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Wednesday 30 September

Quantum Physics

Conditioning-Free Non-Uniform Quantum Fourier and Chebyshev Transforms

Chaowen Guan and Akshit Katiyar

We present an efficient quantum algorithm for the non-uniform Chebyshev transform. It is defined as the projection of a function onto Chebyshev polynomials sampled at given nodes that are uniform in $x\in[-1,1]$, and hence non-uniform in the angle $\theta=\arccos x$, a setting that QFT-based quantum Chebyshev transforms cannot handle. Our construction is based on an improvement of an existing Non-uniform Quantum Fourier Transform (NUQFT) whereby we remove the conditioning from non-uniform node sampling. Hence, error bounds are independent of the geometry-dependent parameter $\kappa$ of prior work. We use the fact that Chebyshev transform matrix is the average of two Type-II non-uniform DFTs, which we implement with a single controlled NUQFT circuit. We provide explicit oracle constructions, including the row-access oracle previously left as an assumption. The resulting $\varepsilon$-accurate block encoding has $O(1)$ normalization and uses $O(L)$ qubits and $\widetilde O(L^2)$ gates, where $L=\log N+\log(1/\varepsilon)$. We give an end-to-end implementation with complexity analysis, including the success probability and output-state error.
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High Energy Physics (Theory) · Cross-listed from math.NT

Resurgent rigidity of mock theta functions: uniqueness and natural boundary crossing

Ovidiu Costin, Gerald V. Dunne and Ali Saraeb

We develop a resurgent transseries approach to mock theta functions and show that the associated Mordell–Appell integrals underlie their modular and resurgent structure. From these integrals, we recover the modular transformation laws, obtain uniqueness characterizations of the mock theta vectors, provide a canonical crossing of their natural boundary, and produce new mock theta functions. After representing the Mordell–Appell integrals as Laplace transforms of elementary resurgent functions, we rotate the Laplace contour to a Stokes line. Their Stokes phenomena and their modular transformation laws reproduce those of the associated unary series and, combined with our uniqueness results, those of the mock theta functions. Conversely, we regard these modular transformation laws as functional equations governing the mock theta vectors. For Ramanujan's order-$3$ pair $(f,\omega)$ and the distinguished mock theta vectors of orders $5$, $7$, and $11$, satisfying the full $SL(2,\mathbb Z)$ transformation laws, we prove that these functional equations uniquely determine a holomorphic solution in the unit disk under canonical minimal-growth normalization. This unique solution is precisely the classical mock theta vector. We show that the normalization is essential: for orders $5$, $7$, and $11$ we determine explicit nontrivial solutions of the homogeneous problem, yielding new mock theta functions with faster-growing coefficients. Finally, we give two intrinsic and natural constructions for crossing the natural boundary $|q|=1$. The first continues the modular functional equations and takes their unique holomorphic solutions on the other side. The second acts on the resurgent asymptotic series at the cusp: we replace $\tau$ by $-\tau$ and apply Écalle–Borel summation. We prove that the constructions agree, giving a canonical and explicit boundary crossing.
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Quantum Physics · Cross-listed from cs.CC

Exponential Quantum Advantage in Numbers-on-Forehead Communication

Haoyu Wang, Pei Wu and Guangxu Yang

We give the first exponential quantum advantage in the general interactive three-party Numbers-on-Forehead (NOF) model for a decision problem. Previous separations hold only for restricted protocols like one-way communication for a relation. We construct an explicit partial Boolean function, the Interleaved Unitary Product problem, that requires only $O(\log n)$ NOF quantum communication but $\widetilde{\Omega}(n^{1/32})$ randomized communication. This function builds on the two-party unitary product problem of Arunachalam, Girish, and Lifshitz (TQC 2024). The main technical obstacle is that discrepancy, the standard lower-bound method for NOF, also lower-bounds quantum communication. We instead develop a regularity-based argument for randomized NOF lower bounds, building on the approach of Kelley, Lovett, and Meka and adapting the regularity decomposition of Abboud, Fischer, Kelley, Lovett, and Meka (STOC 2024) to cylinder intersections. Combined with matrix-product estimates of Arunachalam, Girish, and Lifshitz, this yields our randomized lower bound.
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Quantum Physics

Refined sample complexities from the tomographic rate function

Arick Grootveld, Alexander Maloney, Jason Pollack et al. (+1 more)

Protocols for quantum state tomography can be characterized either by their sample complexity or by the tomographic rate function that governs the large deviation behaviour of error estimates. We establish a framework for the analysis of covariant protocols which allows us to compare these measures. First, we derive the rate functions for several protocols, including random purification-based protocols and the sample-optimal protocol of Haah et al. These rate functions are expressed in terms of a new family of divergences which includes the reverse sandwiched Rényi divergence and Keyl's annealed quantum relative entropy as special cases. We show that these rate functions obey a strict ordering, even though the sample complexity of each protocol is order optimal. We consider a different version of sample complexity based on Wasserstein distance rather than trace distance, and show that the ordering of the rate functions implies analogous strict inequalities for the Wasserstein-type sample complexity. Thus the tomographic rate function is a more fine-grained indicator of the performance of a tomography protocol than the usual sample complexity.
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All authors Arick Grootveld, Alexander Maloney, Jason Pollack, Peixue Wu

Quantum Physics

Testing quantum Gaussianity with constant sample complexity

Mahtab Yaghubi Rad, Ricard Puig, Saksham Hassanandani et al. (+4 more)

Efficiently testing whether a quantum state possesses a given structure is both a fundamental and a practical task in quantum information. Among the most important structured families are Gaussian states, which underpin quantum optics and many-body physics while defining paradigmatic regimes of efficient classical simulation. Despite the central role of Gaussian states, optimal tests of Gaussianity have remained unknown. Here we give optimal and robust algorithms for testing fermionic and bosonic Gaussian states, with sample complexity independent of system size, particle number, and energy. Remarkably, the protocols implement experimentally feasible measurements associated with known exact symmetry characterizations of Gaussianity, using Bell sampling on two copies for fermions and passive interferometry with photon counting on three copies for bosons. We further obtain tolerant testers requiring joint measurements on a larger, but still constant, number of copies. At the heart of our analysis is a unified approach—which we call the gradient-flow method—that applies across all structured families considered here and underlies our optimal testers: representation theory turns approximate satisfaction of the defining symmetry into quantitative control of the gradient of the rejection probability, allowing a continuous descent from the input state to the target family whose length bounds their distance.
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All authors Mahtab Yaghubi Rad, Ricard Puig, Saksham Hassanandani, Luke Coffman, Jens Eisert, Carlos Bravo-Prieto, Antonio Anna Mele

Mesoscale and Nanoscale Physics

Long-lived divergence from equilibrium of electrons, nuclear spins and lattice for a solid state ion trap at low temperature

Guy Matmon, Manuel Grimm, Markus Mueller et al. (+3 more)

A fundamental problem in physics as well as engineering is equilibration. For example, the regulation of thermal and quantum fluctuations enables thermal and quantum annealing of complex systems. A key question is how different subsystems, such as electrons, nuclear spins and phonons equilibrate on their own as well as with each other. Level crossings play a special role in the dynamics of coupled degrees of freedom, for it is here that entanglement can be maximized to speed up relaxation. Here we use optical methods to establish the electronuclear level scheme, including avoided and unavoided crossings, and to examine equilibration of a rare earth ion (Ho$^{3+}$) in a salt (LiYF$_4$), a model system with quantum fluctuations which can be tuned via an external magnetic field transverse to the crystallographic long axis of the tetragonal host. We track the state of the system by monitoring the populations of the levels as a function of swept longitudinal fields, and discover that at low temperatures, depending on the experimental protocol, vastly different non-equilibrium states arise. We find evidence that nuclear spin excitations diffuse and equilibrate without the assistance of phonons, and tend to acquire higher effective temperatures than the electronic spins and the yet cooler lattice. A theory of thermally assisted tunneling rules out the standard scenario of phonon -assisted tunneling, and instead suggests that fast dynamics at level anti-crossings are facilitated entirely by nuclear spin diffusion. This provides a new understanding of thermalization and related slow relaxation phenomena in dense, multi-component interacting quantum systems.
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All authors Guy Matmon, Manuel Grimm, Markus Mueller, Byron J. Villis, Andrew J. Fisher, Gabriel Aeppli

Quantum Physics

Compatibility of quantum instruments

Chloe Kim, Yujie Zhang, Eric Chitambar et al. (+2 more)

Measurement compatibility asks whether a family of quantum measurements can be simulated by one parent measurement followed by classical post-processing. We extend this measurement compatibility to the notion of \emph{$d$-compatibility} for measurements, channels, and instruments whose parent passes a $d$-dimensional quantum system and unlimited classical information to the post-processing. We formulate $d$-compatibility as a common linear factorization of operator spaces and operator systems and show that $d$-compatible families form a closed set, even with infinitely many settings and a separable infinite-dimensional input. To certify $d$-incompatibility, we define the compatibility functional as the smallest product of completely bounded norms over common factorizations through a $d$-dimensional register. Using factorization theory of operator spaces, we show that measure-and-prepare channels defined in terms of mutually unbiased bases and pinching channels defined in terms of Heisenberg-Weyl operators are $d$-incompatible in certain regimes of $d$. We also link $d$-compatibility of multi-instruments to the preparability of Choi assemblages using channel-state duality, and use this connection to show that for bipartite states the (in)compatibility of instruments can be used to certify Schmidt numbers and the implementability of the instrument using one-way LOCC protocols. Finally, our compatibility functional also bounds the generalized robustness of compatibility, which we interpret through a memory-bounded nontransient preparation game.
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All authors Chloe Kim, Yujie Zhang, Eric Chitambar, Marius Junge, Felix Leditzky

Quantum Physics

Two-Stage Quantum-Classical Distribution Network Reconfiguration via Cycle-Edge Encoding

Nowar Alashkar, Cade Kennedy, Phillip C. Lotshaw et al. (+6 more)

Distribution network reconfiguration (DNR) is a combinatorial optimization problem that seeks a low-loss network topology subject to topological and electrical operating constraints. In this work, we propose a two-stage quantum-classical method for DNR. First, an iterative linear-ramp Quantum Alternating Operator Ansatz (LR-QAOA) searches topologically feasible subspaces constructed using a novel cycle-edge encoding. The encoding guarantees that every represented configuration is a spanning tree while allowing the size and coverage of each subspace to be adjusted to the available qubit budget. Second, the resulting sample distribution is used to guide a mixed-integer second-order-cone programming (MISOCP) solver. The method is evaluated on six distribution networks ranging from 33 to 417 buses through ideal simulation and execution on trapped-ion quantum hardware. For the 417-bus network, quantum hardware sampling identifies a configuration within approximately $1.4\%$ of the literature reference loss. Across all six test systems, the MISOCP solver guided by hardware-derived distributions reaches an incumbent within $1\%$ of the target with a lower median solver time than the corresponding unguided solver. These findings establish a concrete framework for applying current quantum hardware to DNR, with the potential to become increasingly competitive as hardware improves.
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All authors Nowar Alashkar, Cade Kennedy, Phillip C. Lotshaw, Shaked Regev, Miguel Angel Lopez-Ruiz, Ananth Kaushik, Paul Smith, Claudio Girotto, Martin Roetteler

Quantum Physics

Superlinear Quantum Query Lower Bounds for Subgraph Detection

Amin Shiraz Gilani and Xingyu Zhou

Subgraph detection asks whether an $n$-vertex graph, accessed through queries to its adjacency matrix, contains a copy of a fixed graph $H$. We prove the first unconditional superlinear lower bounds on the bounded-error quantum query complexity of this problem, answering a longstanding open question. A copy of $H$ is a certificate of constant size, so the adversary method with nonnegative weights cannot prove superlinear lower bounds. For every fixed $r\ge 4$, detecting the clique $K_r$ requires $n^{\lambda_r-o(1)}$ queries, where $\lambda_4=19/18$, the exponents $\lambda_r$ increase strictly with $r$, and $\lambda_r\ge 2-4\sqrt{2/r}+O(1/r)$. More generally, we prove superlinear lower bounds for detecting every fixed connected graph $H$ with chromatic number $c\ge 4$. These bounds approach quadratic as $c$ grows: for sufficiently large $c$, detection requires $n^{2-O(\sqrt{\log\log c/c})-o(1)}$ queries. Chromatic number alone does not characterize the quantum query complexity of subgraph detection: we show that detecting the complete bipartite graph $K_{r,r}$ requires $n^{\beta_r-o(1)}$ queries, where $\beta_{10}=181/180$ and $\beta_r\ge 2-O(1/\sqrt{r})$. Our main technical result is a lower bound for finding an all-ones certificate from a known family when the input bits are sampled independently. Its proof combines Zhandry's compressed oracle [CRYPTO 2019] with conditioning on a randomly planted certificate, adapting an argument of Belovs [FOCS 2026]. Our hard instances are built from graphs containing many copies of the desired subgraph with limited overlap. For cliques, we use a construction of Gowers and Janzer [CPC 2021]; for complete bipartite graphs, we use a random construction.
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Quantum Physics

Quantum List Recovery and Decoding: Achievability and Limitations

Fernando Granha Jeronimo and Xiaojuan Ma

Quantum list recovery (QLR) and quantum list decoding (QLD) seek short lists of logically distinct Pauli corrections consistent with a syndrome and prescribed error constraints. For CSS codes, two issues arise: treating the \(X\)- and \(Z\)-sectors separately can multiply their output list sizes, while distinct classical candidates can collapse after stabilizer quotienting. We study combinatorial upper and lower bounds for balanced folded quantum Reed–Solomon (FQRS) codes and balanced random CSS codes, both studied by Bergamaschi, Golowich, and Gunn (STOC 24). Let \(R\in(0,1)\) be the quantum rate and \(R_1=(1+R)/2\) the common component rate. As the radius \(\rho=(1-R)/2-\gamma\) approaches the quantum Singleton bound, we have, deterministically for FQRS codes and w.h.p. for balanced random CSS codes, \[ L^\star_{\rm QLR} = \ell^{\Theta(R_1/\gamma)}, \qquad L^\star_{\rm QLD} = \Theta\!\left(\frac{1-R}{\gamma}\right) \qquad (\gamma\downarrow0). \] The asymptotically exact QLD radius tradeoff is \[ \rho_L^\star = \frac{L}{L+1}\frac{1-R}{2}. \] These conclusions extend to the average-radius setting. For achievability, building on the work of Brakensiek, Chen, Dhar, and Zhang (STOC 2026), we establish a pairing lemma for joint \(X/Z\) candidate lists that preserves the one-sector coefficient and avoids a product loss in list size. For the QLD converse, we prove a quantum generalized Singleton bound based on the classical projection-and-patching argument with stabilizer distinctness. For the QLR lower bounds, we adapt the folded Reed–Solomon construction of Chen and Zhang (STOC 2025) so that the candidates remain stabilizer distinct. For random CSS codes, we show classical bad lists survive the stabilizer quotient with high probability.
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Quantum Physics

Quantum Algorithms for Minimum Generating Set

Bireswar Das, Udit Kumar, Kavita Samant et al. (+1 more)

In this paper, we present a polynomial-time quantum algorithm for computing a minimum-sized generating set of solvable black-box groups. Next, we consider the class $\Gamma_d$ of black-box groups, where every non-abelian composition factor is isomorphic to a subgroup of the symmetric group $S_d$ for a fixed $d$. We design polynomial-time quantum algorithms to compute the direct product decomposition of abelian factor groups and solve the constructive membership problem for factor groups of groups from $\Gamma_d$. With the help of these algorithms, we design a quantum algorithm for computing a chief series of black-box groups from $\Gamma_d$. Using the chief series, we construct a polynomial-time quantum algorithm for computing minimum generating sets of black-box groups from $\Gamma_d$. Finally, we show that the minimum generating set problem for general black-box groups is in $\textrm{NP} \cap \textrm{coAM}$.
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All authors Bireswar Das, Udit Kumar, Kavita Samant, Dhara Thakkar

Quantum Physics

Self-testing the toric code against classical communication

Gustavo Fróes, Amanda Wei, Carlos de Gois et al. (+2 more)

Device-independent self-testing certifies a multipartite quantum state from the correlations it produces alone, without assumptions on the inner workings of the devices. Most existing self-tests, however, break down as soon as the parties can exchange messages. We consider a relaxed setting in a quantum network, where in the honest version of the protocol, the parties never communicate, yet certification remains sound even in an untrusted case where the untrusted devices secretly exchange classical messages within a bounded distance in the network. We show that the code space of the toric code, distributed over a network with the geometry of a torus, can be self-tested in this setting in a noise-robust way, against communication up to distances proportional to the network diameter. We also develop an algorithmic method for constructing such protocols and extend our results to the surface code and cluster states, robust to one round of nearest-neighbor classical communication
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All authors Gustavo Fróes, Amanda Wei, Carlos de Gois, Denis Rochette, Marc-Olivier Renou

Mathematical Physics · Cross-listed from math.AG

Structure of higher-genus open-closed Gromov–Witten theory of $\mathcal{O}_{\mathbb{P}^{1}}(p-1)\oplus\mathcal{O}_{\mathbb{P}^{1}}(-p-1)$

Shuai Guo, Jingyi Xu and Qingsheng Zhang

We study the closed and open Gromov–Witten potentials of the toric Calabi–Yau threefold $$ X_p=\operatorname{Tot}\bigl(\mathcal{O}_{\mathbb{P}^{1}}(p-1)\oplus\mathcal{O}_{\mathbb{P}^{1}}(-p-1)\bigr),\qquad p\geq 2. $$ We prove closed and open mirror symmetry under a nonvanishing condition on the torus weights, relating these potentials to topological recursion on the mirror curves. We establish polynomial structures for both the higher-genus closed potentials and the stable open potentials. We also establish double-scaling limits for topological recursion on the mirror curves. In particular, our results for the closed potentials prove the higher-genus ansatz and the double-scaling conjecture of Caporaso–Griguolo–Mariño–Pasquetti–Seminara.
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Atomic Physics

Nonrelativistic expansions of Dirac-Coulomb energy and first order relativistic Breit potential corrections for light Atomic and molecular systems

Wanping Zhou, Sanjiang Yang and Chen Tong

The nonrelativistic expansion method is applied to the Dirac-Coulomb energy and first order relativistic Breit potential corrections for light atomic and molecular systems to derive high-order effective energy correction operators for few-body systems. It is found that effective operators at the $m\alpha^8$ order contain incompletely separable divergences. These divergences must be canceled jointly with divergences arising from second- and third-order perturbations of lower-order energy correction operators, and such cancellation can be accomplished automatically by the nonrelativistic numerical expansion approach. Using Gaussian basis sets, we numerically compute contributions to the Dirac-Coulomb energy and relativistic Breit potential corrections up to order $m\alpha^8$ for the ground states of the hydrogen atom, hydrogen molecular ion, helium atom, and hydrogen molecule. These results confirm the reliability of the present method and enable its extension to more complex systems.
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Quantum Physics

A General Theory of Multi-Resource Theories Involving Finite-Group Asymmetry

Yosuke Mitsuhashi and Hiroyasu Tajima

Resource theories provide a universal framework for quantifying properties of quantum states, such as entanglement, magic, athermality, and asymmetry, as resources under various constraints encountered in quantum science. Since realistic settings typically impose several constraints at once, it is important to study multi-resource theories that combine them. Among these, combinations with asymmetry are especially natural, as symmetry is fundamental and ubiquitous in physics. Here we develop a general theory that treats combinations of finite-group asymmetry with a broad range of resource theories in a unified manner. Our key observation is that the effect of combining the two constraints is governed by the accessibility of symmetry information under the underlying resource theory: whether the information needed for the conversion can be extracted from the input and used to control free operations. If this can be done with asymptotically vanishing error, we show that the conversion rate of the combined theory equals the smaller of the rates of the two constituent theories, so combining them incurs no additional cost. This condition holds for LOCC on arbitrary mixed multipartite states, magic-state conversion of multiqubit systems under Clifford symmetries, and Gibbs-preserving operations. Thermal operations, being time-translation covariant, can access only limited symmetry information, giving an additional compatibility condition between the two symmetries. We also analyze symmetry imposed on elementary operations rather than only on the resulting channel. We establish analogous results for LOCC and thermal operations under suitable assumptions, and for magic when the symmetry is represented by Pauli operators. Finally, we show that finite-group symmetry does not reduce the asymptotic ergotropy per copy and hence introduces no new completely passive states.
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Quantum Physics

Quantum oblique eigenprojection

Alexander M. Dalzell and Yuan Su

Every square matrix decomposes its underlying Hilbert space into generalized, nonorthogonal eigensubspaces. We show that a quantum computer can perform such an oblique eigenprojection $\Pi$ given block encoding access to the input matrix. Our approach has a query complexity nearly linear in the inverse gap and a normalization factor close to $\lVert\Pi\rVert$ under a spectral-set condition on the input. This covers common assumptions on the numerical range or diagonalizability and matches known results for orthogonal eigenprojections. We achieve this with a two-sided block preconditioning that uses a discrete Fourier transform of the matrix resolvent. We describe applications to: (i) preparing eigenstates of matrices with complex eigenvalues, extending the quantum eigenvalue transformation algorithm of Low and Su beyond real spectra; (ii) solving continuous-time algebraic Riccati equations, cubically speeding up a prior solver of Rodenas-Ruiz, Zhao, and Lee; and (iii) solving ordinary Sylvester equations, quadratically improving a direct augmented method of Wang and Liu. Our result suggests a promising route to applying nonanalytic matrix functions on quantum computers.
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Quantum Physics · Cross-listed from cs.IT

From Random Quantum Codes to Explicit qLDPC Codes via Local Properties

Fernando Granha Jeronimo, Xiaojuan Ma and Nikhil Shagrithaya

Constructing explicit codes matching the parameters of random codes has been a central and largely elusive question in coding theory. The quantum setting is even more challenging since it is highly desirable that the quantum code be an LDPC code. Local coordinate-wise linear (LCL) [Levi, Mosheiff, and Shagrithaya, FOCS 2025] witnesses provide a unifying language for many coding-theoretic properties, from distance to list decoding and list recovery. In particular, it provides a framework to study properties of random linear codes, which achieve optimal parameters for many properties of linear codes. For CSS quantum codes, however, a local witness has two distinct ranks: its physical rank before quotienting by stabilizers and its logical rank after quotienting. We develop a quantum version of the LCL framework for nested spaces $S \subseteq C$, in which local constraints are imposed on physical representatives while independence is measured in the logical quotient $C/S$. The resulting theory gives a threshold theorem for random CSS codes, and as a consequence shows that the per-sector rate threshold is equal to the classical rate threshold. We also define a quantum analogue of subspace design [Guruswami and Xing, STOC 2013] and show that they can be described in a natural manner within the quantum-LCL framework. Finally, we give explicit constructions for arbitrary folded quantum-LCL properties, in a manner similar to the LCL derandomization of [Jeronimo and Shagrithaya, STOC 2026]. As a consequence, we obtain the first explicit constructions of quantum list-decodable codes and list-recoverable codes that have optimal list sizes, in addition to explicit quantum subspace design codes. We note that all our explicit constructions are qLDPC codes, an important property for quantum error-correcting codes.
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Quantum Physics

An (almost) efficient classical algorithm for sampling from typical Gibbs states

Saleh Naghdi and Eric R. Anschuetz

Gibbs state preparation has emerged as a potential avenue for quantum advantage in the study of physical systems. Although there is known advantage for computing local properties of worst-case Gibbs states, recent results suggest a different picture for average-case local systems: at temperatures where their Gibbs states can be efficiently prepared quantumly, quasi-polynomial time classical algorithms can also compute local expectation values. Yet this leaves open the possibility of an advantage under a stronger notion of simulation: sampling. Gibbs sampling underlies Boltzmann machine-based quantum learning algorithms and quantum supremacy proposals, but its classical average-case complexity for physically relevant models remains unresolved. Here, we give strong evidence against an exponential quantum advantage in Gibbs sampling for an ensemble of local systems known as the quantum $p$-spin model. We describe a classical algorithm for sampling from the Gibbs state to any polynomially small error in total variation distance. Our algorithm is based on a meta-algorithm known as algorithmic stochastic localization (ASL). Our main technical result is a generalized convergence theorem for ASL which reduces approximate sampling from any distribution on the hypercube to estimating the mean of a related "tilted distribution" to sufficiently low additive error. We then extend known quasi-polynomial time algorithms for computing local expectation values of a related disordered model to compute these "tilted means" for the quantum $p$-spin model. Finally, we give a non-rigorous physics argument that this mean-estimation algorithm works down to the spin glass transition temperature. As efficient quantum algorithms also fail at this transition, this suggests they cannot Gibbs sample the quantum $p$-spin model at temperatures below that for which classical algorithms are also (almost) efficient.
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Quantum Physics

Optimal Purity Estimation with Incoherent Measurements

Junseo Lee and Chirag Wadhwa

In this work, we consider the fundamental task of estimating the purity of an unknown state to within $\textit{multiplicative}$ error $\varepsilon$. When one can perform general collective measurements, $\Theta\left(\frac{\sqrt{d}}{\varepsilon^2} + \frac{d}{\varepsilon}\right)$ copies are known to be necessary and sufficient for this problem [AISW20]. However, implementing collective measurements on such a large number of copies can be experimentally demanding, and we thus aim to characterize the copy complexity of this problem with incoherent measurements. In this setting, the only non-trivial result is a non-adaptive algorithm that uses $O\left( \frac{d}{\varepsilon^2} + \frac{d^2}{\varepsilon} \right)$ copies [PTTW26], which is polynomially larger than the best-known lower bound. Our first result is a new algorithm performing non-adaptive incoherent measurements that succeeds using $O\left( \frac{d}{\varepsilon^2} + \frac{d^{3/2}}{\varepsilon} \right)$ copies, improving on the latter term in the copy complexity. Moreover, we show that for any algorithm restricted to non-adaptive measurements, the above copy complexity is optimal. We also develop a new adaptive estimator for the purity of a state that improves on the above complexity in the high-precision regime, i.e., for $\varepsilon = o(1/d)$. We also show that the non-adaptive and adaptive estimators together yield the optimal complexity for incoherent purity estimation; in particular, we show that the copy complexity of this problem is $$ \Theta\left(\min\left\{ \frac{d}{\varepsilon^2} + \frac{d^{3/2}}{\varepsilon}, \frac{d^2}{\varepsilon} + \frac{\sqrt{d}}{\varepsilon^2}\right\} \right). $$
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General Relativity and Quantum Cosmology

Flat limit of artificial cosmology for scalar waves in Schwarzschild-de Sitter

An{\i}l Zenginoğlu and Govind Arun Kumar

How do cosmological waveforms approximate waveforms from isolated systems for a small cosmological constant? This question is motivated by the observed small value of the cosmological constant, and also by Misner's idea to regulate the formally singular terms introduced into the Einstein equations by conformal compactification. We investigate this question quantitatively using scalar waves on Schwarzschild–de Sitter backgrounds. A suitable flat limit requires the foliation to remain regular at the future conformal boundary. We compare bridge foliations extending from the black hole horizon to the cosmological horizon with a regular asymptotically flat limit. Comparisons of cosmological and asymptotically flat waveforms on geometrically matched data show that the flat limit is numerically well behaved and recovers the essential features of the asymptotically flat waveform. We extend Misner's artificial cosmology by introducing a cosmological source that leaves the near-zone geometry unchanged and show that it improves agreement of the ringdown waveform but fails to capture the intermediate polynomial tail behavior accurately.
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Instrumentation and Methods for Astrophysics

Two bits about lossy compression: On the limits of compression in cosmology

Hurum Maksora Tohfa and Matthew McQuinn

Astronomy is in an era of enormous sky surveys and of the large simulation suites needed to interpret them, both costly to store and slow to share. Simulation outputs are stored as 32-bit floats, yet numerical noise and astrophysical uncertainties make better than percent-level pixel accuracy unnecessary. Because cosmological fields are statistically homogeneous with nearly Gaussian mode amplitudes, classic rate-distortion results apply directly, and non-Gaussian structure permits further compression. We use the scientific compression package SZ3, and a neural compressor that fixes the quantization and learns the probability of each quantization bin with an autoregressive transformer. SZ3 beats the Gaussian approach only where the field is smooth on the pixel scale or its values pile up at a single point, while the neural approach matches or beats SZ3 on every field we consider and is 9 to 27% below the Gaussian-optimal coder at fixed distortion, with the largest margin where the field is most non-Gaussian. Because the quantizer, not the network, sets the error, a poorly trained model can waste bits but never cost accuracy. A model trained only on weak lensing convergence maps transfers to $N$-body density fields without retraining, suggesting it has learned generic properties of cosmological structure rather than features of one dataset. Eulerian grids need only 1-4 bits per pixel (bpp) at percent-level accuracy, and particle displacements and velocities 5-6 at the precisions they require. The approach carries over to observational data: on Rubin Observatory Data Preview 1 coadds, with the quantization step set to a quarter of the background noise, the fine-tuned transformer needs 4.0 bpp, 27% fewer than the Gaussian coder.
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High Energy Physics (Experiment)

First double-differential cross-section measurements in proton multiplicity and kinematics for mesonless $\nu_{\mu}$ charged-current interactions on argon using the MicroBooNE detector

MicroBooNE collaboration: P. Abratenko, D. Andrade Aldana, J. Asaadi et al. (+186 more)

We present the first double-differential cross-section measurements of muon neutrino charged-current interactions on argon with no mesons and one or more protons ($N_{p} \geq 1$) in the final state as a function of proton multiplicity and kinematics. The analysis uses the full Booster Neutrino Beam dataset collected by the MicroBooNE detector at Fermi National Accelerator Laboratory, corresponding to a total of $1.30 \times 10^{21}$ protons on target. We measure cross sections as a function of the proton multiplicity, the momenta and muon-proton opening angles of the leading and subleading protons up to and including the fourth-leading proton, as well as the total available kinetic energy of the hadronic system. The treatment of the statistical and systematic uncertainties includes correlations between the different extracted distributions. The measured cross sections are compared to predictions from several event generators using different primary and final-state interaction models. The results reveal strong sensitivity to the modeling of final-state interactions, and none of the generators tested provides a fully adequate description of the data. Significant disagreement between data and predictions is observed in the proton multiplicity distributions, particularly at backward opening angles and for subleading proton kinematics.
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All authors MicroBooNE collaboration: P. Abratenko, D. Andrade Aldana, J. Asaadi, A. Ashkenazi, S. Balasubramanian, B. Baller, A. Barnard, G. Barr, D. Barrow, J. Barrow, V. Basque, J. Bateman, B. Behera, O. Benevides Rodrigues, S. Berkman, A. Bhat, M. Bhattacharya, V. Bhelande, A. Binau, M. Bishai, A. Blake, B. Bogart, T. Bolton, M.B. Brunetti, L. Camilleri, D. Caratelli, F. Cavanna, G. Cerati, A. Chappell, Y. Chen, J.M. Conrad, M. Convery, L. Cooper-Troendle, J.I. Crespo-Anadon, R. Cross, M. Del Tutto, S.R. Dennis, P. Detje, R. Diurba, Z. Djurcic, K. Duffy, S. Dytman, B. Eberly, P. Englezos, A. Ereditato, J.J. Evans, C. Fang, B.T. Fleming, W. Foreman, D. Franco, A.P. Furmanski, F. Gao, D. Garcia-Gamez, S. Gardiner, G. Ge, S. Gollapinni, E. Gramellini, P. Green, H. Greenlee, L. Gu, W. Gu, R. Guenette, L. Hagaman, M. D. Handley, O. Hen, A. Hergenhan, M. Harrison, S. Hawkins, C. Hilgenberg, G.A. Horton-Smith, A. Hussain, B. Irwin, M.S. Ismail, C. James, X. Ji, J.H. Jo, A. Johnson, R.A. Johnson, D. Kalra, G. Karagiorgi, W. Ketchum, A. Kelly, M. Kirby, T. Kobilarcik, K. Kumar, N. Lane, J.-Y. Li, Y. Li, K. Lin, B.R. Littlejohn, L. Liu, S. Liu, W.C. Louis, X. Luo, T. Mahmud, N. Majeed, C. Mariani, J. Marshall, D.A. Martinez Caicedo, F. Martinez Lopez, M. G. Manuel Alves, S. Martynenko, A. Mastbaum, I. Mawby, N. McConkey, B. McConnell, L. Mellet, J. Mendez, J. Micallef, T. Mohayai, A. Mogan, M. Mooney, A.F. Moor, C.D. Moore, L. Mora Lepin, M. A. Hernandez Morquecho, M.M. Moudgalya, S. Mulleria Babu, D. Naples, A. Navrer-Agasson, D. Nawarathne, N. Nayak, M. Nebot-Guinot, C. Nguyen, L. Nguyen, J. Nowak, N. Oza, O. Palamara, N. Pallat, V. Paolone, A. Papadopoulou, V. Papavassiliou, H. Parkinson, S.F. Pate, N. Patel, Z. Pavlovic, E. Piasetzky, K. Pletcher, I. Pophale, X. Qian, J.L. Raaf, V. Radeka, A. Rafique, M. Reggiani-Guzzo, J. Rodriguez Rondon, M. Ross-Lonergan, I. Safa, C. Sauer, D.W. Schmitz, A. Schukraft, W. Seligman, M.H. Shaevitz, R. Sharankova, L. Silva, E.L. Snider, S. Soldner-Rembold, J. Spitz, M. Stancari, J. St. John, T. Strauss, A.M. Szelc, K. Terao, C.Thorpe, D. Torbunov, D. Totani, M. Toups, A. Trettin, Y.-T. Tsai, J. Tyler, M.A. Uchida, T. Usher, B. Viren, M. L. Velazquez Fernandez, L. Wang, M. Weber, H. Wei, A.J. White, S. Wolbers, T. Wongjirad, K. Wresilo, W. Wu, E. Yandel, T. Yang, L.E. Yates, H.W. Yu, G.P. Zeller, J. Zennamo, C. Zhang, Y. Zhang

High Energy Physics (Phenomenology)

Interpreting the High-Recoil LUX-ZEPLIN Event with Bino-/Singlino-like and Higgsino Dark Matter

Subhojit Roy, Pedro Schwaller and Carlos E. M. Wagner

The LUX-ZEPLIN (LZ) experiment has recently reported a nuclear-recoil candidate at $E_R\simeq248$ keV. We study two supersymmetric interpretations based on distinct neutralino couplings to the $Z$ boson. In the elastic case, a bino- or singlino-like neutralino scatters through a diagonal axial $Z$ coupling set by the Higgsino asymmetry $X=|N_{13}|^2-|N_{14}|^2$ rather than by the total Higgsino fraction. Since the spin-dependent blind spot does not coincide with the spin-independent one, Higgs-mediated scattering can be suppressed while retaining $X\sim10^{-2}$. In the MSSM this favors low $\tan\beta$, in tension with the observed Higgs mass for a few-TeV squark spectrum, a tension relieved by the tree-level quartic of the NMSSM. An explicit NMSSM benchmark with $m_\chi\simeq500$ GeV and $X\simeq0.007$, below current LZ limits, obtains its relic abundance from a singlet-like pseudoscalar resonance just above threshold, which also suppresses present-day annihilation. In the inelastic case, a pseudo-Dirac Higgsino scatters endothermically, with a splitting of a few hundred keV generated by gauginos at the PeV scale which can be lowered by opposite-sign bino-wino cancellation, or by weak singlino mixing; the minimal thermal realization is strongly constrained by solar-neutrino searches. The two mechanisms predict distinct recoil spectra away from the candidate.
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Astrophysics of Galaxies

Sub-kiloparsec Test of the Kennicutt-Schmidt Relation in a Strongly Lensed Dusty Star-Forming Galaxy at z~2.78

C. Cornil-Baïotto, J. Molina, G. Mahler et al. (+9 more)

[abridged] Star formation is a key process driving galaxy evolution, but understanding how it proceeds within the interstellar medium (ISM) requires resolving cold molecular gas and dust on sub-kpc scales. At z~2-3, near the peak of cosmic star formation, such resolution can generally only be achieved through strong gravitational lensing. We present an ALMA study of SMMJ0658, a 20x-magnified main-sequence star-forming galaxy at z=2.7768 +/- 0.0002, lensed by the Bullet Cluster (z=0.296) into three images. We use 0.2" and 0.6" ALMA Band-3 observations to test the Kennicutt-Schmidt (KS) relation at sub-kpc scales at cosmic noon. Using a JWST-based strong-lensing model of the Bullet Cluster, we reconstruct source-plane CO(3-2) and rest-frame 803um dust-continuum maps down to ~200pc scales. We derive spatially resolved molecular gas and star formation rate surface densities, depletion times, and the scale dependence of the CO-to-dust flux ratio over 200pc-3.2kpc apertures. The 0.2" ALMA data reveal massive, dense star-forming clumps, with Sigma_mol ~1.3-2.3 x 10^3 M_sun pc^-2, Sigma_SFR ~0.5-2.3 M_sun yr^-1 kpc^-2, and tau_dep ~0.82-2.56 Gyr. CO-dust spatial decorrelation produces a strong scale dependence in tau_dep. We find a KS-relation breakdown scale of 0.8 +/- 0.1 kpc, consistent with individual regions tracing distinct stages of the star-formation cycle. The ALMA and JWST data also reveal evidence for a lensed galaxy pair at z~2.78, although whether SMMJ0658 is undergoing an early-stage interaction remains uncertain. Our results show that the apparent universality of the KS relation breaks down once individual star-forming regions are spatially resolved, in line with observations from the local universe to z~1. We extend this picture to z~2.78, providing new insight into the resolved properties of the clumpy cold ISM and the star-formation cycle at cosmic noon.
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All authors C. Cornil-Baïotto, J. Molina, G. Mahler, G. Rihtaršič, M. Boquien, M. Bradač, E. Ibar, A. H. Gonzalez, T. Verdugo, O. López-Cruz, J. Magaña, V. Motta

Quantum Physics

A Quantum Algorithm for $st$-Transport on Flat Connection Graphs

Stacey Jeffery, Tobias J. Osborne and Galina Pass

We study a generalization of undirected $st$-connectivity to graphs whose edges carry quantum operations. Let $G=(V,E)$ be an undirected graph on $n$ vertices in which each edge $\{u,v\}$ is labeled by a unitary $U_{uv}\in\mathbb{C}^{k\times k}$, with $U_{vu}=U_{uv}^\dagger$. We assume the labels form a flat connection: the ordered product of labels along any path between a pair of vertices $u$ and $v$ is independent of the path. Equivalently, the connection is pure gauge, i.e., gauge-equivalent to the trivial connection; such graphs are exactly the consistent connection graphs of spectral graph theory and the noiseless instances of group synchronization. Consequently, whenever $s$ and $t$ are connected, transporting a state from $s$ to $t$ defines a unique unitary $U_s(t)$. Given states $|\psi_s\rangle,|\psi_t\rangle\in\mathbb{C}^k$ and an oracle that returns the neighbours of a vertex while coherently applying the corresponding edge unitaries, the \emph{$st$-transport problem} is to decide whether $s$ and $t$ are connected and, if so, to estimate the squared overlap between $U_s(t)|\psi_s\rangle$ and $|\psi_t\rangle$ to additive error $\varepsilon$. When $k=1$ and all labels are trivial, this is exactly undirected $st$-connectivity. We give a bounded-error quantum algorithm for $st$-transport that runs in time $\widetilde{O}(n/\varepsilon)$ and uses $O(\log n+\log k+\log(1/\varepsilon))$ space. We do this by designing a transducer and applying a Metropolis-Hastings reweighting to the input graph. We also prove an $\Omega(n)$ quantum query lower bound that holds even when $s$ and $t$ are promised to be connected, so for constant $\varepsilon$ our algorithm is optimal up to polylogarithmic factors.
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High Energy Physics (Phenomenology)

$\mathcal{O}(\alpha\alpha_s^2)$ corrections to the Top Quark mass

Daniele Gaggero and Ciaran Williams

We calculate the three-loop $\mathcal{O}(\alpha\alpha_s^2)$ mixed QCD-EW corrections to the top quark mass and obtain the relationships between the pole ($M_t$) and $\overline{\rm{MS}}$ ($m_t(\mu)$) masses at this order. In performing our calculation, we express the three-loop self-energies as a function of three-loop master integrals (MIs). These MIs are defined so as to solve a differential equation in $\epsilon$-factorized form, allowing for their solution to be expressed as iterated integrals. We discuss the types of differential forms that we encounter, which include periods of elliptic curves, and their role in the final physical result. Using our results, we calculate the shift in $m_t(M_t)$ arising at this order. For $M_t = 172.3$ GeV, the shift is -216 MeV, which is comparable to the currently quoted experimental uncertainty.
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Quantum Physics

Perfect non-local quantum computation is impossible

Marten Folkertsma, Dmitry Grinko, Gina Muuss et al. (+1 more)

Non-local quantum computation (NLQC) asks two parties to apply a joint operation to their quantum inputs using an entangled resource state and one round of simultaneous quantum communication. NLQC has applications across quantum information, including attacks on quantum position verification, communication complexity, and quantum gravity. Every bipartite unitary has an approximate NLQC protocol with finite entanglement, and exact protocols are known for several structured families. However, it has remained open whether every fixed unitary admits an exact protocol with finite-dimensional resources. We show that, even for two qubits, Haar-almost every unitary does not admit such a protocol, even when the resource state and local operations are tailored to the target. The proof first shows that smooth deformations of an exact protocol can only change its target by local unitaries. For a fixed architecture, semialgebraic geometry limits the exact protocols to finitely many connected families, so each architecture reaches only finitely many local-unitary orbits. Taking the union over all architectures, the exactly implementable unitaries form countably many local-unitary orbits. We also show that some natural targets do not admit a protocol: the controlled phase $\mathrm{diag}(1,1,1,e^{i\theta})$ has no exact protocol with finite-dimensional resources whenever $e^{i\theta}$ is transcendental, for instance for $\theta = 1$. Our results also apply to localizable quantum measurements, whose outcome is obtained from local measurements on inputs and a shared entangled resource state without communication. A rank-one projective measurement in a Haar-random basis is almost surely not localizable with a finite-dimensional resource state and finitely many local outcomes.
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All authors Marten Folkertsma, Dmitry Grinko, Gina Muuss, Florian Speelman

Quantum Physics

Randomness of exact unitary designs under symmetry

Christopher Vairogs and Felix Leditzky

We define the unitary design strength of a finite unitary ensemble to be the maximal integer $t$ for which its $t$-th statistical moment is identical to that of the unitary group. In the presence of physical symmetry, not all operators of an ensemble are symmetry-compatible. This motivates us to define the symmetric design strength of a finite unitary ensemble to be the maximal integer $t$ for which the $t$-th moments of its symmetry-compatible sub-ensemble match those of the group of symmetry-compatible unitaries. We show that in sufficiently high dimension and for a broad family of symmetries, which includes the global on-site $\mathrm{U}(1)$ and $\mathrm{SU}(d)$ symmetries, there exist finite unitary ensembles of arbitrarily high design strength whose symmetric design strength is strictly higher. Ensembles with this property may be more versatile under symmetry constraints for protocols that rely on unitary randomization than they are without symmetry. Our results extend the previous work [Mitsuhashi and Yoshioka, PRX Quantum 4.4 (Nov. 2023)] showing that the symmetric design strength of the Clifford group is strictly upper bounded by its unitary design strength for symmetries that do not trivialize the symmetry-compatible unitaries. Due to the special significance of unitary designs with a group structure, we also derive a variety of bounds on the unitary and symmetric design strengths of finite unitary ensembles whose operators form a group. In particular, we provide a simple proof that an arbitrary ensemble of operators forming a finite group must have a symmetric design strength of at most two under the global on-site $\mathrm{U}(1)$ and $\mathrm{SU}(d)$ symmetries. Along the way, we show that there exist uniformly weighted groups of arbitrarily high symmetric design strength in arbitrary dimension and analyze their structure.
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Quantum Physics

A physical and universal model of bosonic computations with Solovay-Kitaev theorem

Dorian Rudolph, Arsalan Motamedi, Dhruva Sambrani et al. (+4 more)

Bosonic quantum systems are among the leading architectures for quantum information processing, offering continuous-variable degrees of freedom with strong error-correction capabilities. However, standard bosonic quantum computation models such as the Lloyd-Braunstein [Lloyd and Braunstein, 1999] and hybrid oscillator-qubit models [Brenner, Dias, and Koenig, 2025; Liu et al., 2026] permit dramatic energy growth, leading to unphysical computational power and the breakdown of fundamental algorithmic tools such as universal and efficient compilation [Brenner et al., 2026; Rudolph et al., 2025]. To address this, we introduce a new model of bosonic quantum computation, Bosonic Energy-Preserving Quantum Computation (BEQC), in which energy is treated as a computational resource. Namely, energy is supplied solely through input coherent states, and all gates are generated by energy-preserving Hamiltonians. Thus, by construction, dramatic energy growth is impossible, making the model physically grounded. We next show that BEQC is a computationally robust and universal model in many respects, including: (1. Computational power) BEQC efficiently simulates all polynomial-energy computations in existing models, and exactly recovers BQP in the polynomial energy setting. It further admits several complexity-theoretic upper bounds when varying the energy, precision, and space parameters of the model. (2. Universal gate sets and state synthesis) BEQC has natural universal gate sets based on linear optics and Kerr interactions. In particular, we obtain a Solovay-Kitaev theorem which circumvents previous no-go results. We give various applications, including (a) a protocol for engineering GKP states with rigorous preparation guarantees, (b) Fock state preparation to exponential precision, and (c) native Fock space simulation of any qubit-based unitary.
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All authors Dorian Rudolph, Arsalan Motamedi, Dhruva Sambrani, Hamid Reza Naeij, Ulysse Chabaud, Sevag Gharibian, Saeed Mehraban

High Energy Physics (Phenomenology)

In medium evolution of the energy-energy correlators

Weiyao Ke

In this work, we present a first-principles analysis of the scale evolution of the two-point energy-energy correlator (EEC) for quark and gluon jets propagating through QCD matter. The EEC is a jet substructure observable that encodes the angular distribution of energy flow within jets and has proven valuable for precision tests of QCD in elementary collisions. Extending this framework to reactions with nuclei, we derive a factorized description of the in-medium EEC using Soft Collinear Effective Theory with Glauber gluon interactions, allowing systematic inclusion of medium-induced interactions. Working in the opacity expansion, we compute the medium-modified quark and gluon jet functions at one loop and perform leading-logarithmic resummation of large-scale logarithms. We find an experimentally accessible kinematic regime where medium effects manifest directly through medium-induced corrections to the anomalous dimensions, providing a transparent probe of in-medium dynamics. We test the theoretical framework by comparing our analytic predictions with EEC measurements in p-Pb collisions and discuss its implications for small collision systems (O-O) and the EIC.
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