Papers

We theoretically investigate the performance of a compact matterwave vortex gyroscope formed by a two-component Bose-Einstein condensate in a toroidal potential. Unlike conventional atomic gyroscopes that rely on the Sagnac effect, the topological stability of the vortex state yields rotation sensitivity independent of the enclosed area, making the device robust against geometric drifts. Using fully quantum multimode simulations, we quantify two interaction-driven mechanisms that degrade performance: phase diffusion from one-axis-twisting and four-wave mixing from intercomponent scattering. We identify regimes where tuning interaction and trapping parameters produces a trade-off between these effects, and find that reducing the intercomponent scattering length can counterintuitively worsen sensitivity. Finally, we compare the vortex gyroscope to a guided Sagnac interferometer, demonstrating superior scaling, establishing it as a promising candidate for compact precision rotation sensing.

We study dissipation driven boundary localization in a Bernevig Hughes Zhang type second order topological insulator by introducing inhomogeneous, spin dependent boundary dissipation. After projection onto the edge subspace, the dominant component of the boundary dissipation lies in the same Pauli channel as the kinetic term. This channel gives both counter-propagating edge modes the same real transfer exponent. The two modes therefore accumulate at the same dissipative domain wall. For the corner states, the dissipative envelope competes with Jackiw Rebbi localization. Increasing dissipation moves their weight from the geometric corners to the dissipative domain wall. Propagating edge states also localize at this wall. Numerical calculations confirm the qualitative predictions of the edge theory. A fixed energy Feshbach reduction captures finite size effects. Inhomogeneous boundary dissipation thus controls boundary state localization without changing the bulk topology.

We introduce an $\mathrm{SO}(3)$-symmetric spin model derived from the algebraic structure of $\mathfrak{so}(3)$: It is obtained as the nearest-neighbor parent Hamiltonian of a Matrix Product State (MPS) built from the generators of the Lie algebra $\mathfrak{so}(3)$ and the identity matrix, and therefore encodes the quadratic relations of the Lie algebra. We characterize the ground space structure of the resulting model and show that for open boundary conditions (OBC), it exhibits a quadratic ground space degeneracy, given by one irreducible representation (irrep) of each odd dimension (integer spin). For periodic boundary conditions (PBC), it has a linear ground space degeneracy, consisting of a singlet — namely, the MPS underlying the model — and a ferromagnet (the irrep with maximal spin), and thus exhibits gapless excitations. We also generalize the construction and the analysis of the OBC ground space to $\mathrm{SO}(d)$ and other compact simple Lie groups. The MPS on which the model is based is an injective MPS, and therefore, its 3-site parent Hamiltonian has a unique ground space and is gapped. The observed critical behavior thus has its origin in the small parent Hamiltonian considered. The model's algebraic ground space scaling thus provides an example distinct from that reported in (Schuch et al., 2025, arXiv:2503.10767), where it was shown that small parent Hamiltonians of injective MPS generically have unique ground states, and examples with an exponential ground space degeneracy were given.

Sensing hinges on two key attributes: high sensitivity and resilience to noise. Here, we present a scheme that unites these features within a single framework. By harnessing the exponential amplification of end-to-end Green's functions-a direct signature of the non-Hermitian skin effect-our scheme achieves an exponential sensitivity scaling of exp({\alpha}L) with {\alpha} a model-specific constant and L the system size. Notably, this enhanced sensitivity is protected by spectral winding numbers and endures under disorder when the non-Hermitian topological phase remains intact. We also explore its feasibility in synthetic non-Hermitian platforms, providing a pathway toward highly sensitive and noise-tolerant sensing.

Zinc oxide (ZnO), a wide-band-gap semiconductor with mature growth techniques, is a promising host for optically active quantum spins. Yet, optically active quantum defects in ZnO remain largely unexplored. Here, we identify and characterize a family of double substitutional impurities in ZnO, formed by main-group donor-acceptor (DA) pairs, as candidates for optically active quantum defects. Using hybrid density functional theory (DFT), we systematically investigate double substitutional DA complexes and their defect physics, including electronic structure, thermodynamic stability, and optical properties. The proposed defects exhibit isolated defect states, strong spin localization on the acceptor site, and $C_{3v}$ symmetry. Importantly, the electronic structure of the DA pairs is largely determined by the atomic properties of their constituent atoms. We further examine their optical characteristics, including zero-phonon lines (ZPLs), radiative lifetimes, and nonradiative decay to assess their viability as color centers. Notably, among the dimers, (Si$_{Zn}$-B$_O$)$^+$ and (Ge$_{Zn}$-B$_O$)$^+$ exhibit visible optical transitions with sub-microsecond radiative lifetimes and robust charge states against optical ionization, while (Si$_{Zn}$-C$_O$)$^{2+}$ shows the smallest Huang-Rhys factor, approximately 5.6. Our results propose a new family of main-group donor-acceptor defects in ZnO as promising candidates for optically active spin defects.

The Fermi-Hubbard model provides a paradigmatic setting for studying strongly correlated quantum matter, where different observables are commonly used to probe charge, interaction, and spin correlations. In this work, we investigate whether these observables contain mutually transferable physical information beyond their apparent distinction. We quantify such physical redundancy through transferability tests among three representative observables of the two-dimensional Fermi-Hubbard model: total density (N), double occupancy (D), and spin-spin correlation (S). Using a neural-network reconstruction framework, we find that the phase diagram of one observable can be reconstructed from another with accuracy close to self-reconstruction benchmarks, especially in trivial phase regimes. This transferability relies on correct physical labeling, persists across finite-temperature regimes, and remains robust under noisy inputs. Our results suggest that separate observables can carry a substantial fraction of one another's physical information, providing numerical evidence for observable-level redundancy in the two-dimensional Fermi-Hubbard system.

Carbon-related defects in hexagonal boron nitride are promising room-temperature single-spin qubits and quantum sensors, but their atomic structures remain largely unidentified. Here we show, using first-principles calculations of electron-spin decoherence, that the atomic structure of each defect is imprinted in its spin coherence. Mapping the Hahn-echo dynamics of seven candidate carbon defects across magnetic field and four isotope-engineered nuclear-spin baths, we find that electron-spin-echo envelope modulation emerges at defect-specific magnetic fields, at which the nearest-neighbor nuclear spins satisfy a cancellation condition set by their hyperfine and quadrupole couplings. Both the fields and the modulation frequencies follow from an analytical model using computed hyperfine and quadrupole tensors alone, and they shift or vanish upon isotope substitution. At low fields, the field dependence of the coherence time separates the defects into two classes according to the sublattice occupied by carbon. These decoherence fingerprints, directly testable in isotope-engineered samples, establish a structural identification route complementary to optical spectroscopy.

Quantum phase estimation is usually introduced as an algorithmic primitive for extracting eigenphases of unitary operators. Here we show that, when implemented through a dispersive light-matter interaction, it can also be used as a nondestructive measurement tool for bosonic fields. We consider a bosonic mode coupled to a multi-qubit register and calibrate the photon-number dependent phase shifts so that the register performs a number-resolved quantum phase estimation readout. Repeating this readout during dissipative evolution enables nondestructive monitoring of photon-number dynamics. We then show that the same readout can be converted into a Wigner tomography reconstruction by applying phase-space displacements before the quantum phase estimation block. Numerical reconstructions for Fock, coherent, and even/odd Schrödinger cat states show the expected nonclassical phase-space structures and near-unity Wigner overlap fidelities. The protocol provides a unified route to nondestructive monitoring and state tomography of bosonic fields, with direct relevance for bosonic-state characterization, calibration, and control in superconducting quantum architectures.

Fracton models have attracted considerable interest as candidates for quantum memories because of their unconventional ground-state degeneracy (GSD) and restricted-mobility excitations. The four-dimensional (4D) Chamon code introduced in our previous work is constructed via the 4D XYZ product of two two-dimensional (2D) toric codes. Its GSD grows exponentially with the system size, similar to that of the three-dimensional (3D) Chamon code, suggesting that it may be regarded as a 4D generalization of the 3D Chamon code. However, the excitation properties of the 4D Chamon code have not been studied in depth, and a high-performance decoding strategy is still lacking. In this work, we first establish the correspondence between the algebraic structure of the 4D Chamon code and the 4D lattice, thereby characterizing the geometric distributions of qubits and stabilizers. Second, we show that the 4D Chamon code supports three types of restricted-mobility excitations analogous to those of the 3D Chamon code, further supporting its interpretation as a 4D generalization of the 3D Chamon code. Finally, we uncover two structural properties relevant to decoding: a hyperplane symmetry and a projection-induced 2D toric-code structure. By exploiting these properties, we develop a two-layer decoding strategy that decomposes the original decoding problem into multiple independent and parallelizable subproblems. Numerical simulations show that the proposed decoder substantially outperforms BP-OSD in decoding accuracy, demonstrating the benefit of incorporating the intrinsic geometric and algebraic structures of the code into decoder design.

An introductory review is provided for those who are interested in exploring applications of qubits and other quantum excitations to the detection of dark matter (and any other physics beyond the Standard Model). Topics covered include the fundamental properties of qubits, the excitation mechanism of qubits due to the electric field induced by dark matter (with attention to the effects of the coherence of dark matter), the dynamics of coupled qubit-cavity systems modeled by the Jaynes-Cummings framework, and the influence of noise and decoherence (especially Markovian noise described by the Lindblad equation). In addition, the article introduces essential concepts in quantum sensing, including the operator-sum representation and positive operator-valued measures, the Cramér-Rao bound, the standard quantum limit and the Heisenberg limit, and the potential enhancement of sensitivity to dark matter achievable with entangled states. Throughout, these topics are discussed with particular emphasis on their application to the detection of wave-like dark matter.

Nitrogen-vacancy (NV) centers in diamond provide room-temperature electron-nuclear spin registers for quantum sensing and quantum information processing, with surrounding 13C nuclear spins serving as long-lived quantum memories. However, coherent control of large nuclear-spin registers is limited by finite electron-spin coherence and spectral addressability. Existing approaches follow two complementary strategies: dynamical-decoupling (DD) gates exploit filter-function resonances to realize selective conditional evolution but permit only discrete rotation angles, whereas dynamical-decoupling radio-frequency (DDrf) control restores continuous tunability at the cost of stringent hyperfine-geometry and RF-power requirements. Here, we introduce hybrid dynamical-decoupling and radio-frequency (H-DDrf) control, which preserves the DD-induced conditional evolution and employs a geometrically phase-matched RF drive to complete the target operation. This approach reduces both RF power and gate duration while maintaining high-fidelity control, thereby expanding the accessible 13C nuclear-spin register for room-temperature NV-based quantum memories and quantum processors.

A set of orthogonal quantum states in multipartite systems is of genuine nonlocality if it is locally indistinguishable in every bipartition. If it is locally reducible when the parties are separated, we say that it has genuine nonlocality of type~\uppercase\expandafter{\romannumeral 1}; otherwise, it has genuine nonlocality of type~\uppercase\expandafter{\romannumeral 2}. For a locally distinguishable set without local redundancy, if there exist some orthogonality preserving local measurements such that each outcome leads to a locally indistinguishable set, then we say that it exhibits the activation of nonlocality. We activate type-\uppercase\expandafter{\romannumeral 1} and type-\uppercase\expandafter{\romannumeral 2} genuine nonlocality of orthogonal product state sets in tripartite systems. In particular, we tackle the local irredundancy problem with partial trace operation and $p$-ary numeral systems to significantly simplify the proofs. Our results also address the open question raised by S. Bandyopadhyay et al.[\href{https://link.aps.org/doi/10.1103/PhysRevA.104.L050201}{Phys. Rev. A 104, L050201 (2021)}]. Furthermore, we observe the activation of hidden genuine nonlocality in multipartite systems, which highlights the applications of nonlocality based on state discrimination in different practical scenarios.

The trace of the average mixing matrix of a quantum walk measures the "laziness" of the walk: the higher the trace, the more likely that the walker returns home in the long run. In this paper, we develop tools to study this graph invariant arising from Laplacian quantum walks. It is known that the complete graph $K_n$ is the laziest connected graph on $n$ vertices. Using our machinery, we show that the star $S_n$ is the second laziest connected graph on $n$ vertices (and hence the laziest tree on $n$ vertices), the complete multipartite graph $K_{n-2,1,1}$ is the third laziest connected graph on $n$ vertices, and the double star $DS(n-3,1)$ is the second laziest tree on $n$ vertices. We also show that on the same number of vertices, more unbalanced double stars are lazier.

Under non-equilibrium conditions, energy/particle currents flow through a quantum system coupled to multiple baths. Although the fluxes increase in the weak coupling regime as the coupling strengthens, the reason why they decrease to zero for large coupling remains unknown. This counterintuitive behavior of energy exchange or transport phenomena is called the turnover effect. It has been predicted in several quantum systems such as photosynthetic complexes, mesoscopic junctions, quantum heat machines, and chemical networks without a single counterexample, and it results in constrained performance due to limited currents. Here, we use scattering theory to study the turnover effect produced by low-zdensity reservoirs of free particles scattered by a quantum system through localized potentials. We find that the turnover effect is a consequence of total reflection that impedes the reservoir particle from reaching the interaction region and exchanging energy with the quantum system. Moreover, we design a protocol based on quantum tunneling to avoid the turnover and to increase the maximum current. This strategy could be used to unleash the full potential of devices based on temperature/chemical potential gradients.

In odd local dimension $D$, complete Wigner positivity yields stochastic phase-space dynamics on Wigner-nonnegative states but does not control signed inputs, entanglement across channel uses, or collective decoding. Using a subsystem-resolved Weyl decomposition, we characterize the equality conditions of the tensor-stable output-purity bound. Cyclic difference sets are precisely the uniform shift supports saturating the universal Parseval lower bound on the worst nontrivial collision mode. For factorized shift–phase noise with shift support $R$, $|R|=r$, and phase distribution $h$ of no larger collision radius, we obtain $S_{\alpha,\min}(\Phi_{R,h}^{\otimes n})=n\log_2 r$ for all $n\ge1$ and $0\le\alpha\le2$, the unrestricted capacity $C=\log_2(D/r)$, and a finite-blocklength strong converse. For a balanced bi-difference-set interpolation $h_\varepsilon=(1-\varepsilon)q_H+\varepsilon u_D$, the unassisted capacity is constant for $0\le\varepsilon\le1$, while the Choi state is NPT for every $\varepsilon<1$ and becomes entanglement breaking at $\varepsilon=1$. At $\varepsilon=0$, all tensor-power minimum-output states are products with local factors in one of two mutually unbiased Weyl bases; for $\varepsilon>0$, only the computational basis remains. For Singer parameters $D=q^2+q+1$ and $r=q+1$, $C_{\mathrm E}/C\to2-\varepsilon$. Finally, for an identity–dephasing profile we determine the exact tensor-power collision-entropy phase diagram, derive rigorous capacity bounds, and isolate a distinct von Neumann crossover, with a tensor-power R'enyi conjecture supported by numerics. Thus complete Wigner positivity can coexist with persistent channel entanglement and a scalable entanglement-assisted advantage.

Nonlinear Hall effects provide a powerful probe of quantum geometry in solids and enable rectification phenomena beyond the constraints of linear response. In this Letter, we predict a layer nonlinear Hall effect (LNHE) in stacked bilayer systems composed of nonmagnetic or antiferromagnetic materials with a vanishing linear Hall conductivity. In such systems, the second- or third-order nonlinear Hall responses are intrinsically layer odd: the contributions from the two constituent layers have equal magnitude but opposite sign, resulting in exact cancellation under layer-exchange symmetry. An out-of-plane electric field $E_z$ can break this symmetry, thereby unveiling the hidden response and converting it into a switchable macroscopic nonlinear Hall signal. Using a minimal $k\!\cdot\!p$ model, we demonstrate that the LNHE can originate from the Berry curvature dipole mechanism. A systematic symmetry analysis of all 80 layer groups further yields a complete classification of the symmetry constraints and stacking configurations that allow for this type of LNHE. Beyond this mechanism, additional symmetry analysis reveals that LNHE may also arise from quantum metric dipole or inversed mass dipole. Remarkably, even in cases where second-order nonlinear Hall responses are symmetry forbidden, a third-order LNHE can still survive in certain stacked bilayer configurations. First-principles calculations on representative bilayers—nonmagnetic 1T$'$-WTe$_2$ and 1T$'$-ReS$_2$—explicitly demonstrate electrically reversible second-order LNHE, in full agreement with our symmetry-based predictions. Overall, our results establish LNHE as a universal phenomenon in a wide range of layered quantum materials and provide a robust route toward electrically tunable nonlinear transport.

We develop a general framework for characterizing the response of an evolving quantum system to repetitive quantum measurements. Modeling each evolution-measurement cycle as a quantum channel induced by an effective Liouvillian generator, we find that the Liouvillian spectral gap determines the measurement-induced decay rate. We analyze how the spectral gap responds to the measurement frequency, and define a quantum Zeno response as a decrease in the gap with increasing measurement frequency, and an anti-Zeno response as the opposite. We illustrate this criterion for both discrete-time and continuous-time quantum measurements. In an exactly solvable discrete-time qubit model, the exceptional-point spectral coalescence or spectral crossings mark the transition between Zeno and anti-Zeno responses, which can be experimentally distinguished from the long-time decay envelope of the survival probability. In a continuous-time superconducting-qubit defect model, the same transition manifests as smooth extrema of the spectral gap. Our results establish a universal spectral criterion for measurement-induced decay, offering a practical route to identify and manipulate these effects in generic quantum systems.

In this thesis, quantum channels are studied from the point of view of Mathematics. We studied the CPTP (completely positive trace preserving) and UCPTP channels, the latter being the unital channels. In both cases, the sets are compact convex, so they are the closure of their extreme points. We constructed extreme CPTP maps for every possible rank. We also constructed extreme UCPTP maps with rank 2 for each possible dimension. For ranks of at least 3, we constructed extreme UCPTP maps for many dimensions and ranks. We also proved that the tensor product of extreme CPTP maps is an extreme CPTP map. For UCPTP maps, we proved that the same is not always true, with many counterexamples. It is known that the category of CPTP maps is semicartesian. We add to this a classification of binary products. We proved that products only exist in trivial cases. For binary coproducts, we obtained the dimensions they should have, if they exist. In both cases, topological techniques were used. For this reason, we also investigated the topology of the closure of the set of extreme points of the CPTP maps. Topological invariants can be computed from decompositions of a space such as CW structures. These are a type of decomposition in which the space is expressed as a gluing of balls. In the search for a CW structure for the closure of the set of extreme CPTP maps, we obtained a partial decomposition that resembles a CW structure of the complex projective space.

We experimentally demonstrate continuous-angle logical $Z$ rotations in the $[[7,1,3]]$ Steane code on the IonQ Forte trapped-ion processor. A round of the protocol applies a transversal physical $Z$ rotation by $\theta$, followed by Steane syndrome extraction and decoding, which induces a syndrome-dependent logical $Z$ rotation. We analytically derive the effect of dephasing noise on the logical rotation angle and logical dephasing rate. Using logical Ramsey interferometry, we observe coherent syndrome-dependent logical rotations from a single round of the protocol. We find that the logical channel reconstructed from process tomography is a noisy logical $Z$ rotation well explained by a dephasing model. We further implement a two-round protocol applying physical rotations $+\theta$ and $-\theta$, and observe cancellation of the total logical angle with low logical dephasing for repeated trivial syndromes. This constitutes a proof-of-principle demonstration of continuously tunable non-Clifford logical gates by transversal rotations and standard error correction in a small quantum code.

Simulating a continuous-time quantum walk (CTQW) on a graph in the circuit model of quantum computing requires decomposing its Hamiltonian into terms that can be Trotterized into hardware-native gates. We consider two such decompositions: the standard Pauli decomposition and the recently introduced matching decomposition. Prior work suggests that the matching decomposition uses fewer CX gates on sparse graphs, while the Pauli decomposition uses fewer on denser graphs. Since CX gates dominate error and runtime on current hardware, we train machine learning models to predict, for a given graph, which of the two decompositions produces the smaller CX gate count. We train and evaluate on the complete population of all 11,117 connected eight-vertex graphs from Brendan McKay's database, so the class balance and overlap are measured directly rather than estimated. We use twelve features: ten topological properties of the graph and two that count the terms the Pauli and matching decompositions produce (n_Pauli and n_match), both computable without transpiling the simulation circuit. Standard topological properties alone provide little predictive power. Instead, the dominant signal comes from n_Pauli, a property of the Hamiltonian decomposition rather than an intrinsic property of the graph; degree variance is the only other feature that carries signal. Across a range of models the Matthews correlation coefficient (MCC) falls in a narrow band, from 0.569 untuned to 0.593 after tuning, so no single architecture stands out. We adopt a single-hidden-layer neural network at MCC 0.593. Applied frozen to a held-out, class-balanced test set of larger graphs (up to 256 vertices) from structured and Erdos-Renyi families, the model transfers, with MCC rising from 0.785 at N=8 to 1 at N>=64.

Hierarchical equations of motion(HEOM) provide exact dynamics of open quantum systems coupled to harmonic baths, but their computational cost becomes prohibitive for systems with many independent local environments. In this work, we develop a symmetry-adapted HEOM formalism to significantly reduce the computational cost for the permutationally invariant Holstein-Tavis-Cummings (HTC) model. The method removes redundant information in two stages. First, all auxiliary density operators (ADOs) related only by relabeling identical molecules and their bath channels are replaced by a single canonical occupation-pattern representative. Second, molecules with the same local hierarchy occupation produce repeated matrix elements within each representative, allowing only the distinct complex variables to be propagated instead of the full (N + 1) $\times$ (N + 1) ADO matrices. The resulting matrix-free equations are evaluated using precomputed connections and molecular multiplicities. At fixed hierarchy depth L and number of bath correlation exponentials m, the number of canonical representatives becomes independent of the ensemble size for N $\geq$ L and the number of unique variables saturates for N $\geq$ L + 2. The formulation easily extends to multiple-exponential bath decompositions, arbitrary initial density operators, static disorders, and cavity loss. Our benchmarks reproduce conventional HEOM dynamics while requiring far fewer propagated variables and substantially less memory.

We investigate the relativistic dynamics of network nonlocality in general $n$-local networks with chain and star topologies using the Unruh-DeWitt detector model. We show that the relativistic degradation of network nonlocality is strongly governed by the underlying topology. While chain networks suffer an irreversible sudden death of non-$n$-locality under relativistic motion, star networks exhibit remarkable resilience against relativistic decoherence. Most strikingly, a minimal star network with three peripheral nodes exhibits a remarkable sudden death-sudden birth transition of network nonlocality as the acceleration increases. This reentrant behavior reveals a dual role of the Unruh effect: it can both suppress and protect network nonlocality, offering a new perspective on the relativistic effects of acceleration on quantum networks. For larger star networks ($n>3$), non-$n$-local correlations persist over the entire acceleration regime. These insights provide valuable conceptual guidance for the structural optimization and design of acceleration-resilient architectures for future relativistic quantum communication and sensing protocols.

A Bell violation by material probes certifies nonlocal behavior, but it does not identify which internal subsystem carried or was measured to produce that behavior. We determine the additional information required to attribute such a violation to a gravitational field. For any setting-independent field-to-probe channel completed before the Bell settings are chosen, an entanglement-breaking channel makes all induced field measurements jointly measurable. A static Newtonian phase pickup belongs to this class, even with arbitrary adaptive probe control. Applied to a recent four-mass proposal, the claimed field-only measurements obey the stronger CHSH bound \(\sqrt2\), whereas the Bell-active operation is the source-to-probe instrument that includes the coherent source herald. At the published parameters, the observed flagged behavior is at least \(0.1630\) from the claimed field-detector family, exceeding its \(0.0898\) distance from Bell locality. We then incorporate a common field slice, gravitational constraints, dressing, detector backreaction, and coherent references into a robust certification theorem. The result isolates the minimum missing information: field-only factorization and a local measurement- incompatibility witness on each wing. More precise phase data cannot replace either requirement.

The dispersion interaction between two infinite sheets of graphene located on a substrate is considered based on the Lifshitz formula, taking temperature into account. The result is obtained in the form of a series that is easy to calculate. The influence of the interband conductivity of graphene, which turned out to be small, is examined.

We investigate generalized Kennedy receivers for coherent-state BPSK communication over turbulent free-space optical channels. An ergodic mutual-information framework is developed to jointly optimize the receiver displacement and input prior probabilities under Gamma–Gamma fading.

We investigate the phase diagram of a non-Hermitian XY chain with staggered Dzyaloshinskii–Moriya (DM) interactions using quantum-information methods. Through an alternating local-spin-rotation transformation, the model is mapped onto a standard DM-free XY chain, and the resulting transformed Hamiltonian exhibits rotation–time-reversal ($\RT$) symmetry. Combining correlation-function analysis with known phase results of the standard XY chain, we construct the phase diagram for the present system. We further adopt quantum-information-based quantities to systematically assess their performance in characterizing quantum phase transitions within this non-Hermitian system. Our results show that single-site entanglement can only detect the Luttinger-liquid (LL)–paramagnetic (PM) phase transition, which corresponds to the exceptional boundary across which $\RT$ symmetry is restored. In contrast, quantum discord (QD) and quantum coherence (QC) identify both phase boundaries: in addition to locating the exceptional boundary, their second-order derivatives resolve the ferromagnetic (FM)–LL transition inside the $\RT$-broken region. Moreover, measurements of QC along different directions capture the DM-induced relative rotation between the two sublattices, thereby distinguishing the staggered-DM chain from a zero-DM chain with identical effective parameters.

We investigate the Lee–Yang zeros (LYZ) of inhomogeneous anisotropic XY spin chains with Dzyaloshinskii–Moriya (DM) interactions in the complex transverse-field plane, focusing on their fundamental connection to quantum phase transitions. We systematically study uniform chains, period-2 and period-3 modulated chains, and Fibonacci quasiperiodic chains of lengths 5 and 8. As the DM coupling strength $D$ increases, the LYZ exhibit qualitatively distinct topological evolutions on the complex plane: the complex zeros of the uniform chain collapse toward the real axis; periodic chains feature either bifurcation of closed zero contours before all zeros become real or a single re-emergence of complex zeros; quasiperiodic chains exhibit repeated annihilation and revival of complex zeros. Analytical derivations demonstrate that this diverse behavior originates from DM-induced shifts of folded bands and the modulation of zero positions by anisotropic pairing at particle–hole band crossings. Our results establish a direct correspondence between LYZ topology and band deformation: isolated contact points of zeros with the real axis correspond to discrete quantum critical fields, while continuous real-zero intervals directly identify gapless chiral phases. Accordingly, beyond locating phase boundaries, LYZ can distinguish characteristic phases and serve as an intuitive probe for band folding and phase diagram restructuring.

A power series for the Wigner-Kirkwood pair commutation function for quantum statistical mechanics in classical phase space is given with terms automatically generated by recursion. The calculated second virial coefficient agrees with the measured values of helium for temperatures greater than 65 K. Prospects for a general quantum Monte Carlo algorithm are discussed.

Understanding how the performance of parameterized quantum circuits scales with available resources is important for characterizing their trainability and effective model capacity. In this study, we numerically investigate data scaling, model scaling, and compute scaling in parameterized quantum circuits and examine Lie-algebraic quantities as alternative measures of model size. In addition to the number of circuit parameters, we consider the dimension of the dynamical Lie algebra, the observable-orbit dimension, and a Jacobian effective dimension defined as the rank of the Jacobian of the parameterized observable orbit. Using a regression task with randomly generated Pauli-string generators, we observe decreasing loss with increasing training dataset size, parameter size, and number of optimization iterations over the ranges investigated. For model scaling, the dynamical Lie algebra and observable orbit dimensions rapidly saturate as the parameter size increases, whereas the Jacobian effective dimension remains strongly correlated with the parameter size and exhibits comparable scaling behavior. These results suggest that the Jacobian effective dimension provides a geometry-aware measure of the locally accessible observable degrees of freedom of finite-depth parameterized quantum circuits and may serve as a useful scaling parameter beyond the nominal parameter size.

Sparse quantum state preparation concerns an $n$-qubit target state that is a superposition of only $d \ll 2^n$ computational basis states. Existing approaches exploit this sparsity by compressing these $d$ basis states and their amplitudes onto a smaller set of qubits, called the dense register, before expanding the prepared state to the full register. Rather than relying on the permutation-based compression used in prior work, we exploit affine relationships among the binary configurations over the finite field $\operatorname{GF}(2)$ to reduce both the non-Clifford gate count and the ancillary qubit count. Invertible affine transformations over $\operatorname{GF}(2)$, comprising Gaussian elimination and all-ones-row removal, first reduce the dense register from $n$ to the rank $r$ using only Clifford gates and no ancillary qubits. An optional binary encoding stage then trades additional Toffoli gates and ancillary qubits for further compression to the minimum $\lceil\log_2 d\rceil$ dense qubits needed to represent $d$ distinct configurations. For chemically relevant wavefunctions, such as those obtained from selected configuration interaction calculations, shared electronic excitation patterns produce many of these affine relationships, enabling substantial Clifford-only compression before binary encoding. Across the molecular benchmarks, our method requires the fewest ancillary qubits among the evaluated sparse state preparation methods while maintaining comparable non-Clifford gate counts when using binary encoding.