bipartite and tripartite Bell inequalities in phase space and observe maximal violations of approximately $2.32$ and $3$, respectively, which coincide exactly with the values achievable for ideal bipartite and tripartite Einstein-Podolsky-Rosen states. Counterintuitively, we find that the tripartite Bell nonlocality can persist even when the genuine tripartite entanglement is absent, providing deeper insight into the relationship between these two types of quantum correlations. Furthermore, we systematically analyze the effects of mechanical dissipation and thermal noise, identifying the parameter regions where Bell violation survives under realistic experimental conditions. Our results establish a comprehensive framework for generating, controlling, and verifying multipartite quantum correlations, paving the way towards phase-tunable quantum networks and noise-resilient tests of quantum foundations.

At atomic resonance the Jaynes–Cummings (JC) vertex of a single bosonic mode coupled to a two-level emitter is blind to $f=\omega/\lambda$ at zero detuning and Kerr; the anti-Jaynes–Cummings (AJC) vertex is not. We show that the mean-rung excited population of the AJC block equals exactly $1/4$ at $f_\star=\sqrt{\bar n+1}$, while the JC population at the same point is $1/2$. The Poisson-averaged packet value at $\bar n=16$ is $0.24650$, within $3.5\times 10^{-3}$ of the exact value, with the deviation reproduced by $-\bar n/[16(\bar n+1)^2]$. At $f_\star$ the modulation depth of the AJC inversion is $1/2$ and the relative sensitivity of the continuum revival-time ratio $r=t_R^{\rm AJC}/t_R^{\rm JC}$ is maximal with value $1/(2\sqrt{\bar n+1})$. Full diagonalization on $2(n_{\max}{+}1)$ states confirms the analytic values. The $1/4$ value can be generated by Floquet-engineered counter-rotating coupling provided that the static transverse rate satisfies $g_0\ll g_1$. Parameter translations for an ideal trapped-ion blue sideband and a flux-tunable circuit-QED coupler are reported.

We investigate local conserved quantities in non-Hermitian bosonic lattice systems whose underlying Yang–Baxter structure remains unclear. Focusing on a one-dimensional bosonic chain with quartic interactions of creation operators, we provide a new representation of the local conserved quantities previously constructed by Sanatani and Shiraishi. Using Fourier transformation and trigonometric identities, we systematically derive these conserved quantities and show directly that they form a mutually commuting family. We further extend the construction to interactions extending beyond a single site, cubic interactions, asymmetric hopping, and an on-site potential. Our results provide a unified framework for constructing and characterizing local conserved quantities in this class of non-Hermitian many-body systems.

Godsil and McKay (1978) showed that the rooted product is a powerful tool for constructing non-isomorphic cospectral pairs of graphs. Despite lacking a convenient tensor product structure, we show that the rooted product is useful for constructing graphs with good quantum state transfer properties. In particular, we prove a simple transference principle: if a graph $X$ has quantum state transfer and $Y$ is a controllable graph, their rooted product $X^Y$ has quantum state transfer (inherited from $X$). This complements a folklore property of Cartesian product which preserves perfect state transfer. However, the rooted product is a significantly sparser graph and, more importantly, can be easily used to construct efficient high-fidelity state transfer even if $X$ has no quantum state transfer. Our proof exploits the fact that a rooted product creates a large number of strongly cospectral pairs of vertices and that its condition number can be controlled by its pendant subgraph.

Automated theorem proving seeks to use computational systems to prove or disprove mathematical and logical statements [1, 2]. It underpins a wide range of applications, and enhancing theorem-proving capabilities remains a central objective in artificial intelligence [3]. Although recent neuro-symbolic systems have achieved remarkable progress [4-7], their operation is ultimately constrained by classical computational architectures. Quantum computing [8], by contrast, enables information encoding and coherent parallelism beyond classical limits [9-14], raising the possibility of accelerating structured symbolic deduction [15]. Here we report the experimental realization of automated geometry theorem proving on a fully programmable superconducting quantum processor. We develop two complementary quantum proving frameworks. The first implements Wu's algebraic elimination method using quantum pseudo-division, with multivariate polynomials represented in superposition states, enabling quantum algebraic theorem proving. The second implements the full-angle method as backward symbolic reasoning through a hybrid quantum strategy-guided architecture, demonstrating a general route toward quantum symbolic proof search. As illustrative examples, we prove two theorems on a superconducting quantum processor: the perpendicularity of the diagonals of a square and a 1978 International Mathematical Olympiad geometry problem. Our results establish, at the experimental level, automated logical reasoning as a viable task for near-term quantum processors and provide a concrete pathway toward quantum-enhanced symbolic intelligence.

Rigorous empirical validation of quantum machine learning on natural language tasks remains scarce. We evaluate a 10-qubit hybrid quantum-classical variational circuit (2,148 parameters) for paraphrase detection across three benchmarks: MRPC, Quora Question Pairs (QQP), and adversarial PAWS. On QQP (n = 10 seeds), the circuit achieves 75.53% +/- 0.75%. accuracy, statistically outperforming parameter-matched classical baselines (DeepMLP: p = 0.015, Cohen's d = 1.20; F1: p < 0.001, d = 2.32) and surpassing DistilBERT-4bit with 31,191 fewer parameters. On MRPC the optimal 2-layer variant reaches 92% of BERT-base accuracy at 54,000 lower parameter cost. Circuit depth analysis reveals a dataset-depth scaling effect; entanglement analysis via the Meyer-Wallach measure identifies multi-qubit entanglement as the primary performance driver (r = 0.85 across four variants). Adversarial evaluation on PAWS reveals emergent robustness: 98.2% recall versus 81.6% classical (+16.6 pp, d = 1.24, p < 0.001), without adversarial training. These results constitute the first systematic parameter-matched multi-benchmark empirical validation of hybrid variational circuits for NLP. All results are from classical simulation; hardware validation is future work.

The NOON states possess Heisenberg-limited phase sensitivity and are crucial for quantum-enhanced metrology. In our work, we develop a Floquet-engineered conditional-routing framework in which a $d$-level quantum controller mediates the dynamics of $d$ bosonic modes. For an arbitrary odd dimension $d=2s+1$, the $d$-level system can act as a “quantum knob" by tuning its initial states to coherently control the direction of chiral excitation flow, such that different controller eigenstates generate distinct cyclic-routing branches of the bosonic excitations. By choosing $s$ harmonics, we construct an exact qudit-controlled cyclic permutation and use it to formulate a general protocol for preparing odd-$d$-mode NOON states. The same framework also enables programmable complex amplitudes through appropriate preparation of the controller state. As concrete realizations, we show that the three-mode case requires only a single harmonic and exhibits two oppositely directed chiral branches together with a stationary branch, whereas the five-mode case requires two harmonics and both nearest- and next-nearest-neighbor chiral hoppings. Meanwhile, taking the three-mode realization as a representative example, we assess the influence of systematic imperfections and dissipation on the conditional-routing dynamics and identify parameter regimes in which the routing operation remains accurate. Our results establish a systematic Floquet construction for controllable chiral routing and multimode NOON-state generation in arbitrary odd-dimensional networks, with potential applications in quantum information processing and quantum metrology.

Motivated by quantum foundations and complexity theory, Aaronson formalized a hidden-variable theory inspired by a proposal by Schrödinger. To any quantum state and unitary, this Schrödinger theory assigns a joint probability distribution via the Sinkhorn algorithm: rescale the columns and rows of the entrywise modulus of the unitary so that the marginals match the Born rule for the initial and final quantum states, respectively. He conjectured that this map is robust, i.e., inverse polynomially small perturbations in the inputs lead to inverse polynomially small perturbations of the joint distribution, which is important for complexity theoretic applications. We present a counterexample to this conjecture: We construct a pure state and two unitaries that are exponentially close, yet the joint probability distributions assigned by the Schrödinger theory differ by at least an inverse-linear term in at least one entry, and by a constant in total variation distance. We also propose a modified version of Schrödinger's theory that satisfies robustness, while retaining all of its other desirable properties. This yields a complete picture of which axioms of Aaronson can be simultaneously satisfied by hidden-variable theories.

Recent work shows that the Schroedinger equation can be solved exactly based only on classical least action rspa.2025.0413. The computation is based on first solving a Hamilton-Jacobi equation for the action, computing the classical propagated density along all stationary action paths, and finally constructing the exact kernel and wave function based on these classical quantities alone. The method requires that the propagated classical square root density along each stationary action path is harmonic (where a sufficient condition is that the Laplacian of the propagated action is purely time-varying), as is the case for basic examples such as the double-slit, quantum tunneling, the Einstein-Podolsky-Rosen experiment, or also as discussed here the relativistic propagator of a Higgs boson. This density is fundamentally different from using the Madelung density, which is the norm of an existing overall quantum wave. In the case of arbitrary nonlinear potentials, this condition can still be verified without loss of generality, by using a harmonic coordinate transformation and an associated time scaling for the propagated classical density and quantum wave, as this paper details. The resulting quantum wave of the time-scaled Schroedinger equation is equivalent to the quantum wave of the original Schroedinger equation, extending a standard result of Duru and Kleinert. Hence, in principle it can replace the approximations of quantum perturbation theory. For 1 to 3-dimensional systems, this harmonic coordinate change transforms a nonlinear potential into the quadratic potential of a linear oscillator, for which an exact analytic action and wave solution are already known. This makes the construction of the quantum wave beyond the hydrogen wave straightforward for basic cases where no exact solution has been derived, such as the quartic potential or the nonlinear pendulum.

Technological advances in neutral-atom platforms have opened a new path toward designing efficient protocols for fault-tolerant quantum computing (FTQC). However, each physical operation is still orders of magnitude slower than on other platforms, such as superconducting qubits. Therefore, architects must identify fast and efficient FTQC architectures, which require reliable modeling tools to explore various design choices across the software, classical hardware, and quantum device stacks of neutral-atom platforms. In this paper, we propose NAQsim, an open-source simulation framework for neutral-atom FTQC architectures based on transversal gates. As its key feature, NAQsim enables detailed full-stack architecture evaluation that opens opportunities to explore previously overlooked performance bottlenecks. As a first use case for NAQsim, we identify one such bottleneck, patch rotations, perform full-stack co-optimization, and finally derive a near-rotation-free architecture (D3-ROT). For practical FTQC benchmark workloads, D3-ROT achieves a 2.27x speedup from this single bottleneck alone, with minimal footprint overhead. These results point to a much broader space of full-stack optimizations that NAQsim makes accessible for transversal surface-code architectures and beyond.

Quantum confinement restructures the electronic phase space of ultrathin metals, but the resulting density-of-states (DOS) change is not generically large. We show that, within a three-dimensional confinement theory based on the suppression of long-wavelength electronic states, the Fermi-level DOS enhancement on the weak-confinement branch is bounded by $(4/3)^{1/3}-1\simeq10.1\%$. Instead, confinement-induced redistribution of electronic phase space can be strongly amplified by resonant denominators in the second-order susceptibility. A minimal double-resonance closure predicts giant amplification when the film thickness approaches $L_c=(2\pi/n)^{1/3}$, where $n$ is the carrier density, and a dominant optical pathway lies within a dephasing linewidth of resonance. Applied to recent Ag(111) measurements, the theory gives an effective phase-space carrier density parameter $n_{\rm eff}\simeq3.6\times10^{20}\,\mathrm{cm}^{-3}$, a tenfold enhancement of $|\chi^{(2)}|$, and hence the observed $\sim100$-fold increase of thickness-normalized second-harmonic-generation efficiency, together with the observed non-oscillatory thickness dependence.

Randomizing the readout time averages the mode interference in a quantum walk. We ask when this makes the site populations of a uniformly coupled $XY$ chain exactly uniform for every initial site. For $N\ge2$ spins, this is possible when $N+1$ is a power of two, a prime, or twice a prime. It is impossible when $15\mid(N+1)$, $21\mid(N+1)$, or $6\mid(N+1)$ with $N\ge11$. Uniformity uniquely fixes the averaged cosine coherences according to the mirror parities of the modes. Equal Bohr frequencies can impose incompatible coherence values. We classify these parity collisions using vanishing sums of roots of unity and prove existence in the positive cases through a phase distribution on a torus.

Recently, continuous variables (CV) quantum computing, i. e. computing employing squeezed states, has attracted significant attention, as it enables to increase the dimensionality of the system. In CV protocols, homodyne detection plays a key role in the realization of the required gates and operations. Multimode squeezed light generated via parametric down-conversion (PDC) benefits from the broadband bandwidth, which encompasses multiple frequency modes. However, its broadband structure simultaneously requires the precise matching of the local oscillator (LO) with the squeezed light modes for their correct homodyne detection and processing. Achieving such matching is usually a challenging task, since the spectral bandwidth of the local oscillator is typically significantly narrower than the bandwidth of the squeezed-light modes. In this work, we propose and experimentally demonstrate a technique for expanding the bandwidth of the LO by passing it through the microstructured fiber. We validate the proposed concept by measuring squeezing in the modes of multimode squeezed light generated in type-0 and type-II PDC. We show that the broadened LO starts to spectrally match the modes generated via type-II PDC. The presented technique might be beneficial for implementing various CV systems and protocols.

A simple pedagogical discussion and visualization of certain Bell inequalities is presented with the help of a system involving two \textquotedblleft twins\textquotedblright, originally discussed in 2605.03104. These twins answer identically when the same `question' is posed, here exemplified with: Did you like breakfast/lunch/dinner? In analogy, for two entangled particles at distant locations, the `twin-like' quantum state is such that the same outcome for the same measurement (i.e. spin direction) is obtained. In the space $(X,Y,Z)$ of mixed moments (i.e. $X$ refers to breakfast-lunch correlation, being $1$ for same answers and $-1$ for opposite ones), the space of Bell local models is contained in a tetrahedron, while the quantum space is bound by an elliptope that embeds the tetrahedron. The whole no-signalling region in the $(X,Y,Z)$ space is the cube $[-1,1]^{3}.$ The twin scenario applies e.g. to the decay of the Higgs into fermions.

Identical particles have dynamically invariant labels in all setups where their degrees of freedom can be partitioned into two parts, which we call internal and visible, with the visible part subject to unitary evolution, while the dynamically invariant internal part accounts for the partial distinguishability of particles. We give the explicit form of the visible state in terms of the indistinguishability function, generalizing the standard symmetrization/antisymmetrization postulate for bosons/fermions with internal modes. The indistinguishability function on the symmetric group accounts for the permutation symmetry of the dynamically invariant label state and gives a self-contained description of the symmetry spectrum of the visible state. It is shown that the indistinguishability of single particles emitted independently from a stable source is completely characterized by the projective measures on the symmetry spectrum. We reveal a hierarchy of successive upper bounds on the projective measure of indistinguishability in terms of marginal projective measures. We point out an experimentally feasible way to get the upper bounds on the indistinguishability of an arbitrarily large number of single photons by direct experimental readout of their marginal projective measures. We also analyze the indistinguishability of coherent superpositions and convex mixtures and resolve a recently posed problem.