Papers

We analyze device-dependent correlation sets generated by fixed local dichotomic measurements for two-qubit systems in the $(2,m,2)$ Bell scenario. We consider three fundamental state spaces for the composite system: the separable state space, the standard quantum state space, and the maximal tensor-product state space, which contains beyond-quantum states compatible with local quantum measurements. We formulate the corresponding correlation sets for general fixed dichotomic measurements and, in the traceless case, derive particularly simple explicit formulae for their support and gauge functions. These functions furnish dual operational characterizations of the three correlation sets: the support functions give optimal witnesses for entanglement and beyond-quantum states, whereas the gauge functions quantify the robustness of these detections against depolarizing noise. We further derive convex-hull representations that elucidate the extremal structures of the correlation sets and the physical states realizing them, showing in particular that extremal quantum correlations are realized by maximally entangled states. The fundamental limits of these dual operational tasks are governed solely by the smaller of the numbers of linearly independent measurement directions available to Alice and Bob. When both parties have three linearly independent measurement directions, our entanglement criterion detects Werner states up to the optimal PPT threshold $p_{\mathrm{crit}}=2/3$. For beyond-quantum-state detection, a nontrivial separation from the quantum set occurs only under the same measurement condition; in that case, the same optimal noise threshold is attained for an extremal state in the maximal tensor-product state space.

Noise in contemporary quantum hardware is highly non-uniform across qubits and couplers, giving rise to localized low-noise "islands" within otherwise noisy device topologies. As quantum workloads scale, executions are increasingly forced to traverse high-noise regions, degrading algorithmic fidelity. Circuit cutting provides a route to circumvent such regions by decomposing large circuits into smaller subcircuits, but its practicality is limited by exponential sampling overhead and the lack of systematic guidance on how cut strategies should align with heterogeneous hardware noise. In this work, we present a hardware-noise-aware circuit cutting framework that explicitly exploits the spatial non-uniformity of noise in quantum devices. Rather than proposing a new cut-finding algorithm, we formalize the problem of device-constraint selection under realistic hardware noise and show that this choice critically determines both execution overhead and effective noise. Using a unified gate- and wire-cutting formulation, we demonstrate that small, hardware-informed relaxations in the device constraint yield exponential reductions in execution overhead while preserving alignment with low-noise hardware regions. Across representative workloads, our method achieves an average reduction in the number of circuit executions ranging from 5-54x for 20-qubit circuits, and enables tractable circuit cutting for 50-qubit circuits and application-level benchmarks where conventional strategies incur prohibitive overhead. These results establish noise-aware device-constraint selection as a necessary ingredient for making circuit cutting resource-efficient and practically deployable on contemporary quantum hardware.

Quantum batteries (QBs) have emerged as a promising route for fast energy storage and on-chip power supply in quantum devices. Given the limited analytical understanding of open Floquet QBs, we employ the kicked-Ising model as a tractable platform to systematically study its performance under realistic conditions, including finite temperature effects and environmental dissipation. Starting from Gibbs states of the transverse-field Ising model, we incorporate thermal and decoherence effects along the evolution, using both analytical and numerical approaches. Taking ergotropy as a central figure of merit, we characterize the injected and extractable energy, and identify regimes where charging remains robust despite environmental effects. Our results provide a systematic framework for assessing QB performance under thermal and dissipative effects.

In the noisy intermediate-scale quantum (NISQ) regime, quantum devices contain hardware-specific noise sources which restrict device-invariant error mitigation strategies. We explore transfer learning approaches to apply noise models learned on one quantum device to a different device with the help of a small amount of data. We create a real-hardware dataset from two IBM quantum devices, ibm_fez (source) and ibm_marrakesh (target), comprising 170 noisy and ideal circuit output distributions, with device calibration features added. We train a residual neural network on the source device to map noisy to ideal outcomes. The zero-shot transfer test shows a KL divergence of 1.6706 (up from 0.3014), establishing device specificity. With K = 20 fine-tuning samples, KL drops to 1.1924 (28.6% improvement over zero-shot), recovering 34.9% of the gap between zero-shot and in-domain KL. Ablation studies reveal that the major cause of mismatches across devices is CX gate error, followed by readout error. The results show quantum noise can be learned and fine-tuned with minimal samples, and provide a plausible approach to cross-device quantum error mitigation.

Phase retrievability of a quantum channel asks whether pure states can be reconstructed from suitable measurements. In this paper, we study this problem from three complementary viewpoints: quantum information theory, operator-valued frames, and the physical realization through quantum interferometry. We first show that a quantum channel is phase retrievable if and only if its complementary channel is pure-state informationally complete. This structural characterization leads to several consequences for phase retrievability, including criteria involving the dimension of the complementary operator system, Choi-rank type bounds, and specific results for entanglement breaking channels and twirling channels. We then introduce an interferometric coupling in which two arm channels are coherently recombined through port operators \(M_i(\theta)=A_i+e^{i\theta}B_i\). Unlike classical mixing, this construction produces interference cross terms that can enlarge the complementary operator system and thereby enhance phase retrievability. From the frame theory viewpoint, the interferometer realizes a coherent coupling of operator-valued frames. To quantify this effect, we introduce injectivity indices for completely positive maps. The examples in Section~5 show that coherent interference can significantly improve phase retrieval behavior even when the arm channels are individually not phase retrievable.

Quantum interior point methods (QIPMs) promise polynomial speed-ups over classical solvers for linear programming by outsourcing the solution of Newton linear systems to quantum linear solvers (QLSAs). However, asymptotic speed-ups do not necessarily translate to practical advantages on realistic problem instances. In this work, I evaluate whether practical advantage of a standard hybrid QIPM pipeline can already be excluded relative to the classical open-source solver HiGHS on a broad and diverse collection of LP instances spanning eight problem families, including public benchmark libraries, such as MIPlib, and relaxations of combinatorial optimisation problems. Following the hybrid benchmarking paradigm initiated by Cade et al., I derive rigorous lower bounds on the quantum runtime under a series of highly benevolent assumptions and compare them against classical runtimes. I equip the QIPMs with the best-performing functional QLSA, the Chebyshev-based method, as identified by Lefterovici et al., and evaluate two Newton system formulations proposed by Mohammadisiahroudi et al.: the modified normal equation system and the orthogonal subspace system. The exclusion analysis yields a consistent negative picture: across all instances and for any realistic quantum cycle duration, the quantum runtime lower bounds already exceed the classical runtimes, establishing that these hybrid QIPMs will offer no practical advantage over good classical solvers for realistic linear programming instances.

In this work, we construct new non-Euclidean neural quantum states (NQS) based on hyperbolic Lorentz recurrent architectures (RNN/GRU). These constructions, together with the Poincare RNN NQS also newly constructed here, extend the class of previously introduced non-Eucllidean NQS which consists only of Poincare hyperbolic GRU. Using the Heisenberg J1J2 and J1J2J3 models consisting of 100 spins in the Variational Monte Carlo (VMC) setting, we show that the four hyperbolic RNN/GRU NQS variants are always able to furnish better representations of the ground state wavefunctions of the quantum systems than their respective Euclidean counterparts with the same architecture. In our experiments, among the four hyperbolic NQS, Lorentz RNN stands out in particular because despite having almost three times fewer parameters, it is capable of surpassing the more complex Poincare GRU and Lorentz GRU to emerge as the best overall hyperbolic NQS ansatz on many instances involving different J2 and (J2,J3) couplings. Given the findings from this work showing that the four newly constructed hyperbolic RNN/GRU NQS ansatze are able to outperform the well-established Euclidean RNN/GRU NQS in Heisenberg spin models, we establish the utility and efficiency of the hyperbolic Lorentz RNN/GRU NQS as well as the Poincare RNN/GRU NQS for future variational studies of quantum many-body systems, especially those exhibiting a hierarchical structure in the form of the different degrees of nearest-neighbor interactions.

This paper introduces the concept of exhaustively parametrised, feasibility-respecting quantum circuits for constrained combinatorial optimisation problems. Such circuits can reach, given the right parameter values, every feasible solution with certainty – including the optimum – with a fixed number of parameters, while avoiding infeasible solutions altogether. This is in sharp contrast to conventional quantum alternating operator ansatz schemes, which are merely guaranteed to reach the optimum asymptotically. We introduce an abstract pipeline for constructing exhaustively parametrised, feasibility-respecting circuits from a transitive group action on a problem's feasible set. Our constructions rely on the simple combination of the group action with group representation and the novel notion of generating sequences: group elements in fixed order, possibly with repetitions, that generate the entire group. That is, we trace expressivity of parametrised quantum circuits back to the most fundamental concepts of group theory. We apply this pipeline to two concrete examples for the travelling salesperson problem, thus showing that exhaustively parametrised, feasibility-respecting circuits are not an empty definition. Furthermore, we provide numerical proof-of-principles on instances with up to nine cities, comparing the suitability of our constructions for parameter optimisation purposes against established mixers.

In realistic quantum information processing tasks, quantum states are inevitably affected by environmental noise, leading to decoherence and degradation of useful quantum resources. The coherence fraction, which serves as an important figure of merit for several quantum protocols, may decrease significantly after the action of a noisy channel. Such degradation can result in unsatisfactory performance in real-world applications. In this work, we investigate whether catalysis can be used to pre-process the input state to enhance the coherence fraction of an output state from a quantum channel. Specifically, we study whether using a processed state $\rho_s'$ as the input to a quantum channel $\Lambda$, instead of the original state $\rho_s$, can yield an output state $\Lambda(\rho_s')$ whose coherence fraction exceeds that of $\Lambda(\rho_s)$. We analyze the conditions under which such an improvement is possible. We also provide a practical application of our setup for the phase discrimination task. Furthermore, we establish a necessary and sufficient condition for an incoherent state preserving CPTP(Completely Positive Trace Preserving) map $\mathcal{E}$ to be a particular type of Strictly Incoherent Operation (SIO). This characterization provides a new structural understanding of SIO and clarifies its role in coherence manipulation. Our results offer practical insights into coherence preservation and enhancement in noisy quantum processes and may be useful for optimizing quantum information protocols under realistic conditions. We also provide numerical examples to support our claims.

We study numerical integration on $[0,1]$ by quantum amplitude estimation (QAE), with emphasis on the cost of constructing the amplitude oracle. We introduce a hierarchy of grid functions $\mathcal{G}_n^{(d)}$ whose angle map $\Theta_g:\{0,1\}^n\to[0,\pi]$ is multilinear of degree at most $d$. Membership is classically checkable in $O(n2^n)$ time by the Walsh–Hadamard transform, and each $g\in\mathcal{G}_n^{(d)}$ admits a canonical encoding circuit with $\sum_{k=0}^d\binom{n}{k}$ multi-controlled $R_Y$ gates. Combining this circuit bound with classical discretisation estimates, we obtain a depth-versus-accuracy trade-off: for $g\in C^\alpha[0,1]$, total gate count $O((\log(1/\varepsilon))^d\varepsilon^{-1})$ suffices for $\varepsilon$-accuracy with constant probability; in the affine case $d=1$ this is $O(\varepsilon^{-1}\log(1/\varepsilon))$ at fixed discretisation. We also show that encoding degree and Sobolev smoothness are independent: for every $s\in(0,1/2)$, $\mathcal{G}_n^{(1)}$ contains restrictions of functions in $W^{s',2}(0,1)$ for all $s'<s$ but not in $W^{s,2}(0,1)$. Experiments on the SpinQ Triangulum (NMR) and IBM Kingston (superconducting) processors at $n=2$ validate the predicted hierarchy: affine encodings run reliably on both platforms, while quadratic encodings exceed the Triangulum coherence budget but execute on Kingston.

Configuring variational quantum algorithms for combinatorial optimization remains a difficult, expert-driven process requiring coordinated choices over solver family, ansatz, objective, and optimizer. We present AutoQResearch, an LLM-guided closed-loop experimentation framework that casts this task as sequential policy search over a curated design space. Instead of a single static configuration, the framework searches for adaptive solver-control policies that condition future decisions on diagnostics such as feasibility, optimality gap, and convergence stagnation. The system operates through a structured workflow: an LLM agent edits a small policy surface under a fixed evaluation harness, candidate policies are screened using cheap scout evaluations, and only the strongest candidates are promoted to full confirmation. This enables controlled autonomous exploration while guarding against proxy overfitting and unstable selection. We evaluate the framework on Maximum Independent Set (MIS) and the Capacitated Vehicle Routing Problem (CVRP). On MIS instances (16–64 vertices), discovered policies substantially outperform static baselines and reveal scale-dependent behavior: CVaR objectives are effective at small scale, while QRAO-based qubit compression provides the most effective explored scaling path. On CVRP curricula (8–12 customers) and a held-out E-n13-k4 benchmark, the framework discovers adaptations involving sampling budget, penalty design, and hybrid repair protocols, yielding high-quality solutions. Methodologically, we find that staged confirmation is essential: cheap proxy evaluations can materially misestimate policy quality and even invert candidate rankings. Overall, the paper positions AutoQResearch as a benchmarked quantum–GenAI co-design workflow for autonomous solver discovery in variational quantum optimization.

We establish a framework for realizing back-action-evading (BAE) measurements and quantum non-demolition (QND) variables in linear quantum systems. The key condition, a purely imaginary Hamiltonian with a real or imaginary coupling operator, enables BAE measurements of conjugate observables. Symmetric coupling further yields QND variables. For non-compliant systems, coherent feedback is designed to engineer BAE measurements. Crucially, the QND interaction condition simultaneously ensures BAE measurements and promotes the coupling operator to a QND observable.

Two-mode squeezed states as paradigmatic entangled resources have broad applications in quantum information processing. Here, we study the generation of stable optical-microwave squeezing in structured environments within a hybrid electro-optomechanical system, where a mechanical oscillator is simultaneously coupled to an optical cavity mode and a microwave mode of an LC resonator. Specifically, an effective Hamiltonian that captures the optical-microwave squeezing interaction is constructed by combining strongly modulated driving fields applied to both photonic modes with a mechanical parametric amplifier. Based on this effective model, the dynamical evolution of two-mode squeezing in structured environments is analyzed. It is remarkably shown that the non-Markovian noise can substantially enhance the squeezing level in comparison to the Markovian case, and that two-mode squeezing can persist even in the absence of external driving fields under non-Markovian conditions, thereby mitigating the detrimental effects of anti-squeezing. Furthermore, the persistence of the two-mode squeezed state is enhanced when the environmental spectral densities of the microwave and optical modes are identical. Our work provides a theoretical framework for generating and persisting two-mode squeezing in structured environments.

We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a quantum state, enabling a compact representation of high-dimensional distributions. Exploiting the circulant structure of finite-difference operators, the evolution is realized in the spectral domain using quantum Fourier transforms and phase rotations. A key result is that the drift component can be implemented exactly in amplitude space, leading to an accurate reproduction of the classical transport dynamics. In contrast, the diffusion term does not admit a linear representation in amplitude space due to the nonlinear relation between probability density and wave function. To enable a quantum implementation, we introduce a unitary surrogate based on a Wick rotation, transforming diffusion into a dispersive phase evolution. This yields a fully unitary propagation that can be implemented efficiently on a gate-based quantum computer. The proposed method is evaluated numerically for different scenarios and shows strong agreement with the exact solution of the Fokker-Planck equation. The approach demonstrates the potential of quantum computing for Bayesian state estimation, as the representable state space grows exponentially with the number of qubits. This allows the efficient representation and propagation of probability densities that would otherwise require complex tensor decompositions on classical hardware, making the method a promising candidate for high-dimensional filtering problems.

This study proposed the hierarchy of quantum kernel networks by combing multi quantum networks with smoothed particle hydrodynamics (SPH). The Lagrangian quantum network model was further developed based on an improved quantum multilayer perceptron (QMLP). A sequential hybrid quantum-classical framework was constructed to ensure robust particle gradient-based optimization and mitigate barren plateaus for computational particle dynamics. This approach combines smoothing kernels with quantum learning, establishing a novel quantum intelligent particle paradigm. The framework was validated through some benchmarks on multifarious quantum neural networks, static multi-level vortex reconstructions and transient scalar advective transports. Numerical results show that while elementary quantum circuits struggle with generalization in unstructured domains, the hybrid crossed-QMLP matches the fitting accuracy of classical SPH in quantum optimized space. Despite current limitations in computational efficiency and hardware implementation, this work paves the way for a new investigation on quantum-particle approach by mapping unstructured Lagrangian particle topologies into integrated quantum networks.

This work studies quantum algorithms to solve high-dimensional stochastic differential equations (SDEs) $\mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t$. Aiming for a speed-up in the dimension $N$ of $\mathbf{X}_t$, we generate quantum states that encode $\mathbf{X}_t$ in the amplitudes, while most of the existing quantum methods for SDEs employ binary encoding. A key challenge is the amplitude encoding of the noise term, and we address this by utilizing the quantum circuit implementation of a pseudorandom number generator (PRNG). We propose two methods: the Dyson series-based method and the Euler-Maruyama (EM)-based method. In the former, we express the noise term via the Dyson series approximation of the time evolution operator, while in the latter, it is approximated using the EM time discretization. Both methods use the quantum linear systems solver to generate the amplitude-encoding state of $\mathbf{X}_t$, making only ${\rm polylog}(N)$ queries to the PRNG circuit and the block-encodings of $A$ and $B$. Additionally, going beyond state preparation, we present methods to estimate expectations of functions of $\mathbf{X}_t$ using the state.

Nonreciprocal relaxation matrices can have skin-localized right eigenmodes, but their imprint on a mixed steady state is not fixed by the density profile alone. We develop an exact steady-state theory for number-conserving Gaussian fermion chains and show that the dominant natural orbital of the correlation matrix provides a mode-resolved diagnostic of hidden skin order. The steady-state correlator admits a biorthogonal decomposition in terms of the left and right eigenmodes of the relaxation matrix $X$ and the source matrix $Y$. This formula separates three ingredients: slow rapidity denominators, source loading by left eigenmodes, and real-space geometry from right eigenmodes. For a local pump, the pump position is read by the left modes, whereas the selected profile is drawn by the right modes. In a single-slow-mode regime, the dominant natural orbital locks to the Euclidean-normalized slow right mode. The density can follow the same boundary trend, but it is a less selective incoherent sum over occupied natural orbitals. We verify this selection law in a nonreciprocal Hatano–Nelson chain and show that, in a nonreciprocal SSH chain, the selected natural orbital crosses over from a topological edge candidate to a slow bulk-skin candidate. These results identify natural-orbital locking as a steady-state diagnostic of nonreciprocal localization in Gaussian open fermion chains.

We study single-copy stabilizer learning, the problem of identifying a stabilizer group of dimension $n-t$ from an $n$-qubit quantum state $\rho$. We obtain two complementary results. First, in the average case, logarithmic-depth local Clifford circuits suffice to efficiently learn almost all stabilizer groups with $t=O(\log n)$, instead of the linear-depth measurements required in previous approaches. We support this result with numerical simulations for systems of up to 100 qubits. Second, we show that, in the worst case, any adaptive single-copy measurement scheme requires a number of samples that scales exponentially in $t$. Together with existing results on two-copy learning, our findings suggest that, for large $t$, identifying Pauli symmetries of a quantum system exhibits a quantum advantage in the learning setting.

The quantization of superconducting transmission-line resonators is usually introduced phenomenologically by modeling the resonator as an effective LC circuit and imposing canonical commutation relations on macroscopic variables such as charge and flux. Although this approach is highly successful, it leaves open why these macroscopic variables should obey quantum commutation relations and how this behavior emerges from the superconducting state. In this work, starting from the microscopic pairing Hamiltonian underlying BCS superconductivity, we derive the low-energy effective Hamiltonian of a circuit-QED architecture containing a superconducting transmission line with distributed capacitive and inductive elements. We establish quantitative relations between macroscopic observables, including current and voltage, and the spatially local superconducting phase, as well as the microscopic parameters of the electron-phonon system. We then extend the third quantization of the superconducting order parameter, introduced in Paper (I) for the global phase, to the spatially local case. This gives a macroscopic field quantization of the superconducting phase. We show that, after restriction to the low-energy excitation subspace, the local superconducting phase becomes a genuine quantum dynamical variable. Thus, the quantum behavior of transmission-line resonators need not be postulated at the macroscopic level, but follows from the third quantization of the superconducting order parameter. These results suggest that capacitive and inductive superconducting circuit elements share the same microscopic origin, providing a unified framework for superconducting circuit quantization.

Magnetic clock transitions (CTs), defined by vanishing first-order sensitivity of the transition frequency to magnetic field fluctuations, provide a powerful route to suppress decoherence in donor spin systems. Here, we present the observation of magnetic field CTs from an ensemble of near-surface $^{75}$As ($I = 3/2$) spins in silicon using low-field ($< 10$~mT) continuous-wave electrically detected magnetic resonance (EDMR). As the CT condition is approached, pronounced linewidth broadening is observed, consistent with a donor Hamiltonian informed linewidth model. These results establish low-field EDMR as a sensitive probe of CTs in near-surface donor systems relevant to silicon-based quantum devices.

Scalable quantum computing is fundamentally bottlenecked not by qubit count or fabrication yield, but by a rigid temporal mismatch: macroscopic classical coordination latency ($\tau_c$) inevitably grows with system diameter, while microscopic quantum coherence ($\tau_q$) remains strictly bounded. Beyond a critical scale, this mismatch breaches the classical control light cone, triggering a superlinear geometric penalty ($\epsilon > 0$) that renders monolithic synchronization physically impossible. We formalize the resulting structural phase transition through a governing scaling law, $1+\epsilon > \gamma$, which mandates modular decomposition and a shift from global unitaries to Local Operations and Classical Communication (LOCC). To manage the resulting resource contention under strict coherence budgets, we introduce a layered semantic architecture and a time-aware Reserve–Commit protocol. By embedding predictive temporal pre-validation, the protocol acts as an architectural semantic classifier: it preemptively aborts transactions that exceed the causal horizon and explicitly converts scheduling-induced failures into location-known erasure metadata, directly relaxing hardware fidelity thresholds for downstream QEC decoders. Under near-term transduction targets ($\eta_{\mathrm{trans}} \sim 0.1$), we project a crossover scale at $N_c \sim 10^5$–$10^6$ physical qubits. This threshold marks a profound architectural convergence: the footprint required for modularity aligns precisely with early fault-tolerant utility, establishing time-aware distributed orchestration, rather than monolithic expansion or centralized classical control, as the physical imperative for utility-scale quantum computing.

The Kerr-nonlinear parametric oscillator (KPO) provides a foundational semiclassical model for cat-state quantum hardware. Standard analyses of the KPO typically rely on autonomous, frozen-time approximations to describe the stabilization of macroscopic coherent states. However, state preparation and gate manipulation are driven by explicitly time-dependent microwave pulses, so the operational dynamics are inherently nonautonomous. In this paper, we show that static algebraic equilibrium pictures are incomplete for describing both state formation and gate-induced transport in the Kerr-cat qubit. For nonautonomous state preparation, we analyze the ramped resonant model by combining a linear nonautonomous stability analysis with a local invariant-graph reduction near the vacuum trajectory. This yields a quintic reduced normal form in the critical direction and identifies two symmetric post-threshold moving branches that organize the local state-formation dynamics. The associated diagnostics separate the reduced branch dynamics from the full two-dimensional phase-twist relaxation observed in the hardware coordinates. For gate execution, we model a fast pulse as a weak aperiodic perturbation of the conservative resonant figure-eight separatrix and apply Melnikov's method to derive a leading-order transport criterion. In this framework, transient lobe dynamics emerge as a semiclassical mechanism for non-adiabatic leakage, and the resulting amplitude-width threshold curve provides a leading-order geometric indicator for the onset of gate-pulse-induced transport.

We study when block-coupled regular graphs can realize prescribed complex quantum-like (QL) bit states as exact synchronized eigenstates. Two regular subgraphs $G_A$ and $G_B$ supply normalized all-ones eigenvectors $V_A$ and $V_B$, and algebraically regular bipartite couplings reduce the full graph-supported operator exactly to a $2\times 2$ effective block on $\mathcal S=\operatorname{span} \{ \lvert 0\rangle, \lvert 1\rangle \}$. Within this reduction we prove that two natural symmetric complexifications are not universal for state synthesis under a real-spectrum requirement: complex symmetric coupling with real diagonal regularities forces the target computational basis amplitude ratio $r=\omega_2/\omega_1$, for $\lvert \psi\rangle = \omega_1\lvert 0\rangle + \omega_2\lvert 1\rangle$, to satisfy $r^2\in\R$, while real symmetric coupling with complex diagonal regularities forces $r+1/r\in\R$. Replacing complex symmetry by Hermitian coupling removes this phase obstruction. For any nonbasis target state, any prescribed real eigenvalue, and any prescribed nonzero signed spectral gap, a Hermitian weighted coupling realizes the target exactly. Additionally, an independently tuned directed-coupling model gives a second universality mechanism. We then pass from continuous effective parameters to finite weighted graphs with entries in $\{0, \pm1, \pm i\}$ (the fourth roots of unity and zero), characterize the balanced discrete coupling lattice by perfect matchings, and show that exact discrete Hermitian realizations are dense in the synchronized pure-state space. These results give a state-synthesis universality taxonomy for complex QL-bits and identify Hermitian conjugate pairing as the robust structural mechanism that supports arbitrary complex amplitudes with real two-level spectra.

Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We present a systematic empirical comparison of four VQC families – multi-layer fully-connected (FC-VQC), residual (ResNet-VQC), hybrid quantum-classical transformer (QT), and fully quantum transformer (FQT) – across five regression and classification benchmarks. Our key findings are: (i)~FC-VQCs achieve 90-96% of the $R^2$ of attention-based VQCs while using 40-50% fewer parameters, and consistently outperform equal-capacity MLPs (mean $R^2{=}0.829$ vs.\ MLP$_{720}$'s $0.753$ on Boston Housing, 3-seed average); (ii)~FC-VQC's Type~4 inter-block connectivity provides partial cross-token mixing that approximates the role of attention – explicit quantum self-attention yields only marginal gains on most datasets while significantly increasing parameter count; (iii)~expressibility saturates at circuit depth~${\approx}\,3$, explaining why shallow VQCs already cover the Hilbert space effectively; (iv)~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; (v)~in our noise study on Boston Housing, FQT degrades gracefully under depolarizing noise while QT collapses. All results are validated across three random seeds. These findings provide practical architectural guidance for deploying VQCs on near-term quantum hardware.

We establish spectral conditions under which a first-order energy linearization of a projected Feshbach Hamiltonian is controlled. When the support of the induced self-energy spectral measure lies entirely above or below the target energy window, the self-energy curvature and linearization remainder have fixed sign in the semidefinite (Löwner) order. The remainder then decreases monotonically under model-space enlargement by complete complementary-space spectral subspaces, and the minimax linearization energy is determined by the endpoint norms. Far-separated asymptotics and the near-boundary divergence caused by an approaching pole are obtained explicitly. The theory is validated by a numerically exact sudden-quench calculation for the two-electron system $HT$ -> $^3HeH^+$: all 56 nontrivially coupled basis-geometry cases have support separated above the target window, while seven cc-pVTZ cases are exactly decoupled by construction and serve as numerical control cases. The same remainder controls the projected resolvent and, through source dressing, the full prepared-state response, with resolvent amplification governing the near-pole sensitivity. These results provide a practical criterion for controlled downfolding in molecular electronic structure and for final-state analyses in neutrino-mass experiments.

We place several known indicators of Kochen–Specker contextuality – the KCBS correlator $\chi$, the contextual fraction $\CF$, the Shannon-entropic $n$-cycle inequality of Chaves and Fritz, and the operational commutator witness $D$ of Paper~I – into a single projector-geometric framework organized around the overlap matrix $\Tcal_{ij} = d^{-1}\tr[(\hat P_i \hat Q_j)^2]$, where $\hat P_i$ and $\hat Q_j$ are the joint-eigenspace projectors of the two compatible observable pairs within a measurement context. The state-independent scalar content of $\Tcal$ is carried by two independent contractions: the mutual information energy $E = \sum_{ij}\Tcal_{ij}$ of Paper~I (equivalently, its logarithmic form $S_2 = -\log_2 E$), and the Maassen–Uffink extremal overlap $c_\MU = \max_{i,j}|\langle a_i,b_i | c_j,b_j\rangle|$. We prove that $S_2$ is non-increasing under coarse-graining, that $S_2(\Gcal) > 0$ is a necessary configuration-level condition for observable contextuality, and that the additive composition $S_2(\Gcal) = \sum_\alpha S_2(\Gcal_\alpha)$ is exact for the KCBS pentagon. We further show that in the spin-$1$ realization of the KCBS pentagon, a shared $m_s=0$ eigenstate in each context forces $c_\MU = 1$, rendering every Maassen–Uffink-type bound trivial – a structural mechanism that makes explicit why outcome-entropic uncertainty relations based on $c_\MU$ are silent on KCBS contextuality, while $S_2 \approx 2.7266$~bits throughout. Applied to KCBS and CHSH, the framework identifies regimes in which every state-dependent witness considered here is silent yet $S_2(\Gcal) > 0$ by an amount set by the projector geometry alone.

Representability determines when a two-particle reduced density matrix (2-RDM) corresponds to a physical quantum state, enabling many-particle quantum calculations with 2-RDMs rather than the wave function. In this Letter, we present a solution of the representability problem for quantum systems without particle-number conservation. The physically allowed set of 2-RDMs can be characterized from a geometrically `orthogonal' set, the polar cone. We derive explicit linear equations for the two-body operators in the polar cone – the intersection of the $p$-positive cone with the two-body operator space – to obtain a systematic hierarchy of representability conditions that do not depend on higher RDMs or the wave function. Moreover, by augmenting these conditions with the particle-number variance, we obtain a unified framework for treating both particle-number-conserving and nonconserving systems. We illustrate with a spin system and molecular H$_4$.

To date, frequency-dependent squeezed light has been used to reduce quantum noise in interferometric gravitational-wave detectors by 6.1 dB (a factor of two). Future upgrades and detectors aim to both reduce quantum noise by 10 dB (a factor of three) and to increase the circulating power in the interferometer arm cavities. Achieving these goals will be extremely challenging due, in part, to the degradations to the squeezed state caused by mode mismatch between the internal interferometer optical cavities and between the auxiliary external cavities. It is therefore imperative to gain a detailed understanding of all sources of mismatch and to obtain experience in mitigating their effects in the current detectors in order to improve astrophysical sensitivity now and in the future. Two types of internal mismatch are identified which are due to the thermal aberrations generated when the test mass optics absorb a small fraction of the circulating arm power. It is found that the dynamics responsible for the degradations caused by the mismatch between the quadratic part of the wavefront of two modes has a characteristic low-pass frequency dependence while the dynamics of the mismatch due to all higher order thermal aberrations has a high-pass behavior. As a consequence, the two types of mismatch are predominantly responsible for different squeezing degradations—some of which are significant for the current detectors and some of which will only be important for future detectors with longer arms. The behavior of these two types of internal mismatch are described, and the implications for detector design, operation, and characterization are discussed.

The challenge of programming classical computers to play traditional, competitive games against human players has helped to advance classical hardware and software. Quantum computers have the potential to play games in a unique way: programmed only with the rules of a game, they should be able to implicitly represent all future paths of a game leading to wins, losses, or draws, and to sample from this path set to identify moves that maximize the likelihood of a win. This permits skilled play without hard-coded or machine-learned strategy. As a proof of principle, we present early results obtained after programming the D-Wave quantum annealer with the rules of tic-tac-toe, enabling it to play against a human or classical computer opponent. We anticipate that, as it has for classical computers, game-playing will serve as an important real-world benchmark for quantum computers.

Young interference is usually read as the gradual statistical accumulation of random detection events. Here we show that a time-reversed Young (TRY) geometry has a different statistical character: the fringe is not a marginal distribution of detector positions, but a conditional response indexed by a programmed source coordinate. With a fixed detector and a scanned source basis, the observable is an operational hybrid correlator between detector signal and source label. The resulting interference is deterministic at the response-function level, while noise enters only through estimation precision. We formulate this distinction using Fisher information, estimator variance, and noise scaling, clarifying why TRY naturally supports calibration, lock-in readout, null-fringe sensing, and source-plane superresolution.