Papers

Magneto-optical traps (MOTs) are a workhorse technology for neutral-atom quantum sensing, simulation, and computing. Here, we demonstrate a MOT optimized for inertial quantum sensing and precision metrology applications. Our MOT traps $4\times10^8$ cesium (Cs) atoms in a robust, modular system that achieves stable operation through two design features: (1) we use divergent cooling laser beams to reduce unwanted reflections and (2) optical elements are mounted in a fiber-coupled, compact, and modular cage rigidly attached to the vacuum chamber. Following polarization-gradient cooling (PGC), the system produces atom samples with temperatures below 10 ${\mu}$K, similar to those achieved in conventional MOTs that use collimated laser beams. In addition, we observe trapping of $2\times10^7$ Cs atoms in a non-conventional MOT geometry, where the cooling laser beams are diagonal to the principal axis of the quadrupole magnetic field.

The physical content of a theory is not intrinsically tied to any single mathematical formalism. Both classical and quantum mechanics admit equivalent representations, notably in phase space and in Hilbert space, related by the Wigner-Weyl correspondence. While this correspondence has long been studied in mathematical physics, its foundational and operational implications are often left implicit. Here we give a systematic account of what changes, and what does not, when classical and quantum theories are expressed in each other's native language. This representational viewpoint separates artifacts (such as the appearance of non-positivity or negativity under certain maps) from robust structural distinctions that persist across representations, in particular noncommutativity and its $\hbar$-dependent $\star$-deformation of the classical algebra. We develop the comparison at the level of states, kinematics, and dynamics, and extend it to measurement by formulating both outcome statistics and state-update rules within the same framework.

Magic, also known as non-stabilizerness, measures the usefulness of a quantum state for quantum computation. While magic is defined relative to a choice of computational basis, in some physical settings the available data determine this basis only up to local phase conventions. In this paper, we generalize the notion of magic and formulate it in a phase-independent manner, and hence define a generalized stabilizer Rényi entropy. As a case study, we consider higher-multiplicity tree-level gluon scattering, interpreting the outgoing helicities as qubits. In this setting, the helicity data naturally determine a local basis for each qubit but leave a phase ambiguity. For $3\to 2$ scattering, we find that the final-state phase-independent magic is generically larger than the maximum attainable in $2\to 2$ scattering. For $2 \to 3$ scattering, we find a nonzero minimal value approached in the soft limit. Moreover, when the three outgoing momenta become symmetric, the magic approaches a local minimum only a few percent above the soft-limit value. In all cases considered, the color dependence cancels from the phase-independent stabilizer Rényi entropy.

We study entanglement harvesting with particle detectors coupled to the renormalized energy density of a massless scalar field. Our analysis identifies the distributional mechanism underlying the persistent ultraviolet divergences previously observed for quadratic detector couplings and discusses that the energy density coupling exhibits the same underlying structure. We show that these divergences are entirely controlled by the switching correlation at coincident interaction times. Consequently, pointlike detectors are UV finite whenever the switchings do not overlap. For Gaussian-smeared detectors, the harvesting correlations are automatically finite in 1+1 and 2+1 dimensions, while in higher dimensions the remaining divergences are removed by non-overlapping switchings. Finally, we derive general expressions for arbitrary zero-mean Gaussian states and illustrate the formalism with a thermal field state.

The realization of large-scale silicon quantum processors requires spin qubits compatible with advanced semiconductor manufacturing technologies, demanding lithographic processes that combine nanometer-scale precision with exceptional uniformity. Although the highest-performing silicon spin qubits demonstrated to date have relied on electron-beam (e-beam) lithography, its serial exposure process limits reproducibility studies and wafer-scale fabrication. Here, we demonstrate high-performance silicon metal-oxide-semiconductor (SiMOS) spin qubits fabricated using extreme-ultraviolet (EUV) lithography in a 300 mm semiconductor pilot line. We report wafer-scale quantum-dot uniformity metrics, including 100 % room-temperature gate-to-gate leakage yield and sub-nanometer control of critical gate dimensions. We characterize four double-dot systems realized in two triple-quantum-dot devices. Gate set tomography (GST) reveals consistently high fidelities across all four systems, with values up to 99.8 % for SPAM, 99.9 % for single-qubit gates, and 99.1 % for two-qubit gates. The devices exhibit highly reproducible exchange turn-on characteristics of 10-13 dec/V, indicating high fabrication uniformity enabled by EUV patterning. These results establish EUV lithography as a viable manufacturing technology for quantum processors based on high-fidelity SiMOS spin qubits.

Dissipative cat qubits exponentially suppress one Pauli error channel with the mean photon number, leaving the conjugate bit-flip error as the dominant failure mode. This strong noise bias makes the full machinery of general quantum error correction unnecessary: a code need only protect against a single error type, and any classical linear code can be promoted to a Clifford stabilizer code that does exactly this. We use this observation to build a bit-flip-only quantum Reed-Solomon (RS) code. Starting from the maximum-distance-separable RS code [7, 3, 5] over GF($2^3$), we binary-expand it to the linear code [21, 9, 6] over GF(2) and realize it as a [[21, 9, $d_X = 6, d_Z = 1$]] bit-flip code whose stabilizers are products of $Z$ operators. Because no phase-flip correction is attempted, the construction discards the redundancy that standard quantum RS codes spend on correcting $Z$ errors – which a strongly biased cat qubit renders unnecessary – and yields a shallow Clifford circuit that samples directly in Stim. Errors are decoded by an optimal bounded-distance syndrome-lookup table. We then introduce a Tornado architecture: a two-layer concatenation that wraps every position of the outer RS code in an inner distance-three repetition code, yielding a [[63, 9, 18]] code decoded by a two-stage inner majority vote and outer lookup decoder. Monte-Carlo simulation shows that at a physical bit-flip rate $p = 0.1$ the Tornado code reaches a logical error rate $p_L \approx 5.3 \times 10^{-3}$, below both parent codes, and that its logical error rate scales as $p_L \propto p^6$ at low $p$, in contrast to $p^2$ for the repetition code and $p^3$ for the standalone RS code. We give the exact construction, the error and circuit model, an asymptotic scaling analysis, and an honest account of the overhead cost and single-shot assumptions.

General relativity (GR) is naturally organized around spacetime events and their causal order, whereas quantum field theory (QFT) is formulated in terms of states, operators, and unitary evolution, without an intrinsic criterion for when a quantum process becomes a definite spacetime fact. We propose an event-centered framework in which events are locally irreversible records generated by quantum-environment interactions and serve as an interface between quantum dynamics and relativistic spacetime structure. Event anchoring is characterized operationally by three jointly sufficient conditions: local classicalization, redundant environmental recording, and irreversibility against recovery. Their joint satisfaction defines local generative freezing. We realize these criteria in an explicit repeated-collision open-system model. The model is illustrative rather than a derivation from relativistic QFT, but it remains globally unitary and yields the freezing time in closed form. For all admissible tolerances, local classicalization is certified no later than channel-level irrecoverability, and generically earlier. Full anchoring occurs only when both irrecoverability and the required record redundancy have been reached, producing irrecoverability-limited and redundancy-limited regimes. At the level of anchored records, physical history is therefore represented as a partially ordered causal skeleton of frozen events on which effective field-theoretic descriptions operate. The framework addresses event anchoring–when a candidate outcome becomes a stable spacetime fact–while remaining compatible with standard QFT and relativistic causality. It does not derive the Born rule or solve single-outcome selection, which belong to the separate problem of event generation.

In quantum information systems made of optical tweezer arrays of ultracold molecules, thermal motion of molecules degrades the coherence of their interactions, which limits entanglement fidelity and the concomitant scientific applicability of these systems. We show that by controlling the geometry of the dipolar interaction, even when a molecule occupies many motional states in the tweezer, coherence can be preserved. We characterize several geometries that suppress sensitivity to thermal fluctuations. We further use programmable, coherence-preserving motion of the molecules during entanglement to refocus dephasing from relative positional jitter of the tweezers, which is relevant even on the 10 nm scale. These methods yield substantially improved dipolar coherence and enable generation of two-molecule entanglement with a Bell state fidelity of $\mathcal{F}= 0.976^{+0.008}_{-0.011}$ in directly laser-cooled molecules.

I derive the charged-particle spectral edge from the quantum instrument of soft QED. I use two projections of that instrument. Tracing over unresolved photons gives the reduced hard-sector channel. Pushing the outcomes to total energy gives the inclusive energy distribution. Its Laplace exponent is fixed by the diagonal soft intensity. For ${\rm d} N_h(\omega)=\eta_h{\rm d}\omega/\omega+{\rm d} N_{h,\mathrm{reg}}(\omega)$, I obtain $\rho_{\mathrm{inc}}(s)\sim C\theta(s-m^2)(s-m^2)^{-1+\eta_h}$. I retain the coherence kernel and derive hard-sector dephasing and the spectral edge from two contractions of one soft environment. The diagonal coefficient $\kappa_{aa}$ fixes the endpoint exponent, while $\frac12(\kappa_{aa}+\kappa_{bb}-2\operatorname{Re}\kappa_{ba})$ fixes the dephasing exponent between hard alternatives. I then classify infrared energy marginals, derive the finite-resolution residue $Z(\mu)=(\mu/\Lambda)^{\eta_h}$, prove stability under infrared-integrable perturbations, and separate the bath exponent from a hard threshold exponent. For the one-electron spectral measure, the hard threshold factor is regular. The resulting edge has the local power law of a gapped unparticle spectrum, while its exponent remains a response coefficient of the unresolved photon sector.

Efficient communication between distant qubits is one of the central challenges in scaling quantum processors. Although engineered spin chain protocols have been extensively investigated theoretically, their experimental realization has remained comparatively limited. Here, we experimentally realize engineered quantum communication protocols through digitally simulated spin Hamiltonian on IonQ's Forte 1/ Forte Enterprise 1 trapped-ion quantum processor. Combining exact numerical simulations with quantum hardware experiments, we benchmark uniform nearest-neighbour and engineered coupling profiles and demonstrate that engineered interactions significantly enhance the fidelity of quantum state transfer. We further show that exploiting the commutation structure of the spin Hamiltonian enables a parallel Trotter decomposition that more faithfully reproduces the target dynamics while substantially reducing the circuit depth and execution time compared to the conventional sequential implementations. Our results demonstrate that programmable quantum processors can effectively realize and efficiently implement quantum communication protocols, bringing Hamiltonian-based quantum communication closer to practical quantum technologies.

Parameterized quantum circuits~(PQCs) constitute a central building block of variational quantum algorithms~(VQAs) and quantum machine learning~(QML) methods. Existing ansatz designs often adopt hardware-agnostic or simplified 1D chain/ring entanglement patterns. However, as quantum hardware continues to develop, native 2D connectivity patterns, such as planar superconducting-qubit architectures, are becoming increasingly important. Inspired by this hardware structure, we construct a native 2D pairwise ansatz and compare its expressibility and trainability with representative 1D ansatze at identical layer depths, despite their different circuit depths. For the fixed 16-qubit system, the 2D ansatz has the smallest KL divergence at $L=1$ and $2$, and its second-order frame potential approaches the theoretical lower bound more rapidly at shallow layer counts than the frame potentials of the three 1D ansatze. We also evaluate the gradient variance of the Pauli-$Z$-string expectation value $\langle Z_0\otimes\cdots\otimes Z_{15}\rangle$ with respect to the first $R_y$ angle. For this Pauli-$Z$ string and fixed parameter, the gradient variance is smaller for the 2D circuit at $L=1$–$4$. The differences narrow at $L=5$, and the four ansatze yield statistically compatible variances at $L=6$.

A Lorentz boost acts on the canonical spin of a massive particle through a momentum-dependent Wigner rotation. We show that, for one fixed observer boost, reducing over an uncertain momentum can strictly contract every pairwise spin-state trace distance without producing a channel that is degradable from the less contracted one. For spin $1/2$, we first characterize the exact inversion-symmetric channel cone generated by a fixed Wigner angle and transverse momentum directions. Inside this cone lies the Pauli family $M_\alpha=\operatorname{diag}(1-\alpha,1-\alpha,1-2\alpha)$, $0\leq\alpha<1/2$. For $0<\alpha<\beta<1/2$, all trace distances between distinct spin states are strictly smaller after $M_\beta$ than after $M_\alpha$, yet the unique linear post-processing factor has a negative normalized Choi eigenvalue. We solve the optimization over all physical converters exactly: $\frac{1}{2}\inf_{\Lambda\in\mathrm{CPTP}}\|\Phi_\beta-\Lambda\circ\Phi_\alpha\|_\diamond=\frac{\alpha(\beta-\alpha)}{2-3\alpha}$, whereas the reverse deficiency is $\beta-\alpha$. Thus the identity dominates the family, while all positive-noise members are pairwise incomparable under CPTP post-processing. The ideal construction is realized as the narrow-packet limit of pure, normalizable five-component momentum states, and explicit perturbation and finite-shot tomography bounds certify an open set of examples. Separately, every nonidentity member fails embedding in a time-homogeneous Pauli-diagonal Lindblad semigroup. Hence ordering all unassisted spin distinguishabilities does not determine the quantum statistical post-processing order.

Credit Valuation Adjustment (CVA) requires repeated risk-neutral expectation estimation, making it a natural test bed for quantum amplitude estimation, whose coherent amplification can in principle reduce Monte Carlo sampling cost. Whether this advantage survives realistic financial encoding and noisy hardware remains open. We develop an end-to-end, noise-aware quantum workflow for CVA, covering market calibration, discretisation, oracle construction, hardware execution and error-budget analysis. The model combines a correlated two-asset exposure with discount and default factors, encoded through a QCBM-based joint time-market distribution and controlled payoff rotations. We introduce contrast-aware Bayesian iterative quantum amplitude estimation (CABIQAE), which incorporates experimentally calibrated Grover-contrast loss into Bayesian inference and circuit-depth selection. Hardware-calibrated experiments show that CABIQAE exploits the limited amplification available on current devices more effectively than noise-agnostic alternatives and achieves a much lower classical post-processing runtime than the noise-aware BAE baseline. The analysis further decomposes the total CVA error into statistical, encoding, discretisation and hardware contributions. The full CVA oracle remains limited by circuit depth and discretisation resolution.

Neutral-atom quantum processors are rapidly scaling toward system sizes of more than ten thousand qubits, allowing for the realization of a new class of quantum computing algorithms and quantum simulation experiments. However, current neutral-atom platforms generally have to find a compromise between the optical accessibility and the storage time of atoms in optical potentials, limiting the available qubit numbers. Here we report on the operation of a novel, cryogenically enhanced, neutral-atom apparatus that overcomes these apparently conflicting requirements. We demonstrate vacuum-limited trapping lifetimes of up to two hours of single $^{88}\mathrm{Sr}$ atoms in an optical tweezer array while preserving full optical access and without the need for complex cryogenic enclosures. Our measurements show that exceptionally long single-atom lifetimes can be achieved with a relatively simple cryostat design. Our architecture can be straightforwardly ported to other atomic species and shows a viable path for scaling up to sorted arrays of tens of thousands of atoms.

Unlike in finite dimensions, quantum information in continuous-variable systems has the peculiar feature that without imposing physical constraints, the sample complexity of state tomography can be unbounded. Remarkably, this is even the case for state-of-the-art protocols for learning Gaussian states, which have finite-dimensional descriptions: the best known rates scale with $\log \log E$, where $E$ is the energy of the system. We prove this is not an artifact of existing analyses, but a fundamental limitation of the measurements used. We show: (1) Any protocol that uses Gaussian measurements, even entangled or adaptively chosen ones, must incur a $\log \log E$ dependence. This answers an open question posed by a number of previous works. (2) There is a smooth tradeoff between the number of rounds of adaptivity and the energy dependence, and we give a matching protocol achieving this interpolated rate. (3) With highly entangled, non-Gaussian measurements, one can learn $n$-mode pure Gaussian states with $O(n^2 / \epsilon^2)$ samples, independent of $E$. This answers an open question posed by Chen et al. (4) A simple protocol based on the single-copy canonical phase POVM of Holevo and Helstrom learns single-mode pure Gaussian states with $O(1/\epsilon^2)$ samples, again independent of $E$. Our results clarify the role of energy in bosonic state tomography and shed new light on the intriguing interplay between adaptivity, entanglement, and magic in quantum learning.

A central model in quantum machine learning is the quantum neural network (QNN), whose design requires balancing expressivity and trainability. Technically, expressivity is studied through circuit-function analysis, such as quantum signal processing, while trainability is analyzed using dynamical-Lie-algebra (DLA) methods. To support certified QNN design, we formalize these major components of QNN theory in a connected lean 4 development checked by a proof kernel, where every analytic input is either proved or exposed as a named hypothesis. On the expressivity side, we prove exact if-and-only-if characterizations of single-qubit QNNs, a resource-counted quantum phase processing theorem, and an overparameterization ceiling that bounds the quantum Fisher information rank by the DLA dimension. On the trainability side, we derive the direct-sum loss-variance law through a de-circularized second-moment interface. A parameterized Casimir-uniqueness engine discharges the required inputs for fully controllable, orthogonal, and matchgate circuit families, while single-qubit and product-Clifford ensembles close the two-design assumptions directly. A capstone theorem pairs the conditional variance law with exact loss reconstruction in DLA coordinates. The development record identifies eight corrections and clarifications that were not explicit in the informal arguments. We expect this work to provide a machine-checkable foundation for QNN theory and a step toward AI-assisted or automated design of quantum machine learning algorithms.

A finite quantum reference token with group-valued misalignment induces a random-unitary channel, but optimal degradation is generally an optimization over all quantum post-processings. For a unitary representation U of a finite group G, we prove that the following conditions are equivalent: U contains every irreducible type; one ancilla-assisted input has an orthonormal G-orbit; signed group measures embed isometrically into channels in diamond norm; and, for every pair of noise laws p,q, $\inf_{\Lambda\in\mathrm{CPTP}} \frac{1}{2}\|\Phi_q^U-\Lambda\circ\Phi_p^U\|_\diamond =\min_{r\in\mathcal{P}(G)}\frac{1}{2}\|q-r*p\|_1$. Thus representation completeness is the exact carrier condition for universal reduction of quantum post-processing to classical convolution. We determine the minimum ancilla dimensions for an orthogonal orbit and for an invariant calibration seed. For an incomplete carrier, with visible Plancherel dimension S(U), we derive the exact conditional-expectation distance $\frac{1}{2}\|\operatorname{id}-\Phi_u^U\|_\diamond=1-1/S(U)$ and an explicit quantum–classical deficiency gap. For irreducible carriers the deficiency is obtained in closed form; the faithful two-dimensional representation of $S_3$ yields an exact ten-percent reduction relative to classical convolution. We also characterize law identifiability through the conjugation representation, provide finite linear programs and decision witnesses, and establish both a finite-dimensional obstruction and stable visible-band reconstruction for infinite compact groups. Deterministic ancillary code reproduces the finite-group examples and numerical regression checks.

We demonstrate a nonreciprocal quantum Mpemba effect. Consider a broad class of open quantum systems, each coupled to two isomorphic reservoirs through symmetric ports. Interchanging the parameters of the two reservoirs – a discrete operation we call the swap – turns the quantum Mpemba effect on or off without changing the initial states. The swap modifies the Liouvillian, yet a structural symmetry pins the eigenvalues while rotating only the eigenvectors. The nonreciprocity therefore leaves no trace in the spectrum and is carried entirely by the eigenvectors. Concretely, the swap alters the far state's projection onto the slowest mode, switching whether it bypasses the slowest relaxation channel. At a Liouvillian exceptional point, the far state's relaxation switches from bypassing the slowest mode to avoiding the critical slowing, with the on–off contrast intact. There the spectrum-independent mechanism takes its purest form.

Nematic symmetry entails conserved quantized quantities such as number of topological defects and vorticity cells. Correspondingly, countless quantum analogies have been found in Active Nematics. We formalize Active Nematics and Liquid Crystal theory into the framework of Quantum Mechanics by introducing a complex valued Nematic Wavefunction to the Beris Edward equations, thus splitting spatiotemporally varying nematic systems into quantized states. We obtain the Planck's energy-frequency relationship for active micro-swimmers such as peristaltic worms and bacterium as a consequence of local complex phase-symmetry of the governing equations, similar to the gauge formulation of Electromagnetism. For organisms operating on diffusive chemotaxis, we obtain predator-prey dynamics that evolve to maximize/minimize pheromones field gradient overlap. Furthermore, when quantizing beating hearts, similar to the orbitals of hydrogen atoms, the state-function allows us to characterize hearts not only through the rhythm, but also the spaciotemporal distribution of contractile activity of various harmonics among healthy and unhealthy hearts.

Logical entangling gates are a major source of physical spacetime overhead in fault-tolerant quantum computation. Phantom codes reduce this cost by implementing every ordered in-block logical CNOT through physical qubit permutations and Pauli-frame updates. Whether this mechanism can coexist with the low-weight stabilizer structure of qLDPC codes is a central question for low-overhead fault-tolerant architectures. We give a deterministic answer within binary CSS hypergraph product (HGP) codes. Up to natural equivalences, the simplex-repetition family is the unique HGP family satisfying the phantom condition. We then evaluate this family under circuit-level noise in logical GHZ-state preparation and Trotterized many-body quantum simulation. The codes retain low-weight stabilizer checks and yield concrete advantages over rotated surface-code baselines in both benchmarks. Reconfigurable neutral-atom arrays offer a natural setting for this approach, supporting nonlocal qLDPC operations while enabling in-block logical CNOTs without additional physical operations. Together, these results make precise how permutation-based logical entangling constrains code design within the HGP framework, demonstrate the circuit-level benefits of the unique family, and guide the search for phantom qLDPC families with better asymptotic parameters for low-overhead fault tolerance on neutral-atom hardware.

Comparing two noisy quantum reference frames as statistical experiments depends on the dimension of the ancillary memory available to the decision procedure. For finite-dimensional channels A and B with invertible A, we show that exact simulation of all measurements assisted by an r-dimensional ancilla is equivalent to r-positivity of the unique factor Gamma = BA^{-1}. The hierarchy can be realized by physical channel pairs: every unital, trace-preserving map that is k-positive but not (k+1)-positive embeds as the factor between the channels D_a and Gamma composed with D_a on an exact interval determined by the smallest Choi eigenvalue. For depolarizing source and target channels D_a and D_b, including negative and singular source parameters, the phase boundary is $\mathcal{D}_a \succeq_r \mathcal{D}_b \Longleftrightarrow -1/(dr-1) \leq b/a \leq 1$ for $a\neq 0$. We derive closed formulas for the restricted level-r deficiency and for the distance to every physical post-processing, $\delta_{\mathrm{phys}}(\mathcal{D}_b\mid\mathcal{D}_a)=(1-1/d^2)\operatorname{dist}(b,I_a)$, where $I_a=\operatorname{conv}\{a,-a/(d^2-1)\}$. The largest physical conversion cost hidden from all tests through level k is $(d-k)/[d(d^2-1)]$. An untouched m-level spectator changes the first detecting external level from k+1 to $\lfloor k/m\rfloor+1$. A transpose–depolarizing construction shows that the separation is not confined to depolarizing factors. The results quantify the distinction between ancilla-restricted statistical simulation and implementation by a single quantum channel.

How large can a set of mutually orthogonal quantum Latin squares (MOQLS) get? We show that a set of n - 2 MOQLS of order n is necessarily classical and construct large non-classical sets of MOQLS of orders that are prime powers, improving both the previously known lower and upper bounds.

Recently, it has been shown that protocols utilizing infinitely fast controls, such as quantum error correction, can in principle restore Heisenberg-limited frequency estimation in the presence of a broad class of non-Markovian noise models arising from coupling to finite-dimensional environments. However, these controls differ substantially from those used to address Markovian noise, and their underlying physical mechanism remains unclear. In this work, we establish a direct connection between these protocols and the quantum Zeno effect, and extend the framework to infinite-dimensional environments. We delineate three types of constructions: (a) protocols that rely solely on measurements, (b) protocols using an active recovery after measurements and (c) protocols using dynamical decoupling and rigorously analyze the performance of each when controls can be applied at only a finite rate. While protocols relying purely on measurements can be engineered for noise models where active recoveries are fundamentally impossible, they result in the quantum Fisher information exhibiting a quadratically worse dependence on the control frequency. Surprisingly, while dynamical decoupling protocols are possible whenever protocols relying only on measurements can be engineered, the quantum Fisher information has the same dependence on control frequency as the active recovery protocols. Numerical simulations suggest that the improvement offered by dynamical decoupling may work in regimes beyond the perturbative setting where our rigorous theorems apply.

Let $\left(M, \mathcal{O}_M \right)$ be a smooth algebraic variety over field $\kappa$ of characteristic $0$ with an algebraic symplectic form $\omega$, or a complex manifold with a holomorphic form $\omega$. Furthermore, let $E$ be a vector bundle over $\left(M, \mathcal{O}_M \right)$ and $\mathcal{O}_{\hbar}$ a deformation quantization of $\mathcal{O}_M$ compatible with $\omega$. Assuming that $E$ possesses a deformation quantization to order $\hbar^k$ we consider the problem of extending it to order $\hbar^\ell$ for $\ell > k$, and establish triviality of an obstruction class as a necessary condition for this extension to exist. Furthermore, in the case $\ell \le 2k+1$, we prove that this condition is also sufficient.

We present an approach to unitary synthesis that implements an arbitrary $n$-qubit unitary operator $U$ by a Clifford+T circuit with T-count $\widetilde{O}(2^n d_F^{\mathcal{C}}(U))$, where $d_F^{\mathcal{C}}(U)$ is the Frobenius norm distance of $U$ to the Clifford group. The T-count is shown to be near-optimal when $d_F^{\mathcal{C}}(U)$ is a constant. Our approach improves the previous best upper bound $\widetilde{O}(2^{4n/3})$ due to Tan (2025) for a large class of unitary operators $U$ as long as $d_F^{\mathcal{C}}(U) \ll 2^{n/3}$.

We show that for Schrödinger operators in a connected domain, the Hohenberg-Kohn theorem holds within the class of Laplace form-bounded external potentials if and only if the single-particle density is strictly positive quasi-everywhere. Furthermore, we show that this condition is satisfied for non-interacting Schrödinger operators whenever a ground-state exists. Consequently, we establish the Hohenberg-Kohn theorem for non-interacting systems, and thereby the uniqueness of the Kohn-Sham potential, within the maximal class of Laplace form-bounded distributions. The main ingredient to establish these results is a characterization of regular states, whose proof relies on tools from classical potential theory. Moreover, this characterization reveals that, in the continuum setting, the fundamental mechanism underlying the Hohenberg-Kohn theorem is the (quasi)-unique continuation of the density rather than of the many-body wavefunction.

We show that geodesic motion in the Riemannian manifold of quantum states provides a direct route to time-independent counterdiabatic driving. Using the relation between the counterdiabatic Hamiltonian and the quantum metric tensor, we prove that a constant-speed geodesic makes the Hilbert-Schmidt norm of the counterdiabatic Hamiltonian constant. For effective two-level systems whose counterdiabatic correction has a fixed operator direction, this further implies that the full counterdiabatic Hamiltonian itself is time independent. We illustrate this result with the Landau-Zener model, three-level Stimulated Raman adiabatic passage and a collectively driven Rydberg ensemble in the blockade regime. Limitations of this approach in realistic many-body systems are discussed, where the two-level reduction is only emergent and leakage out of the effective subspace bounds the achievable speedup. In all cases, time-independent counterdiabatic driving achieves unit-fidelity state preparation on timescales substantially shorter than conventional adiabatic protocols while replacing temporally shaped auxiliary controls by fixed-amplitude fields.

We investigate dynamical quantum phase transitions (DQPTs) in finite-dimensional systems prepared in thermal equilibrium states and subjected to a sudden quench. A mixed-state Loschmidt amplitude is constructed from first principles within a metric-stationary pseudo-Hermitian framework, providing a self-contained derivation of the finite-temperature quench dynamics. Applying this framework to an $N$-level model consisting of a two-level sector coupled to $N-2$ spectator states, we find that temperature controls the DQPTs through the redistribution of thermal weights among the eigenstates. This mechanism leads to a dimensionality-dependent threshold temperature that becomes finite when the Hilbert-space dimension reaches five, above which the Loschmidt amplitude loses all real zeros and the DQPTs are fully suppressed. The thermal suppression mechanism suggests a general principle for controlling dynamical criticality through thermal occupation, while the quasi-Hermitian framework provides the self-consistent foundation for its rigorous derivation.

Quantum key distribution (QKD) promises information-theoretically secure communication, but future networks must bridge fiber and free-space links that naturally employ different photonic encodings, namely time-bin in fiber and polarization in free space. Here we demonstrate a complete hybrid fiber and free-space QKD link that bridges both media within a single end-to-end protocol, converting between the two encodings entirely in the optical domain. Using the decoy-state BB84 protocol operating at 1550 nm, we demonstrate continuous secure-key generation over a 90 m outdoor free-space link. The system operates across atmospheric conditions spanning more than two orders of magnitude in the refractive-index structure parameter Cn^2, from strong daytime turbulence to quiescent nighttime conditions, and we further validate photon-level operation over a 750 m free-space extension. Throughout, the link maintains a session-mean quantum bit error rate (QBER) of 5.6-6.8%, well below the 11% BB84 security threshold. The encoding conversion is performed entirely in the optical domain without measurement or state reconstruction, preserving the security assumptions of the BB84 protocol. Consequently, the time-bin-to-polarization (T2P) and polarization-to-time-bin (P2T) converters remain part of the untrusted quantum channel rather than trusted intermediate nodes. These results establish secure photonic encoding conversion as a practical interface between fiber and free-space quantum communication platforms, providing a building block for future quantum networks applications.

This article explores the potential of Quantum Machine Learning (QML), specifically assessing a Quantum Support Vector Machine (QSVM) and a Variational Quantum Classifier (VQC) for detecting anomalies in real-world financial transaction data. While these QML methods outperform statistical methods, they fall short of cutting-edge deep learning techniques. To bridge this gap, we propose a hybrid quantum-classical ensemble framework that leverages the strengths of both domains. We demonstrate its effectiveness in detecting phishing in Ethereum transaction networks by combining complementary algorithms. The QSVM, whether used individually or in an ensemble, consistently delivered the lowest false negatives and higher recall rates, that are crucial for anomaly detection. To enhance individual models, we encoded the data using novel cascaded Quantum Random Access Coding (QRAC) schemes and compared it with the popular encoding ZZ feature map on both simulators and the IBM Heron quantum processor. For both QSVM and VQC, we consistently observed improvements (13% for QRAC-VQC and 3% for QRAC-QSVM) of QRAC over the ZZ feature map. Notably, certain QML algorithms exhibit remarkable resilience on the IBM Heron quantum processor, approaching simulator-level performance on devices with high quantum volume. This observation underscores the promise of QML despite hardware limitations.