Papers

Quantum gate benchmarking is unavoidably influenced by state preparation and measurement errors. Randomized benchmarking addresses this challenge by employing group twirling to regularize the noise channel, then provides a characterization of quantum channels that is robust to these errors through exponential fittings. In practice, local twirling gates are preferred due to their high fidelity and experimental feasibility. However, while existing RB methods leveraging local twirling gates are effective for benchmarking Clifford gates, they face fundamental challenges in benchmarking non-Clifford gates. In this work, we solve this problem by introducing the Pauli Transfer Character Benchmarking. This protocol estimates the Pauli transfer matrix elements for a quantum channel using only local Pauli operations. Building on this protocol, we develop a fidelity benchmarking method for non-Clifford gates $U$ satisfying $U^2=I$. We validate the feasibility of our protocol through numerical simulations applied to Toffoli gates as a concrete example.

Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework has been particularly fruitful, yielding many state-of-the-art classical algorithms that run efficiently in certain parameter regimes contrary to their worst- or average-case performance. Motivated by the dramatic increase in genomic data and its growing computational demands, we initiate the study of the quantum parameterized complexity of the Closest String Problem (CSP) and the related Closest Substring Problem (CSSP). We present three quantum algorithms for the CSP and one for the CSSP. Each algorithm demonstrates improved performance over classical counterparts in specific parameter regimes, highlighting the promise of quantum approaches in structured combinatorial settings. We also derive a conditional lower bound for the CSP with binary alphabets, showing that our first algorithm is tight in its dominant scaling factor.

In this work, based on an analogy with holographic confining geometries and using complexified fields, we build a holographic toy model of third order photonic exceptional points (EPs) of ternary coupled microrings with gain and loss, which makes an open, non-Hermitian quantum system. In our model, we discuss the Ferrell-Glover-Tinkham sum rule for various combinations of gain and loss systems, and numerically find the behavior of spectra which matches with the experiments. We also discuss the inhomogeneous case of a holographic lattice for three-site photonic EPs. Additionally, we numerically find the behavior of phase rigidity and the Petermann factor around EPs versus various parameters of the model. We also discuss the connections between recent developments in complexified, time-dependent entanglement entropy and EPs, and then, we connect EPs and the $\theta$-vacuum of QCD through topological structures, partition functions, and winding numbers, and find a second-order EP in a perturbed $\theta$-vacuum model. Finally, we examined a controlled non-Hermitian deformation of $\theta$-vacuum toy model, by using the Lindblad formalism and Liouvillian eigenvalues.

We present an efficient tensor-network based algorithm for finding the optimal adaptive quantum channel discrimination strategies inspired by recently developed numerical methods in quantum metrology to find the optimal adaptive channel estimation protocols. We examine the connection between channel discrimination and estimation problems, highlighting in particular an appealing structural similarity between models that admit Heisenberg scaling estimation performance, and models that admit perfect channel discrimination in finite–number of channel uses.

Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However, training a Gaussian process model using standard methods requires matrix inversions with a cubic time complexity, which poses significant computational challenges for inference on larger datasets. Quantum algorithms, such as the HHL algorithm, have been proposed as solutions that overcome the need for classical matrix inversions by efficiently solving linear systems of equations using quantum computers. However, to gain a computational advantage over classical algorithms, these algorithms require fault-tolerant quantum computers with a large number of qubits, which are not yet available. The Variational Quantum Linear Solver is a hybrid quantum-classical algorithm that solves linear systems of equations by optimizing the parameters of a variational quantum circuit using a classical computer. This method is especially suitable for noisy intermediate-scale quantum computers, as it does not require many qubits. It can be used to compute the posterior distribution of a Gaussian process by reformulating the matrix inversion into a set of linear systems of equations. We empirically demonstrate that using the Variational Quantum Linear Solver to perform inference for Gaussian process regression delivers regression quality comparable to that of classical methods.

Two classically equivalent expressions of mutual information of probability distributions (classical bipartite states) diverge when extended to quantum systems, and this difference has been employed to define quantum discord, a quantifier of quantum correlations beyond entanglement. Similarly, equivalent expressions of classical Fisher information of parameterized probability distributions diverge when extended to quantum states, and this difference may be exploited to characterize the complex nature of quantum states. By complexity of quantum states, we mean some hybrid nature which intermingles the classical and quantum features. It is desirable to quantify complexity of quantum states from various perspectives. In this work, we pursue the idea of discord and introduce an information-theoretic quantifier of complexity for quantum states (relative to the Hamiltonian that drives the evolution of quantum systems) via the notion of Fisher discord, which is defined by the difference between two important versions of quantum Fisher information: the quantum Fisher information defined via the symmetric logarithmic derivatives and the Wigner-Yanase skew information defined via the square roots of quantum states. We reveal basic properties of the quantifier of complexity, and compare it with some other quantifiers of complexity. In particular, we show that equilibrium states (or stable states, which commute with the Hamiltonian of the quantum system) and all pure states exhibit zero complexity in this setting. As illustrations, we evaluate the complexity for various prototypical states in both discrete and continuous-variable quantum systems.

While non-Hermitian bulk systems and their sensitivity to boundary conditions have been extensively studied, how a non-Hermitian boundary affects the entanglement structure of Hermitian critical systems remains largely unexplored. Here we present a fully analytical framework by exactly solving a Hermitian gapless chain with a single non-Hermitian impurity acting as a non-Hermitian boundary. When the entanglement cut is placed at the impurity, we uncover a sharp entanglement complexification transition: the logarithmic entanglement entropy retains its scaling form, but the effective central charge evolves from real to complex values, accompanied by a spectral collapse of the correlation matrix. We demonstrate that the real regime follows analytic continuation from a unitary defect conformal field theory (CFT), whereas the complex regime lies entirely beyond this framework. For the latter, we derive an analytical formula in perfect agreement with numerics. Our results reveal that a single non-Hermitian impurity can drive a Hermitian critical system into a nonunitary defect-CFT phase, establishing a rare analytically solvable platform for boundary non-Hermiticity.

Discrepancies between theory and recent qBounce data have prompted renewed scrutiny of how boundary conditions are implemented for ultracold neutrons bouncing above a mirror in Earth's gravity. We apply the theory of self-adjoint extensions to the linear gravitational potential on the half-line and derive the most general boundary condition that renders the Hamiltonian self-adjoint. This introduces a single real self-adjoint parameter $\lambda$ that continuously interpolates between the Dirichlet case and more general (Robin-type) reflecting surfaces. Building on this framework, we provide analytical expressions for the energy spectrum, eigenfunctions, relevant matrix elements, and a set of sum rules valid for arbitrary $\lambda$. We show how nontrivial boundary conditions can bias measurements of $g$ and can mimic or mask putative short-range ”fifth-force”. Our results emphasize that enforcing self-adjointness-and modeling the correct boundary physics-is essential for quantitative predictions in gravitational quantum states. Beyond neutron quantum bounces, the approach is broadly applicable to systems where boundaries and self-adjointness govern the observable spectra and dynamics.

State preparation is a cornerstone of quantum technologies, underpinning applications in computation, communication, and sensing. Its importance becomes even more pronounced in non-Markovian open quantum systems, where environmental memory and model uncertainties pose significant challenges to achieving high-fidelity control. Invariant-based inverse engineering provides a principled framework for synthesizing analytic control fields, yet existing parameterizations often lead to experimentally infeasible, singular pulses and are limited to simplified noise models such as those of Lindblad form. Here, we introduce a generalized invariant-based protocol for finite-dimensional state preparation under arbitrary noise conditions. We transform the finite-dimensional control problem into the equivalent problem for a single-qubit, by restricting the dynamics to a designed SU(2) subspace. The control protocol then proceeds in two-stages: first, we construct a family of bounded pulses that achieve perfect state preparation in a closed system; second, we identify the optimal member of this family that minimizes the effect of noise. The framework accommodates both (i) characterized noise, enabling noise-aware control synthesis, and (ii) uncharacterized noise, where a noise-agnostic variant preserves robustness without requiring a master-equation description. Numerical simulations demonstrate high-fidelity state preparation across diverse targets while producing smooth, hardware-feasible control fields. This singularity-free framework extends invariant-based control to realistic open-system regimes, providing a versatile route toward robust quantum state engineering on NISQ hardware and other platforms exhibiting non-Markovian dynamics.

Recent quantum-inspired methods based on the Simulated Annealing (SA) algorithm have shown strong potential for solving combinatorial optimization problems. However, Grover's algorithm [1] in gate-based quantum computing offers only a quadratic speedup, which remains impractical for large problem sizes. This paper proposes a hybrid approach that integrates SA with Grover's algorithm to achieve sub-exponential speedup, thereby improving its industrial applicability. In enzyme fermentation, variables such as temperature, stirring, wait time, pH, tryptophan, rice flour and so on are encoded by 625 binary parameters, defining the space of possible enzyme formulations. We aim to find a binary configuration that maximizes the active ingredient, formulated as a 625-bit QUBO which is generated by historical experiments and AI techniques. Minimizing the QUBO cost corresponds to maximizing the active ingredient. This case study demonstrates that our hybrid method achieves sub-exponential speedup through gate-based quantum computing.

Protein folding is one of the age-old biological problems that refers to the mechanism of understanding and predicting how a protein's linear sequence of amino acids folds into its specific three dimensional structure.This structure is critical, as a protein's functionality is inherently linked to its final folded form. Misfolding can lead to severe diseases such as Alzheimer's and cystic fibrosis, highlighting the biological and clinical importance of understanding protein folding mechanisms. This work presents a novel turn based encoding optimization algorithm for predicting the folded structures of peptides and small proteins. Our approach builds upon our previous research, where our objective function focused on hydrophobic collapse, a fundamental phenomenon underlying the protein folding process. In this work, we extend that framework by not only incorporating hydrophobic interactions but also including all non bonded interactions modeled using the Miyazawa Jernigan potential. We constructed a Hamiltonian from the defined objective function that encodes the folding process on a three dimensional face centered cubic lattice, offering superior packing efficiency and a realistic representation of protein conformations. This Hamiltonian is then solved using classical and quantum solvers to explore the vast conformational space of proteins. To identify the lowest-energy folded configurations, we utilize the Variational Quantum Eigensolver implemented on IBM 133 qubit hardware. The predicted structures are validated against experimental data using root mean square deviation as a metric and compared against classical simulated annealing and molecular dynamics simulation results. Our findings highlight the promise of hybrid classical and quantum approaches in advancing protein folding predictions, particularly for sequences with low homology.

Resonant phase-matched Josephson traveling-wave parametric amplifiers (RPM JTWPAs) play a key role in quantum computing and quantum information applications due to their low-noise, broadband amplification, and quadrature squeezing capabilities. This research focuses on optimizing RPM JTWPAs through numerical optimization of parametrized resonator elements to maximize gain, bandwidth and quadrature squeezing. Our results show that optimized resonators can increase the maximum gain and squeezing by more than 5 dB in the ideal noiseless case. However, introducing the effects of loss through a lumped-element model reveals that gain saturates with increasing loss, while squeezing modes degrade rapidly, regardless of resonator optimization. These results highlight the potential of resonator design to significantly improve amplifier performance, as well as the challenges posed by current fabrication technologies and inherent losses.

We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted as a Strang splitting combined with a Taylor expansion. Based on this formulation, we develop a numerically exact iterative method for simulation system-bath dynamics. We propose two numerical schemes, which are first-order and second-order in time step $\Delta t$ respectively. We perform a rigorous numerical analysis to establish the convergence orders of both schemes, proving that the global error decreases as $\mathcal{O}(\Delta t)$ and $\mathcal{O}(\Delta t^2)$ for the first- and second-order methods, respectively. In the second-order scheme, we can safely omitted most terms arising from the Strang splitting and Taylor expansion while maintaining second-order accuracy, leading to a substantial reduction in computational complexity. For the second-order method, we achieves a time complexity of $\mathcal{O}(M^3 2^{2K_{\max}} K_{\max}^2)$ and a space complexity of $\mathcal{O}(M^2 2^{2K_{\max}} K_{\max})$ where $M$ denotes the number of system levels and $K_{\max}$ the number of time steps within the memory length. Compared with existing methods, our approach requires substantially less memory and computational effort for multilevel systems ($M\geqslant 3$). Numerical experiments are carried out to illustrate the validity and efficiency of our method.

Quantum annealing (QA) is a practical model of adiabatic quantum computation, already realized on hardware and considered promising for combinatorial optimization. However, its performance is critically dependent on the annealing schedule due to hardware decoherence and noise. Designing schedules that account for such limitations remains a significant challenge. We propose a trust region Bayesian optimization (TuRBO) framework that jointly tunes annealing time and Fourier-parameterized schedules. Given a fixed embedding on a quantum processing unit (QPU), the framework employs Gaussian process surrogates with expected improvement to balance exploration and exploitation, while trust region updates refine the search around promising candidates. The framework further incorporates mechanisms to manage QPU runtime and enforce feasibility under hardware constraints efficiently. Simulation studies demonstrate that TuRBO consistently identifies schedules that outperform random and greedy search in terms of energy, feasible solution probability, and chain break fraction. These results highlight TuRBO as a resource-efficient and scalable strategy for annealing schedule design, offering improved QA performance in noisy intermediate-scale quantum regimes and extensibility to industrial optimization tasks.

We introduce a quantum voting protocol that uses superposition and entanglement to enable anonymous voting with trusted voting machines, in a centralized setting with a single machine and in a distributed setting where several machines are linked to a voting center through quantum channels. A voter selects a candidate through a restricted ballot interface; the machine encodes the vote as a phase-flip operation, controlled by the voter's identity register, on an entangled candidate state. Tallying is performed by interference with a reference branch followed by a measurement of the candidate register, which reproduces the vote distribution without iterative classical counting. Because every tallying run consumes the quantum state, the machines store the cast choices classically and replay the voting stage for each run. The protocol uses only basic quantum gates (Hadamard and controlled-Z). We provide analytical examples (4 voters with 2 candidates and 8 voters with 3 candidates) and numerical experiments that simulate ideal conditions, depolarizing, memory, readout, and gate noise, faulty or mistaken ballots, larger instances with confidence intervals, and sampling convergence. The simulations reproduce the theoretical tally probabilities in the ideal case and show how the tally is distorted by noise and by faulty ballots; no error correction or mitigation is applied. Voter anonymity is formalized as the indistinguishability of tallying transcripts under vote permutations, and an identity-dephasing step renders the identity register exactly maximally mixed under the stated trust assumptions. The numbers of protocol runs needed for exact tallying and for winner identification are analyzed explicitly.

Quantum error correction code discovery has relied on algebraic constructions with predetermined structure or computational search lacking equilibrium-topology analysis. We introduce a game-theoretic framework recasting code optimization as strategic interactions between competing objectives, where Nash equilibria systematically generate codes with desired properties. We validate the framework by demonstrating it rediscovers the optimal $[\![15,7,3]\!]$ quantum Hamming code in 20% of independent runs (Calderbank-Shor-Steane 1996) from competing objectives without predetermined algebraic structure, with equilibrium analysis providing transparent mechanistic insights into why this topology emerges. Applied across seven objectives – distance maximization, hardware adaptation, rate-distance optimization, cluster-state generation, surface-like topologies, connectivity enhancement, and maximization of the quantum Fisher information $\mathcal{F}_Q$ (which quantifies, via the Cramér–Rao bound, the metrological sensitivity of the encoded codespace) – the framework generates distinct code families through objective reconfiguration rather than algorithm redesign. Scalability to hardware-relevant sizes is demonstrated at $n=100$ qubits, discovering codes including $[\![100,50,4]\!]$ with distance-4 protection and 50% encoding rate, with tractable $O(n^3)$ per-iteration complexity enabling discovery in under one hour. This work opens research avenues at the intersection of game theory and quantum information, providing systematic, interpretable frameworks for quantum system design.

High-order harmonic generation (HHG) in solids has emerged as a versatile platform for exploring ultrafast and quantum-coherent phenomena in condensed matter. Recent advances reveal Berry-phase and topological effects in harmonic emission, strong-field control of excitons and lattice motion, the generation of nonclassical light states driven by quantum and squeezed fields, and the emergence of orbital-angular-momentum transfer in solid-state high-harmonic generation. Nanostructured and hybrid plasmonic-semiconductor platforms enable enhanced and spectrally tunable HHG, while interferometric and cryogenic setups allow attosecond-resolved phase measurements. On the theoretical side, multiband and topological models incorporating dephasing, propagation, and electron-hole coherence effects have deepened our understanding of the interplay between interband and intraband dynamics. These developments establish solid-state HHG as a bridge between ultrafast spectroscopy, quantum optics, and material science, paving the way toward quantum-engineered attosecond sources and coherent control of light-matter interactions in solids.

We investigate the physical consequences of having a spectrum that satisfies random matrix theory (RMT) for generic Lindbladians, and compare its implications for spatially local and completely random Lindblad dynamics in one spatial dimension. We find that Lindbladians whose spectrum is described by RMT exhibit quasiuniversal early-time dynamics for quantities nonlinear in the density matrix, in the sense that for generic, highly entangled initial states, the early time evolution is independent of the choice of initial state. We numerically investigate how locality generically imposes constraints on the size-dependence of Lindblad eigenoperators. This size dependence implies that linear observables, such as expectation values of local operators, are highly sensitive to eigenmodes outside the bulk of the spectrum in the thermodynamic limit, and plays a central role in limiting operator growth in the presence of dissipation. We find that when single-site dissipation dominates, an operator's decoherence scales approximately linearly with its Pauli weight, even in the presence of two-site jump operators. When two-site only dissipation dominates, however, this generic trend in operator size can be violated for numerically accessible system sizes, leading to long-lived high Pauli-weight operators.

Utilizing tantalum (Ta) in superconducting circuits has led to significant improvements, such as high qubit lifetimes and quality factors in both qubits and resonators, underscoring the importance of material optimization in quantum device performance. In this work, we explore superconducting gap engineering in Ta-based devices as a strategy to expand the range of viable host materials. By alloying 20 atomic percent hafnium (Hf) into Ta thin films, we achieve a superconducting transition temperature ($T_c$) of 6.09~K, as measured by DC transport, reflecting an increased superconducting gap. We systematically vary deposition conditions to control film orientation and transport properties of the Ta-Hf alloy films. The enhancement in $T_c$ is further confirmed by microwave measurements at millikelvin temperatures. Despite the 40% increase in $T_c$ relative to pure Ta, the loss contributions from two-level systems (TLS) and quasiparticles (QPs) remain unchanged in the low-temperature regime. These findings highlight the potential of material engineering to improve superconducting circuit performance and motivate further exploration of engineered alloys for quantum technologies.

We show that chaos-assisted tunneling (CAT) imposes an intrinsic limit to the protection of Kerr-cat qubits. In the static effective description, tunneling between the quasidegenerate cat states can be exponentially suppressed, ensuring long lifetimes. However, our Floquet analysis reveals that when the nonlinearities increase, chaotic states mediate tunneling between the cat states, producing large quasienergy splittings. We compute tunneling rates using both full quantum simulations and semiclassical WKB theory, finding quantitative agreement and confirming that the splittings are directly linked to chaos. These results provide the first evidence of CAT in the Kerr-cat qubit and demonstrate that chaos sets a fundamental bound on the coherence of dynamically protected superconducting qubits.

When quantum systems are shared by multiple parties in a network, the measurement outcomes of the parties can exhibit non-classical correlations, i.e., correlations that cannot be obtained if the parties shared classical systems instead. This phenomenon is known as quantum nonlocality and is typically demonstrated in the Bell scenario. However, the Bell scenario is fundamentally simpler to investigate than general networks, since the latter come with non-convex optimization problems that are often intractable. The triangle network is one of the simplest networks exhibiting this non-convexity due to the presence of three independent sources. Although some special cases of quantum nonlocality are known in the triangle network, general methods to certify classical incompatibility are still lacking, which suggests that our understanding of networks is still rather limited. For instance, the Elegant Joint Measurement (EJM) distribution is a simple and highly-symmetric outcome distribution that can be obtained with quantum systems and measurements in the triangle network. This distribution was conjectured to be non-classical eight years ago. In this article, we provide the first proof of non-classicality of the EJM distribution. To do so, we show how to combine inflation, a causal inference technique, with powerful symmetry reductions and Frank-Wolfe algorithms for large-scale optimization. We then use these methods to obtain computer-assisted proofs of non-classicality in exact arithmetic.

The interplay of non-classical volume, von Neumann entropy, entropy production, and ergotropy is investigated in various open quantum systems. Two categories of open quantum system models are utilized: spin-spin and spin-boson interaction models. The spin-spin interaction models include the quantum collision and central spin models. On the other hand, the spin-boson interaction models consist of non-Markovian amplitude damping channel, Markovian generalized amplitude damping channel, and the Jaynes-Cummings model. Across these various open quantum systems, universal interrelations emerge, where the non-classical volume shows contrasting evolution with entropy, and entropy production contrasts with ergotropy. The initial state of the reservoir in these open quantum systems is shown to have an impact on these interrelations. These findings establish an interesting link between quantum information and the thermodynamics of open quantum systems.

An algorithm which encodes the $L\times L$ 2D toric code logical state with a circuit of depth $2L+1$, using only local controlled-NOT($CX$) and Hadamard($H$) gates, is presented.

We develop a topological framework for preparing families of non-stabilizer states, and computing their entanglement entropies, in $SU(2)_1$ Chern-Simons theory. Using the Kac-Moody algebra, we construct Pauli and Clifford operators as path integrals over 3-manifolds with Wilson loop insertions, enabling an explicit topological realization of $W_n$ and Dicke states, as well as their entanglement properties. We further establish a correspondence between Clifford group action and modular transformations generated by Dehn twists on genus-$g$ surfaces, linking the mapping class group to quantum operations. Our results extend existing topological constructions for stabilizer states to include families of non-stabilizer states, improving the geometric interpretation of entanglement and quantum resources in topological quantum field theory.

Quantum Genetic Algorithms (QGAs) are an emerging field of multivariate quantum optimization that emulate Darwinian evolution and natural selection, with vast applications in chemistry and engineering. The appropriate application of fitness functions and fitness selection are the problem-encoding step and the slowest step in designing QGAs for specific physical applications. In this paper, we provide a comprehensive review of these crucial steps. Our survey maps cases of quantum advantage, classifies and illustrates QGAs and their subroutines, and discusses the two main physical problems tackled by QGAs: potential energy minimization of particles on a sphere, and molecular eigensolving. We conclude that the encoding used by the Thomson problem is a decisive step toward the use of QGAs in a variety of physical applications, while Grover's search as a selection step in Reduced QGAs is the main driver of quantum speedup.

We introduce a non-Hermitian photonic filter that harnesses dissipation to selectively isolate a desired topological state. In science and engineering, dissipation is often used to filter incoherent waves, producing a pure coherent output. Here, we apply this principle to topological states, creating a linear filter that effectively isolates a specific topological state regardless of the initial input's coherence properties. This approach creates a dissipation-free topological subspace, where the desired states are preserved and their topological protection is enhanced. Our work provides a versatile and simple method for topological state selection, opening the door to new applications in integrated topological photonics.

Credit scoring is a high-stakes task in financial services, where model decisions directly impact individuals' access to credit and are subject to strict regulatory scrutiny. While Quantum Machine Learning (QML) offers new computational capabilities, its black-box nature poses challenges for adoption in domains that demand transparency and trust. In this work, we present IQNN-CS, an interpretable quantum neural network framework designed for multiclass credit risk classification. The architecture combines a variational QNN with a suite of post-hoc explanation techniques tailored for structured data. To address the lack of structured interpretability in QML, we introduce Inter-Class Attribution Alignment (ICAA), a novel metric that quantifies attribution divergence across predicted classes, revealing how the model distinguishes between credit risk categories. Evaluated on two real-world credit datasets, IQNN-CS demonstrates stable training dynamics, competitive predictive performance, and enhanced interpretability. Our results highlight a practical path toward transparent and accountable QML models for financial decision-making.

We show that odd order Rényi entropies $S^{(2q+1)}$ of a system of interacting scalar fields can be calculated as the free energy of $2q+1$ replicas of the system with additional quadratic inter-replica couplings in the subsystem at the time of measurement of the entropy. These couplings replace boundary field matching conditions. This formalism works both in and out of thermal equilibrium, for closed as well as open quantum systems, and provides a general dictionary between measurable correlation functions and entanglement entropy. $S^{(2q+1)}$ can be analytically continued to calculate the von Neumann entropy $S^{\mathrm{vN}}$. We provide an exact formula relating $S^{(2q+1)}$ and $S^{\mathrm{vN}}$ with correlation functions in a non-interacting theory. For interacting theories, we provide rules for constructing all possible Feynman diagrams for $S^{(2q+1)}$. We show that the boundary matching conditions cannot be completely eliminated while calculating Rényi entropies of even order due to presence of zero modes in replica space.

We apply the correlation matrix Hamiltonian reconstruction technique to the two-dimensional Gutzwiller-projected Fermi sea and {\pi}-flux states on finite-sized square and triangular lattices. Our results indicate no spin Hamiltonian with simple local interaction terms stabilizes such states for finite system sizes. We develop a quantitative assessment of the importance of local interactions to the stabilization of these liquid states. Lastly, we systematically assess arguments for the origin of local terms driving a Gutzwiller-projected ground state.

Variational methods have offered controllable and powerful tools for capturing many-body quantum physics for decades. The recent introduction of expressive neural network quantum states has enabled the accurate representation of a broad class of complex wavefunctions for many Hamiltonians of interest. We introduce a first-principles method for building neural network representations of many-body excited states by adiabatically continuing eigenstates of simple Hamiltonians into the strongly correlated regime. With controlled access to the full many-body gap, we obtain accurate estimates of critical exponents. Successive eigenstate estimates can be run entirely in parallel, enabling precise targeting of excited-state properties without reference to the rest of the spectrum, opening the door to large-scale numerical investigations of universal properties of entire phases of matter.