Papers

Stabilizer operations describe a fragment of quantum theory that is known to be efficiently classically simulable, thanks to the Gottesman-Knill theorem. For this reason, nonstabilizer resources such as magic states are necessary for universal quantum computation. Interestingly, the operational and axiomatic approaches to the resource theory of magic differ: the set of free operations in the former, namely, stabilizer operations (SO), is strictly smaller than that in the latter, namely, completely stabilizer preserving operations (CSPO). A simple example showing the separation is given by a three-qubit stabilizer product basis whose states cannot be perfectly discriminated using SO, but which do admit perfect discrimination using CSPO. Such an ensemble of states is said to exhibit nonstabilizerness without magic (NSWM). Here we obtain a principled understanding of this phenomenon, proving necessary and sufficient conditions for its existence. We first derive a simple criterion to decide whether, given a stabilizer basis, its states can be perfectly discriminated using stabilizer operations alone. We then consider the case where the stabilizer basis contains only product states and use its link with process functions—classical models of paradox-free causal loops—to prove the following: the states in a stabilizer product basis require nonstabilizerness for perfect discrimination if and only if the corresponding process function violates a causal inequality. This provides a new operational meaning to causal inequality violations as witnesses of nonstabilizerness, a form of computational nonclassicality.

Understanding the complexity of low-energy quantum states is a central problem in quantum complexity theory and many-body physics. Here we prove the no low-energy trivial magic (NLTM) conjecture, constructing a family of local Hamiltonians for which every state within a positive energy density window requires circuit depth $\Omega(\log n)$ to prepare from arbitrary stabilizer state that may themselves be highly entangled. Notably, our result is intrinsic in the sense that the same Hamiltonian family and energy density threshold apply to arbitrary qudit stabilizer inputs with any bounded local dimensions. Our construction builds on non-Abelian gauged sheaf codes obtained using the cup product structure on good quantum locally testable codes. We establish constant operator soundness for the associated Hamiltonians, enabling their protected logical structure to constrain all states at sufficiently low energy density. By excluding shallow stabilizer-based classical witnesses, Our result substantially strengthens NLTS and advances our understanding of low-energy complexity relevant to quantum PCP.

Purifications are often used as a convenient mathematical representation of quantum states and channels when constructing protocols for quantum information processing tasks. Although powerful, this perspective can suggest that the purifying degrees of freedom and its correlations with an environment are just a useful change of representation. Here we show how they can instead be exploited as an operational resource in sequential quantum channel discrimination, even when the environmental reference frame is unknown or averaged. In contrast to state discrimination and parallel channel discrimination, for which bare and averaged-purification access are equivalent, sequential access to purified resources exhibits a strict advantage in probability of success. We prove this strict separation via two main results. In the first, we construct a pair of families of qubit-qubit channels with a strict separation in the two-query case, and in the second, we show an example of a pair of qubit-qubit channels whose purifications are perfectly distinguishable with three queries while no finite number of bare (non-purified) queries suffices for perfect discrimination. These separations imply an advantage of sequential over parallel strategies for channel discrimination and establish the impossibility of converting bare channel queries into averaged-purification queries via transformations that allow arbitrary interventions between queries, strengthening previous results.

The volume estimation problem is a classic task in computational geometry. The development of randomized algorithms for this problem spurred the development of many influential algorithmic techniques related to Markov Chain Monte Carlo and simulated annealing, and the problem connects to several important geometrical results, like the KLS conjecture. In this work, we quantize the state-of-the-art $\widetilde{O}(d^{3.5}+d^3/\varepsilon^2)$-query randomized algorithm developed by Cousins and Vempala, and obtain a $\widetilde{O}(d^{3.5} + d^{1.75}/\varepsilon)$-query quantum algorithm, improving over the $\widetilde{O}(d^{3.5} + d^{2.25}/\varepsilon)$ state-of-the-art bound. Our key technical contribution is a framework for amortizing the cost of a quantum walk. The framework is based on the recent transducer toolkit introduced by Belovs, Jeffery and Yolcu. It is this amortized quantum walk framework that allows us to exploit the amortized analysis of the ball walk by Cousins and Vempala, thus overcoming the key barrier that previously barred its quantum implementation.

Betti numbers are central to topological data analysis but fail to capture torsion in integral homology. Torsion can distinguish topological structures with identical Betti numbers, and examples from classical topological data analysis show that it can affect the topology inferred from data. Related torsion-sensitive quantities are also known to have practical applications in graph-based machine learning, including biomedical applications. We investigate how quantum spectral methods can access this additional information. Log pseudodeterminants, obtained by summing the logarithms of the nonzero boundary-Laplacian eigenvalues, summarize spectral information about a simplicial complex. Under explicit topological assumptions, an alternating combination of these quantities gives the size of a higher critical group, the higher-dimensional analogue of a graph sandpile group. With stronger certification, a related construction recovers the size of the torsion subgroup in homology itself. This is, to our knowledge, the first provably correct quantum estimator of integral-homology torsion order. We give a new quantum algorithm for estimating these quantities, with explicit dependence on how the input is queried, the required accuracy, and the spectral gaps. Exact spectra for balanced multipartite clique complexes provide favorable gaps, and a related construction gives an explicit torsion-bearing benchmark. With compact query access, the algorithm need not construct the exponentially large boundary matrices explicitly. For a restricted torsion-bearing family, a tailored amplitude-estimation routine uses quadratically fewer queries than any randomized classical algorithm given comparable access when estimating the log pseudodeterminant. Estimating the full, unnormalized quantity to fixed additive error still costs in proportion to the candidate-space dimension $D$.

Distillable entanglement—the maximum rate of Bell states extractable from the given noisy entangled states via local operations and classical communication (LOCC)—has been a central quantity to characterize the operational value of entangled states. However, this operational meaning had been known to be valid only under a crucial assumption: both parties know the description of the input state and can choose the protocol tailored to it, which does not necessarily reflect the natural operational setting. Here, we show that the distillable entanglement is the fundamental operational quantity even without this assumption. We present a universal LOCC protocol—whose description does not depend on the input state and thus works universally for any input—that achieves the distillable entanglement of an arbitrary unknown input state. Our result therefore lifts the distillable entanglement to a robust notion of an operationally meaningful quantity and clarifies that input-state knowledge is not necessary to achieve the optimal rate of entanglement distillation. Our protocol is based on state merging for compound states, together with the uniform convergence property of the finite-block quantity toward distillable entanglement.

Open quantum systems can rapidly lose most microscopic information, leaving only a few degrees of freedom to govern their long-time dynamics. Classical Markov state models (MSMs) describe such metastable dynamics as transitions among a few representative phases and are widely used to reduce complex-system dynamics in condensed matter and chemical physics. In quantum systems, however, phase labels alone are insufficient when coherence persists between metastable states. Even when the slow modes are known, their spectral projection need not produce valid quantum states. We construct quantum Markov state models (QMSMs) that describe the surviving information and its evolution on a small physical state space containing classical sectors and quantum matrix blocks. We quantify metastability by assuming that the evolution channel $\mathcal C$ changes little when applied a second time, with sufficiently small defect $\eta=\|\mathcal C^2-\mathcal C\|_\diamond$, and that the number of slow degrees of freedom is bounded independently of the full system size. Under these assumptions, we construct compression and reconstruction channels whose composition recovers every reduced state exactly, while the reverse composition gives an exactly idempotent channel approximating $\mathcal C$, answering Kitaev's exact-rounding question [Kit25]. Our constructions give an optimal diamond-norm bound of $\mathcal{O}(\eta^{1/3})$ on all input states, as well as an improved bound of $\mathcal{O}(\eta^{1/2})$ on metastable states prepared by $\mathcal C$, with constants depending only on the slow dimension. The reduced transition channel can be iterated to predict the microscopic dynamics with controlled error. We illustrate the QMSM through a weakly driven dissipative spin chain supporting either a metastable logical qubit or long-lived classical phases.

We develop a submodular framework for the von Neumann entropy of discrete quantum convolutions, providing a noncommutative counterpart to the direct side of entropic additive combinatorics. We first introduce globally weighted quantum convolutions, which form compatible families indexed by admissible subsets of a fixed collection of inputs. Our main theorem reveals a polymatroidal geometry underlying their entropy growth: relative to any fixed admissible input block, the entropy gains admit a normalized, monotone, submodular extension to all subsets of the remaining inputs. The theorem yields convolutional strong subadditivity, quantum Ruzsa triangle inequality, and quantum entropic Plünnecke–Ruzsa inequalities for arbitrary input states. For repeated inputs, it gives sharp comparisons of entropy growth across admissible scales; in particular, the quantum doubling constant controls all higher admissible convolution entropies with optimal exponents. Together, these results bring submodular methods from additive combinatorics into the quantum setting and provide a systematic route to broad families of convolutional entropy inequalities.

Designing a material with a desired property amounts to solving an inverse problem: finding the couplings of a microscopic Hamiltonian whose ground state exhibits that property. For strongly correlated quantum systems, solving this problem efficiently remains largely out of reach. To address this challenge, we present a general framework for ab initio inverse design based on Foundation Neural-Network Quantum States, a recent approach in which the ground states of a family of Hamiltonians are encoded in a single variational wave function. Because the ansatz depends explicitly on the couplings, any target property is a differentiable function of them, and the search for the right Hamiltonian reduces to gradient-based optimization in coupling space. We apply this approach to search for nonmagnetic phases of frustrated Heisenberg models on the square lattice with an increasing number of free next-nearest-neighbor couplings, aiming to identify new quantum spin liquid candidates. With a single coupling, the method recovers the known nonmagnetic window of the square $J_1$-$J_2$ Heisenberg model, whereas letting the two diagonal couplings vary independently reveals an extended nonmagnetic region connecting the square-lattice and anisotropic-triangular-lattice regimes. In a search space of eight independent couplings within a $2\times2$ unit cell, which contains several paradigmatic frustrated spin models, the optimization spontaneously converges to the $J_1$-$J_2$-$\delta$ Heisenberg model, in which the diagonal couplings alternate between two values on neighboring plaquettes, a model recently proposed in the context of altermagnetism. Finite-size scaling up to $16\times16$ clusters in this optimal model shows that the ground state has no magnetic, dimer, or plaquette order, establishing it as a new quantum spin liquid candidate, distinct from those previously proposed on the square lattice.

We compute one-loop unpolarized quark and gluon quasi- and pseudo-distributions in $\overline{\mathrm{MS}}$ and match them to light-cone PDFs. Decomposing the gluon correlator into six covariant form factors, we derive the $6\times6$ renormalization mixing matrix: its eigenvectors classify multiplicatively renormalizable combinations, and any lattice operator choice projects onto our results without a further loop calculation. Evaluating all Fourier transforms in $d$ dimensions, we resolve the structure of the exterior $|x|>1$ in quasi-distributions. The correlator carries a short-distance logarithm with a branch cut at $\nu=0$. By the Paley-Wiener theorem, the analytic part transforms into $|x|\le1$, so the exterior is generated solely by this branch cut. At leading power, the exterior carries no independent non-perturbative physics: it is fixed by the light-cone PDF through the renormalization group. In LaMET, lattice data therefore cannot determine the exterior independently of the interior, and unconstrained exterior parameters in reconstructions risk absorbing genuine power corrections into the leading-twist PDF. In the gluon channel, the matching kernel of Balitsky, Morris and Radyushkin differs from our $\overline{\mathrm{MS}}$ result by a finite polynomial, identical across index choices. We trace this to contracting an internal loop index over two instead of $d-2$ transverse directions, omitting an evanescent operator on the collinear pole. Using our basis, we show that the independent kernel of Yao, Ji and Zhang agrees with ours, separated from Balitsky et al. by the same polynomial. While the ratio scheme protects the momentum fraction $\langle x\rangle_g$, this kernel difference suppresses the extracted normalized second and third gluon moments by $11\%$ and $13\%$ at $\alpha_s=0.3$, so the true $\overline{\mathrm{MS}}$ gluon is systematically harder than reported.

Quantum measurements and channels determine how information is extracted, encoded, and transmitted in quantum protocols. Optimizing their performance often requires numerical methods that remain practical as Hilbert space dimensions increase. The Reimpell-Werner iteration offers a practical approach to these tasks through repeated matrix updates that respect the constraints. Here, we generalize this iteration to linear objectives with arbitrary Hermitian cost matrices. We prove that the iterates converge to a global optimum whenever the initialization satisfies suitable support overlap conditions. For each fixed problem, choice of iteration parameters, and admissible initialization, $\mathcal{O}(1/\varepsilon)$ iterations suffice asymptotically to bring the objective value within $\varepsilon$ of the optimum. These results provide a rigorous foundation for the iteration and broaden the class of optimization problems to which its convergence guarantees apply.

With the STAR's Beam Energy Scan II, a rich amount of data exists to search for the QCD critical point. However, a central challenge is that the critical point cannot be directly extracted from data but rather is probed dynamically in an expanding, cooling system that may be far-from-equilibrium. In this talk, we show the latest results from equations of state with a movable critical point generated by the MUSES collaboration, run in the 3+1D relativistic viscous hydrodynamics code CCAKE. We discuss numerical improvements to CCAKE that include “glass” initial conditions and adaptive smoothed particle hydrodynamics, allowing us to rapidly and accurately obtain numerical solutions to the hydrodynamic equations of motion. We can quantify the interplay between beam energy, location of the critical point, and rapidity range.

Quantum one-time programs (Broadbent, Gutoski and Stebila, CRYPTO 2013) or OTPs for short, enable a functionality to be encoded into a quantum token that can be evaluated on a single chosen input and then becomes unusable. While powerful, this primitive is inherently stateless and tied to a setting in which a quantum token needs to be issued and distributed for every single evaluation of a circuit. This raises a natural question: can the one-time computation paradigm be extended to richer, stateful forms of controlled access, and would such an extension offer inherent advantages beyond standard OTPs? We introduce $\textit{query-limited RAM programs}$ (QLPs), a RAM-generalization of QOTPs that supports structured, stateful computation under bounded or policy-driven access. QLPs allow controlled sequences of evaluations while preventing adversarial forking or rollback of computational state. This enables new applications beyond stateless one-time programs, including quantum tokens for Turing Machines whose size depends only on $\textit{code length}$ (and not runtime), transferable $k$-time or budget-limited programs, and low-communication mechanisms for delegating computation in settings such as Software-as-a-Service. To construct QLPs, we introduce $\textit{one-shot programs}$, unifying one-shot signatures (Amos, Georgiou, Kiayias and Zhandry, STOC 2020) with the single effective query paradigm (Gupte, Liu, Raizes, Roberts and Vaikuntanathan, STOC 2025). We prove that one-shot programs generically imply query-limited programs, demonstrating that the strengthened unclonability guarantees of one-shot signatures translate into enhanced functionality. Along the way, we clarify the relationship between signature-token primitives and quantum one-time programs via generic constructions, essentially showing that one-time signing programs imply one-time general computation.

Neutrino telescopes observe neutrinos through the muons produced by charged-current interactions. Most of those muons are born kilometers outside the detector, and how much energy they lose on the way is stochastic. We show that we can compute analytically the distance a muon travels before it falls below the detection threshold, while describing the statistical properties of its losses. Our result reproduces Monte Carlo propagation to within $3\%$, and with two parameters per detector it matches the effective areas published by IceCube, KM3NeT/ARCA, and P-ONE to about $1\%$. We then show how this model can be used in point-source sensitivities, energy reconstruction, and consistency checks between detectors. The calculation disentangles muon-transport physics from a detector's response, so a new detector or loss model can be quickly benchmarked.

The classical cost of simulating free-fermion (matchgate) circuits depends on both the input state and the computational task. We develop classical algorithms for circuits with non-Gaussian inputs, addressing exact sampling and both additive-error and exact estimation of expectation values. For inputs consisting of $n$ copies of the four-mode magic state, we give exact sampling algorithms, generalizing the Clifford and Clifford algorithm for Boson sampling, for passive and active free-fermion dynamics with worst-case arithmetic cost $O(2^n)$ per sample, without any multiplicative polynomial prefactor. The passive algorithm enables an exact simulation of the non-interacting regime of a recent trapped-ion experiment. We also extend recently developed additive-error estimation of number correlators and related observables from passive to active dynamics with runtime polynomial in $n$ and the inverse additive-error, for input states formed by products of $n$ four-mode even parity states. Our estimator uses a Gaussian-state decomposition adapted to each sampled state to control its second moment. This includes estimation of individual output probabilities. Finally, we show that for even-parity product inputs composed of constant-size blocks, expectation values of Majorana monomials of logarithmic weight can be computed exactly in polynomial time, improving on prior Majorana propagation-style algorithms with quasi-polynomial runtime. The exact algorithm processes the input blocks by dynamic programming, sharing calculations across subsets of Majorana factors. Our suite of algorithms provide classical benchmarks for fermionic quantum simulations across a broad spectrum of computational tasks.

We develop a general framework for higher-order quantum resources that treats the resourcefulness of quantum states, channels, and supermaps (also called processes) in a unified manner. By generalizing well-established concepts from resource theories of states and channels, we introduce and study supermap resource monotones and supermap distillation and dilution. As free supermaps, we consider free networks (supermaps that can be implemented with free channels), compatible supermaps (sets of supermaps closed under arbitrary composition), and maximally free superchannels. Specializing to approximate channel-to-channel conversions, we show that under mild assumptions, the conversion error with respect to the diamond distance and the worst-case infidelity coincide. We then apply the general framework to resource theories of dynamical coherence, where we establish the existence of largest sets of compatible supermaps. By characterizing these sets with semidefinite constraints, we show that they are strictly larger than the corresponding free networks but do not contain all maximally free superchannels. We finish by investigating the operational differences of these sets in one-shot channel distillation and dilution, providing solutions for both tasks in the parallel setting and for dilution in the adaptive setting.

Quantum cryptography leverages unclonability to enable a wide range of cryptographic applications that are impossible classically, such as digital currency protected against counterfeiting by quantum mechanics. Security requires that no efficient user can produce even one additional valid banknote beyond those already in their possession. However, existing security bounds weaken as the number of banknotes available to a user increases. In this paper, we study a construction of quantum money whose asymptotic query security does not deteriorate as long as the number of banknotes available to a user remains below the scale required for state tomography. In particular, we show that the construction based on an $n$-qubit Haar-random state and a reflection oracle achieves optimal query security: unless a user holds $\Omega(2^n)$ banknotes, their existing banknotes cannot asymptotically speed up counterfeiting — their best possible attack is the same as if they do not have any banknotes. To establish this result, we develop a framework based on the compressed-oracle technique for defining and analyzing progress measures for quantum tasks such as Haar state cloning. Furthermore, we prove a tight lower bound for generating $r$ additional copies, give a matching attack, and apply our results to quantum copy-protection.

In the IKKT matrix model, the dimension, geometry, and metric signature of spacetime must emerge from the matrix dynamics. We classify the Lie-algebraic saddles of the model: classical solutions in which the ten Hermitian matrices realize a finite-dimensional real Lie algebra in a unitary representation. For this class the equations of motion collapse to a single algebraic equation for a symmetric bilinear form $h$ on the algebra, and the signature of the emergent spacetime can be read off from $h$. Two facts control the outcome. First, when the complexified algebra is simple, a Casimir obstruction allows only $h=0$; this explains why fuzzy spheres and the expanding-universe solutions need mass terms or infrared regulators. Second, semisimple algebras admit saddles only through couplings between distinct simple ideals; such saddles first appear in six dimensions and reach every signature only from twelve. These facts yield criteria for the emergence of time. Every nondegenerate Lorentzian saddle in at most eleven dimensions—hence every Lorentzian background of the ten-dimensional model—has a nonzero solvable radical. The only nontrivial possibility of the semisimple part is the Lorentz algebra $\mathfrak{so}(1,3)$, which is purely spacelike, and every timelike direction has a component in the radical. When the semisimple part is nontrivial, it acts on the radical only from ten dimensions on; at ten dimensions, the radical must be abelian and must carry the Weyl-spinor representation, which solves the Lorentzian equations of motion; a nonabelian radical first appears in eleven dimensions. As a result, space can be semisimple; time must be solvable.

We develop a mixing time method for estimating the sample complexity of quantum state discrimination. We start with considering the minimum-error discrimination of geometrically uniform pure state ensembles, and prove that its sample complexity has a tight estimate given by a quantum homogeneous mixing time [George et al., 2026] and a quantum version of the generalized Dobrushin coefficient [Wolfer, 2020]. This quantum mixing time further reduces to a classical one when the generating group $G$ forms a Gelfand pair with the stabilizer subgroup $H$ of the generator state. In this case the generalized Dobrushin coefficient can be fully expressed by representation-theoretic quantities of the commutative Hecke algebra $\operatorname{End}_G(\mathbb C[G/H])$. In particular, this method reduces the sample complexity estimation of learning quantum coupon collector states [Arunachalam et al., 2020] and learning phase states to classical mixing time problems. We apply this framework to answer the open problems of learning degree-$d$ phase states over $\mathbb F_q$ in [Alrabiah et al., 2026] and generalized Boolean phase states over $\mathbb Z_q$ [Arunachalam et al., 2023]. The framework also applies to hypergraph state ensembles, giving estimates expressed fully in terms of hypergraph data and recovering estimates for graph state ensembles in [Montanaro and Shao, 2022]. Finally, we extend the discussion to arbitrary mixed state ensembles with uniform priors, prove a sandwiched bound for minimum-error discrimination sample complexity by a quantum weakly mixing time, and provide a tight estimate for the minimax discrimination sample complexity from [D'Ariano et al., 2005] by a Dobrushin-type coefficient. We also discuss the method of strengthened data processing inequality [Gao and Rouzé, 2022] and give an upper bound in terms of a strengthened data processing inequality constant.

We prove the first non-trivial upper bound for the quantum query complexity of Boolean Matrix Product Verification ($\mathsf{BMPV}$), answering a longstanding open question in quantum query complexity. For $n\times n$ matrices, our upper bound is $\widetilde O(n^{17/12})$, improving on the standard $O(n^{3/2})$ bound obtained using Grover search by Buhrman and Špalek [SODA 2006]. We complement this result by showing an $\Omega(n^{5/4})$ lower bound, which improves over the previous best known lower bound of $\widetilde\Omega(n^{19/18})$ by Childs, Kimmel, and Kothari [ESA 2012]. Our approach centers on a connection with Orthogonal Vectors ($\mathsf{OV}$), which asks whether an indexed list of $n$ Boolean vectors of dimension $n$ contains two vectors with disjoint supports. In particular, we prove equivalences between $\mathsf{OV}$ and $\mathsf{BMPV}$ and establish the above bounds for $\mathsf{OV}$. We also prove a tight $\widetilde \Theta(n^{3/2})$ bound for a variant of $\mathsf{BMPV}$ that asks whether the product contains a given row vector. Together, these results imply a polynomial separation between the quantum query complexities of deciding whether a graph has radius at most two and whether it has diameter at most two.

The von Neumann, Tsallis, and Rényi entropies are fundamental measures of quantum information. A common estimation strategy multiplies the worst-case costs of spectral transformation and statistical readout, leaving gaps to query lower bounds. We reduce this overhead with multi-level algorithms that use local normalization and precision allocation, while variable-time estimation accounts for the probability of reaching expensive spectral tests. With controlled purified access and its inverse, we obtain bounds for additive error $\varepsilon$, rank upper bound $R$, and fixed order $\alpha$. Tsallis entropy estimation has near-optimal rank-independent query complexity $\widetilde O(\varepsilon^{-1/(\alpha-1)})$ for $1<\alpha<2$, when the allowed dimension and rank accommodate the lower-bound instances, and $\widetilde O(1/\varepsilon)$ for $\alpha\ge2$, where $\widetilde O$ suppresses logarithmic factors. The first saves a factor $1/\varepsilon$; the second extends known integer-order scaling to noninteger orders. We also improve the von Neumann entropy bound from $\widetilde O(R/\varepsilon^2)$ to $\widetilde O(R/\varepsilon)$ and obtain $\widetilde O(R/\varepsilon)$ for noninteger Rényi orders $1<\alpha<3$, with further bounds at other orders. Our functional-estimation theorem replaces the global product by a sum of local costs weighted by function magnitudes and spectral masses. We further estimate fixed logarithmic moments and entropy variance using $\widetilde O(R/\varepsilon)$ queries, providing efficient access to fluctuation parameters that enter finite-blocklength quantum compression and pure-state entanglement conversion. More broadly, our framework extends beyond entropy to a broad class of density-matrix functionals, offering a systematic approach toward optimal query complexity in quantum spectral estimation.

Combined baryon acoustic oscillation and cosmic microwave background data have begun to mildly favor departures from $\Lambda\mathrm{CDM}$. This is usually framed as 2-parameter dynamical dark energy. However, a 1-parameter "cosmic glitch in gravity" model, whose cosmological gravitational coupling differs from Newton's constant as in Hořava gravity, fits at least as well. $\textit{Planck}$+ACT+SPT and DESI~DR2 give $G_\mathrm{cosmo}/G_\mathrm{N}=0.9920\pm0.0025$, a $3.3\,\sigma$ preference for weaker cosmological gravity, robust to adding CMB lensing and supernovae. Fitted to the CMB alone, the glitch predicts DESI distances; $w_0w_a$CDM does not.

Simulating open quantum systems reveals how environmental coupling shapes relaxation, excitation transport, and the dynamics of quantum correlations. On quantum hardware, dissipative channels add operations and might seem to increase cost. However, we show that a broad class of Pauli noise, including depolarization, can ease quantum and classical simulation by exponentially suppressing high-weight components of Heisenberg-evolved observables. For bounded-degree Lindblad dynamics, this permits system-size-independent Trotter steps when estimating local observables. Combining this compression with Richardson extrapolation, we provide classical and quantum error bounds with respect to the 2-norm of the propagated observable. These give high-probability expectation-value guarantees for random input states or random Hamiltonians acting on a fixed state and control (out-of-time-order) correlators. Concretely, we show that expectation values of local observables at time $t$ can be estimated to accuracy $\varepsilon$ using circuits of maximum depth $O\!\left(\left[1+\left(t/\gamma\right)^{3/2}\right]\log^2(1/\varepsilon)\right)$, independent of the system size $n$. Classically, we show that sparse Pauli propagation runs in time polynomial in $n$, $t$ and $1/\varepsilon$ for every fixed $\gamma>0$, with polynomial degree $O(1/\gamma)$ in the weak dissipation limit. The gap between our quantum and classical upper bounds leaves room for a substantial polynomial quantum advantage as dissipation weakens, an observation further supported by our numerical results.

Classical shadow tomography is widely touted as supplying a family of methods for extracting information from quantum systems with polynomially scaling sample-complexities. In the current era of quantum computers possessing on the order of hundreds of qubits, however, polynomial scaling can nonetheless be prohibitive. Thus, there is a strong practical need for obtaining sample-complexity bounds which are as tight as possible. Here we address this in the case of fermionic (matchgate) shadows. For an arbitrary observable $O$ of Majorana degree $2k$, we improve the previously known sample-complexity bound of $\mathcal{O}(n^{2k}\|O\|_\infty^2)$ to $\mathcal{O}(n^{k}\|O\|_\infty^2)$, which is asymptotically tight. For example, for the estimation of the energy per mode of an open fermionic 50-site Hubbard chain with hopping and on site strenghts respectively given by $t=1$, $V=4$, and for a target additive precision of 0.1, this reduces the number of required shots from $\sim 10^9$ to $\sim 10^5$. That is, the new bound reduces the required number of shots by approximately $99.98\%$.

The control of open-system dynamics provides a powerful mechanism for using quantum information to process sequential tasks. While quantum reservoir computing typically relies on Markovian dissipation to process sequential data, the computational role of non-Markovian memory effects remains largely unexplored. We introduce a framework for quantum reservoir computing where non-Markovianity is explicitly modeled and regulated using fractional derivatives. By employing fractional time subordination, we generate tunable, heavy-tailed relaxation dynamics that govern the information backflow between the system and its environment. Non-Markovian information backflow regulates the overall temporal retention of the system, maximizing short-term linear memory capacity. Within an optimal operating regime, fractional non-Markovianity redistributes the reservoir memory towards recent inputs, improving both linear memory capacity and nonlinear prediction accuracy at short delays, at the expense of long-range temporal retention. System-environment interaction proves being not merely a requirement for quantum reservoir computing, but an active resource that embeds memory retention directly into the quantum evolution.

Gauss constraints make it nontrivial to open, close or join a gauge system while retaining its interior physics. Boundary reconstructions are constructed on a pure SU(3) ladder at six site-singlet cutoffs, with all allowed intertwiner multiplicities. Replacements of prescribed length are obtained using legal column paths and physical self-loops. On their stated physical domains, the channels preserve unnormalized conditional interior matrices, including their weights and within-branch coherence. Lowest-cutoff dephasing controls show that path probabilities alone do not preserve the matched magnetic observables. In that example, coherent resources lower the output energy without purification or global ground-state preparation. Matched interior Hamiltonian terms cancel exactly, so the energy cost is bounded independently of longitudinal length. The vacuum and flux energy densities are then established separately by same-sector gluing and stability. The open and periodic vacuum-subtracted line-energy densities are shown to be equal by two same-length boundary comparisons using the qualified periodic minimizing domain. These limits hold at fixed lattice spacing, transverse width, coupling and chosen cutoff.

The waveform is obtained from one balance of energy and radiation on Helmholtz orbits of the retarded mass kernel, with a spherical-Bessel flux. That balance follows from the Dirac–Maxwell equation with a modified vertex, the single $U(1)$ coupling being replaced by the eight operators of the source interaction. After contact that balance is the energy loss of one packet: a bounded well for a black-hole remnant and the Coulomb ladder of one star for a neutron-star remnant. Ringdown starts from the spherical projection of that end state, which contains its spin. The comparisons use model waveforms at the published parameters. For GW250114, at the Coulomb-radius contact and after a shift of $-16\,\mathrm{ms}$, the noise-weighted norm ratio against the NRSur7dq4 median in $100$–$200\,\mathrm{Hz}$ stays between $1.36$ and $1.94$ across the published distance interval. Stopping at $2.4$ times that radius lowers the ratio to $1.11$, which the same interval moves from $0.94$ to $1.35$. With contact placed on the published merger time and with no time shift, that ratio is $3.32$ at the Coulomb radius and $2.30$ at $2.4$ times that radius. At the larger radius, the unretarded limit of this balance, with unit spherical-Bessel weights, reaches contact at $94\,\mathrm{Hz}$, and in $20$–$100\,\mathrm{Hz}$ the norm ratio to the Helmholtz balance is $1.12$ after a shift of $+27\,\mathrm{ms}$. For GW170817, $|h_{+}|$ near $100\,\mathrm{Hz}$ is $8.0\times10^{-23}$, and the mismatch against the $2.5$PN inspiral is a difference in phasing.

We introduce shadow quantum singular value transformation (Shadow QSVT): given an initial state $|{\psi}\rangle$, a Hermitian matrix $H$, a polynomial $f$, and a set of observables $\{O_1,\dots,O_m\}$, the goal is to estimate $\langle{\psi}|f(H)^{\dagger}O_j f(H)|{\psi}\rangle$ for all $j\in\{1,\dots,m\}$. Shadow QSVT provides a systematic route to reduce the quantum resources required by standard QSVT, which constructs a unitary block-encoding of $f(H)$. It uses structure in the input state and observables, together with the fact that many applications require only observable estimates rather than synthesizing the full unitary. We present three algorithms that exploit structure in the initial state and observables to reduce quantum circuit depth. First, we develop a state-aware QSVT algorithm that prepares the target state with low circuit depth when the Krylov subspace associated with $H$ and $|\psi\rangle$ is low-dimensional or admits an accurate low-dimensional approximation. Second, we introduce an observable-aware Shadow QSVT algorithm that combines a new observable-aware Krylov subspace with history states to further reduce circuit depth and gate complexity. Finally, we develop Classical Shadow QSVT, which constructs a classical representation from $H$, $f$, and $|\psi\rangle$ without prior knowledge of the observables or explicit preparation of the target state proportional to $f(H)|\psi\rangle$. This representation enables estimation of the target quantities for observables specified after the quantum computation. Together, these three algorithms provide tools for reducing the circuit depth of QSVT-based computations across a range of settings.

We study photon superradiant scattering by a Kerr black hole in the presence of an axion-photon coupling and investigate how this coupling modifies the electromagnetic amplification factor. We solve the coupled axion and electromagnetic equations in a fully relativistic framework. We distinguish two regimes according to the relation between the sourced axion frequency and the axion mass. In the radiative regime, the axion can propagate to spatial infinity and carry away energy, thereby suppressing photon amplification. In the subthreshold regime, the axion is confined by the mass barrier and exchanges energy with the black-hole horizon through quasibound-state excitations. In this regime, photon amplification can be either enhanced or suppressed, depending on whether the relevant axion modes satisfy the superradiance condition.

We determine which representation sectors control the slowest convergence of random Pauli rotations and several local random quantum circuits. For $d=2^n$, the continuous Pauli walk has exact all-representation gaps $$\Delta_{\mathsf{SU}(d)}=\frac{d-8}{8(d-1)}\quad(n\ge4),\qquad \Delta_{\mathsf{PU}(d)}=\frac{d(d-3)}{8(d^2-1)}\quad(n\ge3).$$ The special-unitary gap is attained in $\bigwedge^8\mathbb{C}^d$ and is invisible to balanced moments, while the projective gap is already attained in a balanced fourth-moment representation. We obtain exact discrete and orthogonal Pauli analogues, exact finite-Clifford chain/path gaps, and dimension-independent all-representation Haar brickwork lower bounds; on three qubits every weighted Haar-$\mathsf{SU}(4)$ edge walk reduces to one universal principal-angle constant. For real complete-graph models, the entire ordinary fourth-tensor gap reduces to a quadratic-size occupation operator, is simple for every $n\ge4$, and has an expansion beginning $$\Delta_n^{(4)}=\frac{10}{9n}-\frac{88}{105n^2}+O(n^{-3}),$$ with competing branches separated only beyond all algebraic orders. For the two finite real Clifford complete-graph walks, this fourth-tensor mode is the exact all-representation group gap for every $n\ge144$; in the same range it simultaneously governs every ordinary even tensor degree $k\ge4$. Thus different representation scopes can have genuinely different slow modes.