Papers

We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$ qLDPC code with constant encoding rate and distance $d = \Omega(n^{1/a})$. For good qLDPC codes, the time overhead is minimized and reaches $O(d^{1+o(1)})$. In contrast, code surgery based on gauging measurement and brute-force branching requires a time overhead of $O(dw^{1+o(1)})$, where $d\leq w\leq n$. Thus, our scheme is asymptotically faster for all codes with $a < 2$. This speedup is achieved by developing techniques that enable parallelized code surgery under constant qubit overhead and leverage classical locally testable codes for efficient resource state preparation. These results establish a new paradigm for accelerating fault-tolerant quantum computation on qLDPC codes, while maintaining low overhead and broad applicability.

The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of constructing solvable models from known instances. In doing so, we relate the evolution of deformed and undeformed theories and investigate their complexity. For a certain class of deformations, the resulting Krylov subspace is unchanged, and we observe time evolutions with a reorganized basis. The tridiagonal form of the generator in the Krylov space is maintained, and we obtain generalized Toda equations as a function of the deformation parameters. The imaginary-time-like evolutions can be described by real-time unitary ones. As possible applications, we discuss coherent Gibbs states for thermodynamic systems, for which we analyze the survival probability, spread complexity, Krylov entropy, and associated time-averaged quantities. We further discuss the statistical properties of random matrices and supersymmetric systems for quadratic deformations.

Tensor-network renormalization group (TNRG) is an efficient real-space renormalization group method for studying the criticality in both classical and quantum lattice systems. Exploiting symmetries of a system in a TNRG algorithm can simplify the implementation of the algorithm and can help produce correct tensor RG flows. Although a general framework for considering a global on-site symmetry has been established, it is still unclear how to incorporate a lattice symmetry in TNRG. As a first step for lattice symmetries, we propose a method to incorporate the lattice-reflection symmetry in the context of a TNRG with entanglement filtering in both two and three dimensions (2D and 3D). To achieve this, we write down a general definition of lattice-reflection symmetry in tensor-network language. Then, we introduce a transposition trick for exploiting and imposing the lattice-reflection symmetry in two basic TNRG operations: projective truncations and entanglement filtering. Using the transposition trick, the detailed algorithms of the TNRG map in both 2D and 3D are laid out, where the lattice-reflection symmetry is preserved and imposed. Finally, we demonstrate how to construct the linearization of the TNRG maps in a given lattice-reflection sector, with the help of which it becomes possible to extract scaling dimensions in each sector separately. Our work paves the way for understanding the lattice-rotation symmetry in TNRG.

Decomposing arbitrary unitary transformations into physically realizable operations is fundamental to quantum information, quantum control, and linear optics. Layered programmable architectures implement such transformations by alternating tunable phase masks with fixed mode mixers. However, establishing their universality at fixed depth remains challenging: we show that neither a sufficient parameter count nor successful synthesis of sampled targets guarantees global coverage. We prove that an architecture is universal exactly when every reachable transformation can absorb a diagnostic input Fourier multiport by reprogramming its phase masks. The associated Fourier absorption residual (FAR) requires no external target ensemble, vanishes exactly for universal architectures, and bounds worst-target synthesis error. For four-mode Fourier architectures, a permutation obstruction rules out universality with five masks, even under small unitary mixer perturbations, whereas a constructive factorization establishes universality with seven. Beyond exact universality, comparison with a universal reference of the same depth yields certified uniform approximation bounds in terms of unitary mixer errors. Finally, numerical simulations using a geodesic phase optimizer illustrate the distinction between Fourier absorption and direct target synthesis.

Active control of the radiative properties of quantum emitters through engineered light-matter interactions is a key challenge in nanophotonics and quantum optics. In this work, we demonstrate dynamic modulation of dipole's decay rate by exploiting the tunable plexcitonic modes (graphene plasmons and QD-excitons) in the strong coupling regime. By integrating a quantum dot inside a graphene spherical shell and tuning the local optical response of hybrid modes via voltage-bias, we achieve continuous and reversible control over the decay rate, leading to significant enhancement or suppression of dipole emission from near- to far-infrared regime. Furthermore, the plexcitonic peaks shows much sharper linewidths in contrast to bare graphene plasmons even in the off-resonant coupling which indicates higher sensitivity of the systems at tuned wavelengths. We demonstrate the phenomenon with the numerical solution of 3D Maxwell's equations using MNPBEM tool. Our approach demonstrate a versatile platform for programmable emission control and offer a promising pathway for developing reconfigurable quantum photonic devices, such as tunable single-photon sources and ultrafast optical switches.

The closest vector problem (CVP) is a fundamental optimization problem in lattice-based cryptography and its conjectured hardness underpins the security of lattice-based cryptosystems. Furthermore, Schnorr's lattice-based factoring algorithm reduces integer factoring (the foundation of current cryptosystems, including RSA) to the CVP. Recent work has investigated the inclusion of a heuristic CVP approximation `refinement' step in the lattice-based factoring algorithm, using quantum variational algorithms to perform the heuristic optimization. This coincides with the emergence of probabilistic computing as a hardware accelerator for randomized algorithms including tasks in combinatorial optimization. In this work we investigate the application of probabilistic computing to the heuristic optimization task of CVP approximation refinement in lattice-based factoring. We present the design of a probabilistic computing algorithm for this task, a discussion of `prime lattice' parameters, and experimental results showing the efficacy of probabilistic computing for solving the CVP as well as its efficacy as a subroutine for lattice-based factoring. The main results found that (a) this approach is capable of finding the maximal available CVP approximation refinement in time linear in problem size and (b) probabilistic computing used in conjunction with the lattice parameters presented can find the composite prime factors of a semiprime number using up to 100x fewer lattice instances than similar quantum and classical methods.

We formulate a Floquet-Markov Lindblad master equation for translationally cold two-level atoms driven by a strong monochromatic wave and coupled to a common electromagnetic bath. The resulting dipole-dipole interaction reproduces the anisotropic Heisenberg model.

We study the decoherence of an anisotropic anharmonic oscillator in a magnetic field, coupled to a bath of harmonic oscillators at high and low temperatures. We solve the anharmonic oscillator problem using perturbative techniques and derive the non-Markovian master equation in the weak coupling limit. The anharmonicity parameter {\alpha} enhances decoherence due to the deconfining effect of anharmonicity. The oscillatory nature of the time evolution of heating function indicates information backflow. The von-Neumann entropy is also calculated for the system, which increases with {\alpha}, consistent with the deconfining effect noted in the decoherence analysis. We have also proposed a cold ion experimental set up for testing our theoretical predictions. The study is of relevance to the domain of quantum technology where decoherence significantly affects the performance of a quantum computer.

Quantum emitters coupled to traveling photons in waveguides, known as waveguide quantum electrodynamics (WQED), offer a powerful platform for understanding light-matter interactions and underpinning emergent quantum technologies. While WQED has been extensively studied in one dimension, two-dimensional (2D) WQED remains largely unexplored, where novel photonic scattering phenomena unique to higher dimensions are expected. Here, we present a comprehensive scattering theory for 2D WQED based on the Green function method. We show that the mean displacement between emitted and injected photons serves as a quantum analogue of the Goos-Hänchen shift. When a photon is injected into a single off-centered port, the quantum Goos-Hänchen (QGH) shift can be enhanced in backward scattering under resonant conditions with subradiant states. When a photon is injected into the center port, there is no QGH shift due to the mirror symmetry of structure. However, for multiple-port injection with transverse momentum, the QGH shift is recovered and proportional to the derivative of phase with respect to transverse momentum. Unlike the classical Goos-Hänchen shift, these effects can be flexibly tuned by the injected photon's frequency. Our work provides a general framework for exploring and manipulating photonic scattering in complex WQED networks.

We propose a symmetry-adapted eigensolver for strongly correlated systems that separates where the wave function is sampled from where it is defined. The lattice is divided into equal blocks: parallel quantum circuits absorb the entanglement within each block, while a matrix product state (MPS) backbone bridges the blocks and restores global correlations. The resulting real-space amplitude $\phi(a_{\rm real})$ acts only as a sample generator—configurations are drawn from $|\phi(a_{\rm real})|^2$ directly, block by block, without any Markov chain. The variational state itself is defined in a symmetry-adapted basis by two separate rules: the modulus of $\psi(a_{\rm symm})$ is the square root of the total weight accumulated over the entire equivalence class, $\widetilde{p}(a_{\rm symm})=\sum_{a_{\rm real}\in\{g a_{\rm repr}\}}|\phi(a_{\rm real})|^2$, whereas its phase is inherited from the single representative amplitude $\phi(a_{\rm repr})$. The modulus rule is what makes the scheme both exact and cheap: the distribution$\widetilde{p}(a_{\rm symm})$ sampled in the symmetric basis is exactly the one induced by the mapping from the real-space distribution $p(a_{\rm real})$, so every generated configuration is an unbiased sample of $|\psi(a_{\rm symm})|^2$; the phase rule then fixes the only freedom that remains. Because amplitudes within a class are combined in probability rather than summed with symmetry characters, $\psi$ is not a group projection of the circuit-MPS state; the class-wide aggregation instead supplies long-range, symmetry-enforced entanglement that the MPS never has to carry itself.

In this work, we introduce a solid-state platform for building quantum simulators using implanted spin centers in solid-state materials. We build upon the proposal for an $S=1$ chain of spin centers coupled through the magnetic dipole-dipole interaction and subjected to an external magnetic field as a quantum simulator for critical floating phases. We introduce another magnetic field and map the system to the interacting Kitaev chain. This setup, tunable through the applied fields and the orientation of the spin centers within the crystal, exhibits a variety of rich quantum behavior which notably includes floating phases, a $Z_2$ symmetry-breaking phase, and lines of both Berezinskii-Kosterlitz-Thouless (BKT) and Pokrovsky-Talapov transitions. Furthermore, we employ several novel methods to calculate the Luttinger liquid parameter in our model with incommensurate correlations. We find that these methods provide a route to identify BKT transitions with less computational resources than utilizing entanglement entropy and central charge.

We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a unitary matrix generated by a parameterized quantum circuit with universal expressivity, while a classical optimizer adjusts circuit parameters under the global unitary constraint. As a representative application, we consider the non-unitary propagator of a Lindbladian superoperator acting on the vectorized density matrix, which is relevant for simulating open quantum systems. We further validate the approach experimentally on superconducting devices in the Quafu quantum cloud computing cluster. Compared with standard dilation protocols, our method significantly reduces quantum resource requirements and improves robustness against device noise, achieving high-fidelity simulation. Its generality also enables compatibility with non-Markovian dynamics and Kraus-operator-based evolutions, providing a practical pathway for the noise-resilient simulation of non-unitary processes on near-term quantum hardware.

The $\mathbb{Z}_2$ lattice gauge theory is a paradigmatic model that exhibits gauge-field-mediated-confinement of pairs of particles into mesons, drawing connections to quantum chromodynamics. In the absence of any additional attractive interactions between particles, mesons are not known to bind in this model. Here, we show that resonant pair-production terms give rise to two separate mechanisms to form stable “hadron” bound states of two mesons: either induced by an effective attractive interaction, or a new dynamical binding mechanism induced by an effective repulsion. The repulsively bound hadron is a high-energy state stabilized by being energetically separated from the two-meson continuum through quantum fluctuations of the gauge fields. We study the dynamical formation of this bound state starting from local excitations. We use matrix product state techniques based on the time-evolving block decimation algorithm to perform our numerical simulations and analyze the effect of model parameters on hadron formation. Furthermore, we derive an effective model that explains its formation. Our findings are amenable to experimental observation on modern quantum hardware such as superconducting qubits, trapped ions, and Rydberg atom arrays.

We present two new quantum algorithms for reaction-diffusion equations that employ the truncated Chebyshev polynomial approximation. This method is employed to numerically solve the ordinary differential equation emerging from the linearization of the associated nonlinear differential equation. In the first algorithm, we use the matrix exponentiation method (Patel et al., 2018), while in the second algorithm, we repurpose the quantum spectral method (Childs et al., 2020). Our main technical contribution is to derive the sufficient conditions for the diagonalization of the Carleman embedding matrix, which is indispensable for designing both quantum algorithms. We supplement this with an efficient iterative algorithm to diagonalize the Carleman matrix. Our first algorithm has gate complexity of O(d$\cdot$log(d)+T$\cdot$polylog(T/$\varepsilon$)). Here $d$ is the size of the Carleman matrix, $T$ is the simulation time, and $\varepsilon$ is the approximation error. The second algorithm is polynomial in $log(d)$, $T$, and $log(1/\varepsilon)$ - the gate complexity scales as O(polylog(d)$\cdot$T$\cdot$polylog(T/$\varepsilon$)). In terms of $T$ and $\varepsilon$, this is comparable to the speedup gained by the current best known quantum algorithm for this problem, the truncated Taylor series method (Costa et.al., 2025). Our approach has two shortcomings. First, we have not provided an upper bound, in terms of d, on the condition number of the Carleman matrix. Second, the success of the diagonalization is based on a conjecture that a specific trigonometric equation has no integral solution. However, we provide strategies to mitigate these shortcomings in most practical cases.

This News & Views article provides a perspective on the 2025 Nobel Prize in Physics, including the groundbreaking discovery of macroscopic quantum tunneling and energy quantization in superconducting circuits, the history and causes giving rise to this breakthrough, and its impact on subsequent progress in quantum computing.

Hayashi's Pinching Inequality, which establishes a matrix inequality between a semidefinite matrix and a multiple of its "pinched" version via a projective measurement, has found many applications in quantum information theory and beyond. Here, we show a very simple proof of it, which lends itself immediately to natural generalisations where the different projections of the measurement have different weights, and where the matrix inequality can be reversed. As an application we show how the generalised pinching inequality in the case of binary measurements gives rise to a novel gentle measurement lemma, where matrix ordering replaces approximation in trace norm.

Although coupled ion-electron transfer (CIET) has emerged as a powerful framework to rationalize the kinetics of Faradaic reactions, its mechanism has lacked a fully microscopic, first-principles description. Here we show that the coupling of electron-transfer to ion-transfer can be understood as an extension of Marcus theory in which the ensemble of diabatic nuclear configurations is conditioned on a classical collective variable describing the interfacial anisotropy. This formalism enables direct construction of the CIET free-energy surface from constrained ab initio trajectories, providing a first-principles route to electrochemical current-overpotential relations. We demonstrate this method for CO2 redox on a gold electrode and find that the resulting two-dimensional saddle-point barriers differ substantially from one-dimensional treatments that consider only electron- or ion-transfer coordinates individually.

Quantum networks are a backbone of future quantum technologies thanks to their role in communication and scalable quantum computing. However, their performance is challenged by noise and decoherence. We propose a self-configuring approach that integrates superposed quantum paths with variational quantum optimization techniques. This allows networks to dynamically optimize the superposition of noisy paths across multiple nodes to establish high-fidelity connections between different parties. Our framework is in principle capable of adapting to unknown noise without requiring detailed characterization or benchmarking of the corresponding quantum channels. We also discuss the role of vacuum coherence, a quantum effect central to path superposition that impacts protocol performance. Additionally, we demonstrate that our approach remains beneficial even in the presence of imperfections in the generation of path superposition.

Quantum annealing is a framework for solving combinatorial optimization problems. While it offers a promising path towards a practical application of quantum hardware, its performance in real-world devices is severely limited by environmental noise that can degrade solution quality. We investigate the suppression of local field noise in quantum annealing protocols through the periodic application of dynamical decoupling pulses implementing global spin flips. As test problems, we construct minimal Multiple Object Tracking QUBO instances requiring only five and nine qubits, as well as cutting stock instances of five and six qubits. Moreover, using the Sherrington–Kirkpatrick model, we demonstrate the robustness of our protocol to problem structure and size. To further place our results in a practical context, we consider a trapped-ion platform based on magnetic gradient-induced coupling as a reference architecture, using it to define experimentally realistic noise and coupling parameters. We show that external magnetic field fluctuations, typical in such setups, significantly degrade annealing fidelity, while moderate dynamical decoupling pulse rates, which are achievable in current experiments, restore performance to near-ideal levels. Our analytical and numerical results reveal a universal scaling behavior, with fidelity determined by a generalized parameter combining noise amplitude and dynamical decoupling pulse interval. While our analysis is grounded in the trapped-ion platform, the proposed noise mitigation strategy and resulting performance improvements are applicable to a broad range of quantum annealing implementations and establish a practical and scalable route for error mitigation in near-term devices.

Plasmonic nanoantennas offer new avenues to manipulate the propagation of light in materials due to their near field enhancement and ultrafast response time. Here we investigate the epsilon-near-zero (ENZ) response in an L-shaped nanoantenna structure under the phenomenon of plasmonic analog of enhancement in the index of refraction. Using a quantum mechanical approach, we analyze the modulation in the response of probe field and emergence of ENZ frequency region both in the linear and nonlinear plasmonic system. We also demonstrate the active tuning of ENZ frequency region in a nanoantenna structure by modulating the phase of control pulse. The analytical and 3D FDTD simulation results show a significant spectral shift in the ENZ modes. Our proposed method offers the possibility to design and control optical tunable ENZ response in plasmonic metasurfaces without the use of ENZ material. Such metasurfaces can be used in on-chip photonic integrated circuits, further localization of incident fields, slow light operations and various quantum technologies.

We present a quantum algorithm for simulating rovibrational Hamiltonians on fault-tolerant quantum computers. The method integrates exact curvilinear kinetic energy operators and general-form potential energy surfaces expressed in a hybrid finite-basis/discrete-variable representation. The Hamiltonian is encoded as a unitary quantum circuit using a quantum read-only memory construction based on the Walsh-Hadamard transform, enabling high-accuracy quantum phase estimation of rovibrational energy levels and dynamics simulations. Our technique provides asymptotic reductions in both logical qubit count and T-gate complexity that are exponential in the number of atoms and at least polynomial in the total Hilbert-space size, relative to existing block-encoding techniques based on linear combinations of unitaries and variational basis representation. Compared with classical variational methods, it offers exponential memory savings and polynomial reductions in time complexity. The quantum volume required for computing the rovibrational spectrum of water can be reduced by up to 100 000 times compared with other quantum methods, increasing to at least 1 million for a classically intractable 30-dimensional (12-atom) molecular system. For this case with a six-body coupled potential, estimating spectroscopic-accuracy energy levels would require about three months on a 1 MHz fault-tolerant quantum processor with fewer than 300 logical qubits, versus over 30 000 years on the fastest current classical supercomputer. These estimates are approximate and subject to technological uncertainties, and realizing the asymptotic advantage will require substantial quantum resources and continued algorithmic progress.

Intense light-matter interaction largely relies on the use of high-power light sources, creating fields comparable to, or even stronger than, the field keeping the electrons bound in atoms. Under such conditions, the interaction induces highly nonlinear processes such as high harmonic generation, in which the low-frequency photons of a driving laser field are upconverted into higher-frequency photons. These processes have enabled numerous groundbreaking advances in atomic, molecular, and optical physics, and they form the foundation of attosecond science. Until recently, however, such processes were typically described using semi-classical approximations, since the quantum properties of the light field were not required to explain the observables. This has changed in the recent past. Ongoing theoretical and experimental advances show that fully quantized descriptions of intense light-matter interactions, which explicitly incorporate the quantum nature of the light field, open new avenues for both fundamental research and technological applications at the fully quantized level. These advances emerge from the convergence of quantum optics with strong-field physics and ultrafast science. Together, they have given rise to the field of quantum optics and quantum electrodynamics of strong-field processes.

Modern mechanical sensors increasingly measure motion with precision sufficient to resolve the fundamental thermal noise floor over a broad band. Compared to traditional sensors – achieving this limit only near resonance – this capability provides massive gains in acquisition rates along with access to otherwise obscured transient signals. However, these stronger measurements of motion are naturally accompanied by increased back-action. Here we show how resolving the broadband thermal noise spectrum reveals back-action-induced correlations in the noise from many mechanical modes, even those well-separated in frequency. As a result, the observed spectra can deviate significantly from predictions of the usual single-mode and (uncorrelated) multimode models over the broad band, notably even at the mechanical resonance peaks. This highlights that these effects must be considered in all systems exhibiting measurement back-action, regardless of whether the resonances are spectrally isolated or the readout noise is high enough that the noise peaks appear consistent with simpler models. Additionally, these correlations advantageously allow the thermal noise spectrum to reach a minimum – equivalent to that of a single mode – in a band far from the resonance peak, where the mechanical susceptibility is comparatively stable against frequency noise.

Robust and efficient eigenstate preparation is a central challenge in quantum simulation. The Rodeo Algorithm (RA) offers exponential convergence to a target eigenstate but suffers from poor performance when the initial state has low overlap with the desired eigenstate, hindering the applicability of the original algorithm to larger systems. In this work, we introduce a fusion method that preconditions the RA state by an adiabatic ramp to overcome this limitation. By incrementally building up large systems from exactly solvable subsystems and using adiabatic preconditioning to enhance intermediate state overlaps, we ensure that the RA retains its exponential convergence even in large-scale systems. We demonstrate this hybrid approach using numerical simulations of the spin- 1/2 XX model and find that the Rodeo Algorithm exhibits robust exponential convergence across system sizes. We benchmark against using only an adiabatic ramp as well as using the unmodified RA, finding that for state preparation precision at the level of $10^{-3}$ infidelity or better there a decisive computational cost advantage to the fusion method. These results together demonstrate the scalability and effectiveness of the fusion method for practical quantum simulations.

Engineering quantum resources that survive against environmental temperature is of great interest for modern quantum technologies. However, it is a tricky task to synthetize such quantum states. Here, we propose a scheme to generate highly resilient tripartite entanglement and quantum coherence against thermal fluctuations. Our benchmark model consists of a mechanical resonator driven by two electromagnetic fields, which are optically coupled. A modulated photon hopping $J$ captures the optical coupling, and each optical cavity hosts saturable gain or loss. When the saturable gain/loss are off, we observe a slightly enhancement of both tripartite entanglement and quantum coherence for an appropriate tuning of the phase modulation. When the saturation effects are turned on, we observe a significant enhancement of the tripartite entanglement, up to one order of magnitude, together with a moderate improvement of the quantum coherence. More interestingly, our results show that the threshold thermal phonon mumber for preserving tripartite entanglement in our proposal has been postponed up to two order of magnitude stronger than when the saturation effects are not accounted. The inclusion of saturable gain/loss in our proposal induces noise-tolerant quantum resources, and may lead to room temperature quantum applications such as quantum information processing, and quantum computional tasks. Our findings are quite general, and suggest saturation nonlinear effects as a tool for engineering thermal-immune quantum correlations.

Intrinsic noise in pre-fault-tolerant quantum devices poses a major challenge to the reliable realization of unitary dynamics in quantum algorithms and simulations. To address this, we present a method for simulating open quantum system dynamics on a quantum computer, including negative dissipation rates in the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. Our approach lies beyond the standard Markovian approximation, enabling the controlled study of non-Markovian processes within a quantum simulation framework. Using this method, we develop a quantum algorithm for calculating ground-state properties that exploits feedback-controlled, noise-assisted dynamics. In this scheme, Lyapunov-based feedback steers the system toward a target virtual state under engineered noise conditions. This framework offers a promising strategy for harnessing current quantum hardware and advancing robust control protocols based on open system dynamics.

Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which quantifies the overhead of representing non-Clifford operations as linear combinations of Clifford unitaries. However, finding optimal decompositions rapidly becomes intractable as it constitutes a superexponentially large optimization problem. In this work, we exploit symmetries in the computation of the stabilizer extent, proving that for real, diagonal, and real-diagonal unitaries, the optimization can be restricted to the corresponding subgroups of the Clifford group without loss of optimality. This “strong symmetry reduction” drastically reduces computational cost, enabling optimal decompositions of unitaries on up to seven qubits using a standard laptop – far beyond previous two-qubit limits. Additionally, we employ a “weak symmetry reduction” method that leverages additional invariances to shrink the search space further. Applying these results, we demonstrate exponential runtime improvements in classical simulations of quantum Fourier transform circuits and measurement-based quantum computations on the Union Jack lattice, as well as new insights into the nonstabilizer properties of multicontrolled phase gates and unitaries generating hypergraph states. Our findings establish symmetry exploitation as a powerful route to scale classical simulation techniques and deepen the resource-theoretic understanding of quantum advantage.

We study the complexity of Hawking radiation for an evaporating black hole from the perspective of the stabilizer theory of quantum computation. Specifically, we calculate Wigner negativity – a magic monotone which can be interpreted as a measure of the stabilizer complexity, or equivalently, the complexity of classical simulation – in various toy models for evaporating black holes. We first calculate the Wigner negativity of Hawking radiation in the PSSY model directly using the gravitational path integral, and show that the negativity is $O(1)$ before the Page transition, but becomes exponentially large past the Page transition. We also derive a universal, information theoretic formula for the negativity which interpolates between the two extremes. We then study the Wigner negativity of radiation in a dynamical model of black hole evaporation. In this case, the negativity shows a sharp spike at early times resulting from the coupling between the black hole and the radiation system, but at late times when the system settles down, we find that the negativity satisfies the same universal formula as in the PSSY model. Finally, we also propose a geometric formula for Wigner negativity in general holographic states using intuition from fixed area states and random tensor networks, and argue that a python's lunch in the entanglement wedge implies a stabilizer complexity which is exponentially large in $\frac{1}{8G_N}$ times the difference between the areas corresponding to the outermost and minimal extremal surfaces.

Quantum mechanical lattice models with local, bounded interactions obey Lieb-Robinson causality. We show that this implies a domain of analyticity of the retarded Green's function $G^R(\omega,{\bf k})$ of local lattice operators as a function of complex frequency $\omega$ and momentum ${\bf k}$, similar to the lightcone analyticity property of relativistic field theories. Low-energy effective descriptions of the dynamics must be consistent with this microscopic analyticity constraint. We consider two canonical low-energy fermionic Green's functions describing non-Fermi liquids, the marginal Fermi liquid and the `Hertz liquid'. The pole in these Green's functions must be outside of the Lieb-Robinson domain of analyticity for all complex momenta captured by the low-energy theory. We show that this constraint upper bounds the magnitude of the dimensionless non-Fermi liquid coupling in certain Hertz liquids. We furthermore obtain, from causality, an upper bound on the magnitude $|G^R(\omega,{\bf k})|$ within the analytic domain. We use this bound to constrain the quasiparticle residue of the non-Fermi liquids.

Multiparameter quantum estimation faces a fundamental challenge due to the inherent incompatibility of optimal measurements for different parameters, a direct consequence of quantum non-commutativity. This incompatibility is quantified by the gap between the symmetric logarithmic derivative (SLD) quantum Cramér-Rao bound, which is not always attainable, and the asymptotically achievable Holevo bound. This work provides a comprehensive analysis of this gap by introducing and contrasting two scalar measures. The first is the weight-independent quantumness measure $R$, which captures the intrinsic incompatibility of the estimation model. The second is a tighter, weight-dependent measure $T[W]$ which explicitly incorporates the cost matrix $W$ assigning relative importance to different parameters. We establish a hierarchy of bounds based on these two measures and derive necessary and sufficient conditions for their saturation. Through analytical and numerical studies of tunable qubit and qutrit models with SU(2) unitary encoding, we demonstrate that the weight-dependent bound $C_{T}[W]$ often provides a significantly tighter approximation to the Holevo bound $C_{H}[W]$ than the $R$-dependent bound, especially in higher-dimensional systems. We also develop an approach based on $C_{T}[W]$ to compute the Holevo bound $C_{H}[W]$ analytically. Our results highlight the critical role of the weight matrix's structure in determining the precision limits of multiparameter quantum metrology.