Quantum Physics
Characterizing Quantum Advantage for Generalizations of the Boolean Hidden Matching Problem
Mark Bun, Joao F. Doriguello, John Kallaugher et al. (+1 more)
We study the one-way communication complexity of the $f$-Boolean Hidden Partition problem. Here, Alice is given an $n$-bit string and Bob is given $\Omega(n)$ disjoint blocks of its indices together with a string of labels. Under the promise that the evaluations of $f$ on these blocks either agree with all of the labels or disagree with all of them, Bob must determine which is the case using a single message from Alice. This problem generalizes the Boolean Hidden Matching and Hidden Hypermatching problems, which capture the special case where $f$ is the parity function. We establish classical and
quantum communication bounds for $f$-Boolean Hidden Partition in terms of the sign degree $d$ of $f$, proving a
conjecture of Doriguello and Montanaro (TQC 2020). Their prior work gave logarithmic communication upper bounds for classical protocols when $d \le 1$ and
quantum protocols when $d \le 2$, as well as
polynomial lower bounds for certain structured functions with larger sign degree. We show that for every $f$ of sign degree $d \ge 2$, the randomized classical communication complexity of this problem is $\Theta(n^{1-1/d})$ while its
quantum communication complexity lies between $\Omega(n^{1-2/d})$ and $\bO{n^{1-1/\lceil d/2 \rceil} \log n}$. This completely characterizes the functions $f$ admitting
polynomial quantum advantage as those for which $d \ge 2$, with a new infinite family of exponential separations given by the case $d = 2$.
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All authors Mark Bun, Joao F. Doriguello, John Kallaugher, Nadezhda Voronova
Quantum Physics
Computational entanglement distillation beyond pure states: efficient protocols and fundamental limitations
Takeru Utsumi, Jacopo Rizzo, Ryuji Takagi et al. (+1 more)
The information-theoretic approach to
entanglement typically relies on arbitrarily many input copies and unboundedly complex operations; however, the available resources are constrained in reality. This motivates the study of
entanglement theory with limited resources. One of its central questions is which quantities characterize
entanglement manipulations, and so far, only the idealized case of pure states has been well explored. In this work, we address
entanglement distillation from mixed states and identify the Rényi coherent information as the quantity determining the optimal rate in the worst case under two distinct resource constraints. We first characterize the sample-efficient regime, in which unbounded computational power is allowed. Our universal protocol achieves this rate without knowledge of the input state under certain
polynomial rank constraints. This rate is optimal among universal protocols: we construct states whose distillable
entanglement is nearly extensive, yet from which no universal sample-efficient protocol attains a rate above their Rényi coherent information. We then push this characterization to the computationally efficient frontier: the same bound holds for any efficient protocol even when the input state is known, and another universal protocol achieves this rate efficiently under additional
polynomial constraints on the marginal ranks. Overall, our results give the Rényi coherent information a novel operational meaning in two computational settings: universal
distillation with limited copies and efficient
distillation even with knowledge of the input state.
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All authors Takeru Utsumi, Jacopo Rizzo, Ryuji Takagi, Lorenzo Leone
Quantum Physics
Quantum-optimized phase closure for robust interferometric imaging
Zhenning Liu, Emil T. Khabiboulline, Lorcan O. Conlon et al. (+7 more)
Closure phase enables imaging with ground-based interferometric arrays by canceling
telescope-dependent phase errors due to atmospheric fluctuations. It can be obtained by measuring fringe phases on individual baselines forming a triangle and summing them. We show that closure phases can be measured more accurately with fewer
photons by performing joint measurements on multiple
photons. We first establish that at least three
photons from the same atmospheric temporal phase-stability window are required for closure-phase information to survive the unknown
telescope-dependent phase noise, and show that joint three-
photon measurements already provide an advantage over single-
photon measurements in the minimal three-
telescope setting. We then turn to large arrays and consider estimating all bispectra—complex quantities whose phases are the closure phases—under a global mean-square error criterion. Although an $m$-
telescope array contains $\Theta(m^2)$ independent triangle bispectra, we show that physical constraints on the visibilities make the total information content grow only nearly linearly with $m$ at fixed accuracy. Exploiting this structure, we construct an efficient protocol using at most three-
photon joint measurements with
photon cost $\tilde{O}(m)$, whereas any sequential single-
photon protocol requires $\Omega(m^2)$
photons. When the number of detected
photons per temporal stability window scales linearly with the array size, this allows the required exposure time to remain independent of $m$ up to logarithmic factors. We further analyze the complementary high-precision regime using multiparameter
quantum metrology and find a similar advantage for collective measurements. Overall, our results show that
quantum information processing techniques can substantially improve the sensitivity and robustness of optical interferometry.
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All authors Zhenning Liu, Emil T. Khabiboulline, Lorcan O. Conlon, Brittany McClinton, Aqil Sajjad, Saikat Guha, Jayadev Rajagopal, Alexey V. Gorshkov, Daniel Gottesman, Stephen T. Ridgway
High Energy Physics (Experiment)
How to scale your HEP ML models: A recipe for robust architecture comparisons at scale
Matthias Vigl, Nikita Pond, Jackson Barr et al. (+5 more)
Much of the recent progress in machine learning domains such as
language models has come from scaling laws that predict performance as a function of training effort. In high-energy physics (HEP) similar behavior has now been observed. To aid further study, we present a systematic procedure to derive robust scaling laws and compare design choices on the relevant budget axes for HEP tasks. We first validate the full scaling trajectory on toy problems and then apply the procedure to multi-task
transformers on the ~11 billion-jet ATLAS JetSet2
dataset, in both the compute- and data-constrained regimes. For the latter, we predict, to the best of our knowledge for the first time, the jointly optimal model size, training horizon, learning rate and batch size under early stopping. At compute-optimal scaling, we recover a near-equal $\sqrt{C}$ dependence of model and
dataset size, and find that auxiliary objectives lower the primary jet-classification loss at equal compute budget. Expanding the inputs toward lower-level data systematically lowers the loss while leaving the scaling exponent nearly unchanged. The onset of the power-law regime is itself set by scale: below a threshold in
dataset size the loss carries little information about high-compute scaling, underscoring the value of large, high-quality full-simulation
datasets as a foundation for scaling studies and the development of foundation models in HEP.
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All authors Matthias Vigl, Nikita Pond, Jackson Barr, Alexander Froch, Dan Guest, Nicole Hartman, Michael Kagan, Lukas Heinrich
Quantum Physics
Sabee Grewal, Angelos Pelecanos, Jack Spilecki et al. (+2 more)
We give a shadow
tomography algorithm that uses $O(\log(m) \log(m/\delta) / \varepsilon^2)$ copies of the input state. Specifically, given a
quantum state $\rho$ and observables $O_1,\ldots,O_m$, the
algorithm outputs estimates of $\mathrm{tr}(O_i\rho)$ for all $i\in[m]$ that are all accurate to within $\pm\varepsilon$, except with probability at most $\delta$. The key idea is to work in the average-case setting: for a random state drawn from a known prior, a pretty good measurement on $O(\log(m)/\varepsilon^2)$ copies gives a constant-error guarantee on all but a small fraction of the prior. Boosting this guarantee gives an average-case shadow
tomography algorithm, and the minimax principle then (non-constructively) implies the existence of a measurement with the same worst-case guarantee. We also identify an obstruction to further improvement with this approach. While pretty good measurements amplify success over the randomness of the prior, they do not amplify success over the randomness of measurement. This issue appears to be inherent, and gives rise to the remaining $\log(m)$ factor separating the complexity of the
quantum problem from its classical counterpart.
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All authors Sabee Grewal, Angelos Pelecanos, Jack Spilecki, Ewin Tang, John Wright
Solar and Stellar Astrophysics
Production of White Dwarf Debris Disks from Planetary Collisions and Poynting-Robertson Drag
Fred C. Adams and Konstantin Batygin
This paper explores the production of debris disks around white
dwarfs, which are observed to experience frequent pollution events. In this scenario, planetary collisions occur just outside the surface of a highly evolved AGB
star, after the end of its mass loss phase, as it starts its transition into a white
dwarf. The collisions vaporize a fraction of the planetary material, which subsequently expands, cools, nucleates droplets, and condenses into rocky bodies with characteristic size of order $s\sim1$ cm. The rocky debris disk evolves through the action of Poynting-Robertson drag, driven by the
stellar luminosity, which is initially large but steadily decreases with time. This scenario provides an alternate channel for delivering rocky material to the immediate vicinity of a white
dwarf.
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Quantum Physics
Informed Trading model with quantum walks
H. W. Shawn Liew and Patrick Rebentrost
The seminal Kyle model offers a framework to understand the price impact of an informed trader in a
market model for a single asset. We study variants in which the asset's future value is modeled by a classical random walk and by a continuous-time
quantum walk, respectively. With these assumptions, we analytically approximate and numerically identify the
market equilibrium between risk-neutral
market maker and informed trader. In the classical
equilibrium, the informed trader possesses a linear strategy, whereas the
market maker's pricing rule resembles a logistic curve. The informed trader's profit is also identified to grow sub-linearly with time t. In the
quantum equilibrium, the informed trader's strategy forms multiple clusters and the pricing rule exhibits multiple jumps correspondingly. Despite the increasing non-linearity of the
equilibrium, the informed trader's profit grows linearly with time t.
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General Relativity and Quantum Cosmology
Puncture Evolution with Physics-Informed Neural Networks
Estuti Shukla, Ashwin Suriyanarayanan, David Radice et al. (+2 more)
We investigate the application of physics-informed neural networks (PINNs) to solve the
vacuum Einstein equations in spherical
symmetry. Our neural network architecture is designed to solve the 1+1D moving-puncture
evolution, by minimizing a loss that combines a data term, the
Ricci tensor of the reconstructed spacetime, and the moving-puncture gauge conditions. It represents the lapse, the shift and the Z4c conformal variables $\chi$ and $\widetilde{\gamma}_{rr}$, which remain regular at the puncture. We consider the
evolution of a single, non-spinning black-hole in the puncture gauge and show that PINNs can interpolate numerical relativity (NR) data, predict its
evolution, and reconstruct spacetime in regions where no data is provided. As an interpolant, the network provides a compact, differentiable representation of the NR data. Given only early-time and outer-boundary data, it evolves the puncture forward in time and reproduces the main features of the NR solution. Given only exterior data and no gauge condition, an ill-posed inverse problem, it recovers the interior of a Schwarzschild spacetime in coordinates of its own choosing, which we verify by learning the coordinate transformation to the Kerr–Schild form. Finally, we assess the strengths and limitations of PINNs for NR and outline their prospects for future applications.
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All authors Estuti Shukla, Ashwin Suriyanarayanan, David Radice, Romit Maulik, Sebastiano Bernuzzi
Quantum Physics
Engineering logical gates with irrep surface codes
Yabo Li, Zijian Song, Vieri Mattei et al. (+3 more)
Fault-tolerant
quantum computation typically relies on a fixed set of logical primitives, while realizing other desired operations can require substantial resources. We introduce irrep surface codes (ISCs), two-dimensional topological
quantum error-correcting codes engineered to transversally implement a prescribed set of logical gates. The engineered gates only need to satisfy two conditions: (i) they generate a finite group, which, up to global phases, is forced by the Eastin-Knill
theorem, and (ii) they are irreducible, meaning that any operator commuting with the set of gates must be proportional to the identity. This accommodates arbitrary finite groups of diagonal gates and arbitrary reversible classical gates, since each can be embedded into a larger irreducible finite group of gates. It also enables logical gates outside every finite level of the Clifford hierarchy. To incorporate these operations into surface-code computations, we further develop
lattice-surgery protocols to transfer the encoded information between surface codes and ISCs obeying either of two sufficient conditions. Together, these results establish a systematic method for tailoring topological codes to desired logical operations and integrating them into conventional computations.
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All authors Yabo Li, Zijian Song, Vieri Mattei, Naren Manjunath, Apoorv Tiwari, Tyler D. Ellison
High Energy Physics (Theory)
de Sitter Wavefunction from Quadrangular Polylogarithms: Polygon Graphs
Livia Ferro, Tomasz Lukowski, Shruti Paranjape et al. (+5 more)
We present an explicit formula for the $n$-gon graph contribution to the integrand of the cosmological wavefunction for conformally coupled $\phi^3$ theory in de Sitter space. Our result relies on the fact that its symbol satisfies total compatibility with respect to the $B_{2n-1}$ cluster
algebra. We introduce $B$-type quadrangular polylogarithms, constructed from centrally symmetric quadrangulations of a $4n$-gon, and show that the $n$-gon wavefunction coefficient is expressed by a natural weight-$n$ function of this class. We prove our formula by directly relating the recursive differential equation satisfied by these wavefunction coefficients to a recursive coproduct formula for $B$-type quadrangular polylogarithms, with the remaining additive constant fixed by the soft limit.
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All authors Livia Ferro, Tomasz Lukowski, Shruti Paranjape, Lecheng Ren, Marcus Spradlin, Anastasia Volovich, He-Chen Weng, Yao-Qi Zhang
Quantum Physics
Fast convergence of propagation algorithms for open quantum systems
Giorgio Facelli, Hamza Fawzi, Omar Fawzi et al. (+3 more)
We establish general conditions for the rapid convergence of propagation
algorithms for computing expectation values of local observables in
quantum many-body systems, covering both
spin and fermionic systems. Our results apply to evolutions that are sufficiently contractive, providing a general mechanism by which contractivity controls the growth generated by local interactions and enables efficient classical simulation. As a first application, we consider noisy time
evolution generated by local
Hamiltonians on arbitrary interaction graphs. We show that the dynamics can be efficiently simulated when the noise strength $\lambda$ is sufficiently large compared to the degree of the interaction graph. More generally, for systems with an interaction strength $u$, our bounds determine a time horizon $t_{\text{max}}$ as a function of the interaction strength $u$, the noise strength $\lambda$, and the interaction structure below which the
algorithm is efficient. In the noiseless limit, $\lambda=0$, our analysis extends the efficiently simulable time scale from $\log(1/u)$ proved in Facelli, Fawzi, and Fawzi (2026) to $t_{\text{max}} \sim 1/u$ matching the recent improvement by Zhao, Marvian and Tong (2026). As a second application, we apply the same framework to the computation of local observables in Gibbs states of local
Hamiltonians. We consider a pseudo-Lindbladian whose steady state is the Gibbs state and show that, at sufficiently high temperature, its propagation
algorithm converges rapidly. In particular, for weakly-interacting systems with interaction strength $u$, our result applies up to inverse temperatures $\beta\sim\log(1/u)$.
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All authors Giorgio Facelli, Hamza Fawzi, Omar Fawzi, Cambyse Rouzé, Sam Slezak, Daniel Stilck França
Quantum Physics
Complexity separations for optimal matchgate-Clifford synthesis
Berta Casas, Diego García-Martín and Yuxuan Zhang
Clifford and matchgate
circuits are canonical families of classically simulable
quantum circuits. Their intersection, the matchgate-Clifford group, plays an important role in randomized fermionic protocols and in matchgate synthesis. Its adjoint action is isomorphic to the group of unit-determinant signed permutations of $2n$ Majorana modes, and we study optimal exact synthesis in this group. That is, given a target
unitary and a gate set, output an $n$-
qubit circuit implementing the target using the fewest operations. We show that the complexity of this problem strongly depends on the gate set. In particular, we study gate sets consisting of Majorana braids with different connectivity graphs. For path and complete graphs, we prove that the problem is classically solvable in $\mathcal{O}\left(n^2\right)$ time, and we provide explicit gate-optimal compilers. In addition, we prove that when the connectivity graph is a tree, the decision version of the optimal synthesis problem becomes NP-complete. Finally, we
benchmark our optimal compiler on chains of up to $n=80$
qubits against those of Qiskit and Tket, obtaining
circuits with constant factor improvements $\times2.57$ and $\times2.28$ in the total number of gates, respectively.
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Quantum Physics
Fermions and the Tsirelson Problem in Real Quantum Theory
Timothee Hoffreumon and Mischa P. Woods
In a previous work, we showed that real
quantum theory (RQT) cannot be experimentally distinguished from ordinary
quantum theory (QT). In this paper, we investigate whether this indistinguishability survives two natural extensions of the setting: allowing separated measurements to be represented by commuting rather than tensor-product observables, and imposing superselection rules, as in fermionic information theory. We show that it does in both cases. Our first result is a positive answer to the Tsirelson problem in RQT: commuting and tensor-product measurements generate the same finite-dimensional correlations. This is surprisingly not a trivial consequence of the standard complex proof, as it does not carry over to the reals. The proof obstruction becomes particularly relevant in the presence of superselection rules, which is why we first establish the equivalence in RQT before extending the framework to superselected RQT. Our second result is a local, real
quantum formulation of superselected theories. We extend the RQT framework to accommodate a representation of superselection over the reals and show, in particular, that it admits a fermionic version whose predictions are experimentally indistinguishable from those of fermionic information theory. More generally, the construction extends to all superselected QTs.
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Quantum Physics
Hypercontractivity and entropy decay for infinite-dimensional quantum Gibbs samplers
Simon Becker, Cambyse Rouzé and Robert Salzmann
We derive rates of exponential relative-
entropy decay for a broad class of infinite-dimensional
quantum Gibbs samplers. A key technical ingredient is a perturbative stability theory for hypercontractive estimates and logarithmic Sobolev inequalities. For suitably chosen dissipative couplings, we obtain exponential
entropy decay for full multimode Bose-Hubbard samplers with arbitrary hopping and repulsive density interactions. For harmonically confined
quantum Coulomb gases and molecular systems, we prove exponential
entropy decay for every fixed finite-rank low-energy truncation of the interaction. Finally, we exhibit a periodic charging model with a positive spectral gap but no finite-time $L^2$-to-$L^p$ bound for any $p>2$.
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Strongly Correlated Electrons
Unraveling Fermi liquid charge and heat transport in RuO$_{2}$
Harrison LaBollita, Fabian B. Kugler, Antoine Georges et al. (+1 more)
RuO$_2$ is a multi-orbital
Fermi liquid for which an array of complementary experimental measurements has recently become available, making it a stringent testbed for quantitative many-body electronic structure theory. Using realistic dynamical mean-field calculations, we compute the spectroscopic and transport properties of RuO$_2$ in the paramagnetic state. We identify RuO$_2$ as a moderately correlated
Fermi liquid and obtain (semi-)quantitative agreement with experiment for its optical conductivity, electrical resistivity, and thermopower. This broad agreement across complementary observables establishes a “precision” many-body description of RuO$_2$ and allows remaining discrepancies to be identified as meaningful tests of the theory. In particular, the calculated electronic thermal resistivity significantly undershoots the experimentally inferred low-temperature thermal resistivity, raising an important puzzle concerning the relative relaxation of charge and heat currents in the
Fermi liquid regime. We explore low-temperature electron-
phonon scattering as a possible mechanism for resolving this discrepancy, while a fully quantitative description remains an open problem. More broadly, our results demonstrate the power of combining precision DFT+DMFT calculations with complementary experimental probes to build and critically test quantitative descriptions of correlated
quantum materials.
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All authors Harrison LaBollita, Fabian B. Kugler, Antoine Georges, Cyrus E. Dreyer
Quantum Physics
A classical oracle separation between QMA and QMA(2)
Sabee Grewal, Saachi Mutreja and Kabir Tomer
We exhibit a classical oracle relative to which QMA \neq QMA(2). The separation is based on a separable
Hamiltonian problem defined by signed edge constraints on a graph. The YES instances have zero-energy product states, while the NO instances, constructed using the antisymmetric subspace, have entangled zero-energy states but no low-energy product states. For the QMA lower bound, we use compressed-oracle techniques to track the information learned by a
quantum computation making few queries to a YES instance. The key step is to map the resulting superpositions of partial oracle records to the NO family without significantly changing the verifier's behavior.
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Quantum Physics
Nonadditivity in fermionic quantum Shannon theory
Farzin Salek, Amir-Reza Negari, Graeme Smith et al. (+2 more)
We study collective state preparation and channel encoding in fermionic systems under parity superselection and composition governed by the canonical anticommutation relations. For a two-mode Gaussian state $\tau$, we obtain the exact
entanglement of formation, $E_{\mathrm F}^{\mathrm{phys}}(\tau^{\otimes m})=\lceil m/2\rceil\log2$ for every $m\geq1$. Two copies have the same formation value as one, violating additivity and strong superadditivity, while regularization halves the single-copy value. For an associated Gaussian channel, we determine the minimum output
entropy and Holevo information at every blocklength and prove nonadditivity of both. Together, these results give exact answers to the fermionic counterparts of the four additivity questions associated with Shor and Hastings. One physical use carries no classical information, whereas two uses transmit one bit perfectly. The unassisted classical and zero-error classical capacities both equal one half bit per mode. A sharp finite-block bound gives a strong converse: the decoding success probability vanishes at every rate above capacity. These optimizations cover all physical pure-state decompositions and channel inputs, with Gaussian ensembles and classical codes attaining the optima. The formation and minimum output
entropy formulas hold for every Rényi order $\alpha\in(0,\infty]$. We also determine the unassisted
quantum and zero-error
quantum capacities, both equal to one half logical
qubit per mode, and prove a strong converse:
entanglement fidelity vanishes at every rate above capacity. For a noisy Gaussian family, we determine the one- and two-copy formation values and prove strict nonadditivity at full rank. For $\tau$, Bell violation under local parity-preserving measurements first appears at three copies.
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All authors Farzin Salek, Amir-Reza Negari, Graeme Smith, Jens Eisert, Debbie Leung
High Energy Physics (Phenomenology)
One Event, Two Frontiers: From LZ to LHC
Md Sadique Anwar, Nivedita Ghosh, Sahabub Jahedi et al. (+1 more)
The 248 keV
nuclear-
recoil event observed by the LUX-ZEPLIN (LZ) experiment could potentially arise from dark matter (DM) interactions with nucleons. We investigate elastic scattering interpretation, focusing on Lagrangians that yield a local significance of $3\sigma$ or higher for some DM mass. We identify DM parameter space compatible with the LZ event and assess its consistency with
collider constraints by recasting the ATLAS monojet plus missing-transverse-momentum search at $\sqrt{s}=13$ TeV, based on $139~\mathrm{fb}^{-1}$ of data. For most of the effective interactions, we find that LHC constraints exclude the DM interpretation of the LZ event for DM masses below $\lesssim\,$TeV subject to the effective field theory (EFT) validity. In particular, we derive, for the first time, LHC constraints on several explicit momentum-dependent Lagrangians, including $\mathcal{L}_{10}$. For many interactions, these constraints are sufficiently strong that the corresponding parameter space below DM mass $\lesssim\,$TeV may be challenging to probe even with future direct detection experiments. Our results, therefore, have broader implications beyond the interpretation of the LZ event itself.
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All authors Md Sadique Anwar, Nivedita Ghosh, Sahabub Jahedi, Tarak Nath Maity
Quantum Physics
The Grothendieck Game and Self-Testing Continuous Groups
Alexander Kulpe, Giulio Malavolta, Simon Schmidt et al. (+1 more)
Self-testing certifies
quantum states and measurements from observed correlations alone, without requiring a description of the devices that produce them. In this work we establish, to the best of our knowledge, the first robust self-test of the full continuous family of measurements generated by Majorana operators. We achieve this by showing that the Grothendieck game, a two-player nonlocal game in which the players receive directions on a sphere and return binary answers, is a self-test of Majorana observables. That is, any near-optimal performance certifies an entire continuously parameterized family of
quantum measurements. We further extend this certification to products of Majorana observables, obtaining a robust self-test of the
spin representation of the continuous pin group.
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All authors Alexander Kulpe, Giulio Malavolta, Simon Schmidt, Michael Walter
Quantum Physics
Finite-bath projected ensembles in dual-unitary circuits
Rahul Arvind and Nicholas Hunter-Jones
We study the emergent randomness in projected ensembles generated by dual-
unitary circuits. Specifically, we consider
evolution by solvable dual-
unitary brickwork
circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that this projected ensemble of states forms a
quantum state design in the limit where the bath size is large, but the rate of convergence at finite bath size has not been rigorously established. Under three inverse-
polynomial assumptions, local permutation mixing, a bound on recurrent backward motion, and contraction at the measured boundary, we fill this gap and prove that a bath of
polynomial size suffices to form approximate $k$-designs. In establishing our results, we develop a microscopic transport interpretation of emergent randomness in the projected ensemble, in which deviations from local permutation operators appear as defects, and make connections with the theory of
quantum walks.
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Quantum Physics
Discovering New Problems for Decoded Quantum Interferometry
Rhik Mazumder and Pradeep Niroula
Decoded
quantum interferometry (DQI) uses classical error correction to solve optimization problems, but it is hard to tell which problems could give it a
quantum advantage. We develop soundness rules that screen candidate problems by their code parameters, decoding guarantees and classical baselines. For the standard objective of counting satisfied constraints, we prove that under worst-case Hamming decoding DQI's guarantee can exceed Prange completion by at most $(\sqrt{2}-1)/2$. Optimal
polynomial intersection (OPI) attains this margin cap asymptotically, so no candidate in this setting can exceed OPI's margin. We also derive a performance law for real-valued objectives: the objective fixes both the solution quality and which errors the decoder must correct. An AI-
agent search guided by these rules found two candidate applications. Alternant max-agreement on McEliece-type public keys tests what a secret decoder is worth to DQI against classical solvers that see only the public instance. Multiplicative
polynomial intersection, a knapsack-type problem built from discrete logarithms, pairs a cosine objective with a public decoder for signed errors. For both we prove decoding guarantees and finite-length comparisons with Prange restarts, and on the larger instances we tested, DQI's expected quality exceeds what our classical solvers reach within fixed budgets.
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Quantum Physics
Efficient Logic with Ultra-High-Rate Quantum Codes
Nishad Maskara, Rohan Mehta, Zhiyang He et al. (+4 more)
Quantum low-density parity-check (qLDPC) codes offer a promising route to reducing the
qubit overhead of fault tolerance, with recent ultra-high-rate constructions achieving encoding rates above one half. In this work, we develop fast and parallel logical computation methods for ultra-high-rate codes. We first utilize the group
symmetries of the codes to partition the logical
qubits into orbits, and then apply parallel surgery methods to implement group-invariant collections of logical Pauli-product measurements. These measurements are highly programmable, as we may arbitrarily couple logical orbits as long as each measurement is repeated across the whole orbit(s). To reduce the space and time overheads, we develop a technique called chain-map convolution, which uses the group structure to boost both the spatial and temporal distances of our protocol in a highly efficient manner. As case studies, we construct distance-preserving parallel measurement gadgets for the [[256, 68, 12]], [[576, 148, 18]] pair-partition codes, and a [[1152, 580, 12]] rate-$1/2$ code, with only around $2.5\times$ space overhead and 3-4 rounds of syndrome extraction each. The same methods also enable parallel injection of cultivated magic states into high-rate codes. Finally, we extend programmability through subgroup restrictions, revealing a tradeoff between logical control and the spacetime resources required for fault tolerance and highlighting the crucial role structured parallelism plays in reducing overhead. These results provide new methods for designing qLDPC logical operations with low spacetime overhead, opening a route toward more efficient fault-tolerant
quantum architectures.
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All authors Nishad Maskara, Rohan Mehta, Zhiyang He, Varun Menon, J. Pablo Bonilla Ataides, Mikhail D. Lukin, Hengyun Zhou
Mathematical Physics · Cross-listed from math.AT
The Euler characteristic of $Pin^{\pm}$ manifolds
Renee S. Hoekzema, Luuk Stehouwer and Simona Veselá
We completely determine the possible parities of the Euler characteristic of closed $Pin^{\pm}$-
manifolds of a given dimension. As an application we partially calculate the controlled cut-and-paste groups $SKK_{2k+1}^{Pin^{\pm}}$, which were previously undetermined.
Quantum Physics
Quantum minimum description of density matrices
Patrick Hayden, Alexander Maloney, Jinzhao Wang et al. (+1 more)
We study a variant of Schumacher compression. The task asks for the minimal
memory cost for compressing many copies of a density
matrix with known spectrum and unknown eigenbasis, without preserving its purification. For fixed dimension and distinct positive
eigenvalues, we obtain the cost through its additive constant. Achievability uses a generalization of Werner's cloning map to $\mathrm{GL}(d,\mathbb C)$ irreducible representations, with finite trace-distance bounds controlled by highest-weight differences and row gaps. The matching converse follows from a quantitative form of Koashi–Imoto incompressibility for irreducible group orbits under a spectral-gap assumption. We also identify the relation between this
quantum minimum description length and universal lossless coding overhead, and its connection to free
entropy is explained in a companion letter. We provide a Lean certificate for our proofs.
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All authors Patrick Hayden, Alexander Maloney, Jinzhao Wang, Yuxiang Yang
Quantum Physics
Free entropy and quantum minimum description length
Patrick Hayden, Alexander Maloney, Jinzhao Wang et al. (+1 more)
In free probability, Voiculescu's free
entropy counts
matrix microstates that approximate an operator. It is a non-commutative analog of the Shannon
entropy, distinct from any
quantum entropy of a density operator, but it has had no physical meaning in
quantum theory. We define a finite-dimensional physical free
entropy at finite resolution and show that it directly characterizes, up to an explicit constant, the minimal
quantum memory needed to program many copies of a state with known
eigenvalues and unknown eigenbasis. This task is a variant of Schumacher compression, and we call its optimal cost the
quantum minimum description length. We briefly discuss how free
entropy differs from
quantum entropies and its potential applications in
quantum physics.
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All authors Patrick Hayden, Alexander Maloney, Jinzhao Wang, Yuxiang Yang
Quantum Physics · Cross-listed from cs.CC
Separating ClonableQMA and QCMA Relative to a Classical Oracle
Alper Cakan, Kai-Min Chung, Wei-Hsiang Hung et al. (+1 more)
Since the introduction of the complexity class QMA as a
quantum-verifier analogue of NP (Kitaev, 1997), many have wondered whether
quantum proofs are necessary or classical proofs suffice - that is, whether QMA = QCMA or QCMA != QMA (Aharonov and Naveh, 2002; Aaronson and Kuperberg, CCC '07). This longstanding question was recently answered by works of Bostanci, Haferkamp, Nirkhe, and Zhandry (STOC '26) and Bostanci, Huang, and Vaikuntanathan (FOCS '26), which showed that
quantum proofs are more powerful than classical ones in the classical-oracle setting. However, it remains unclear what exactly makes
quantum proofs more powerful than classical ones. In the information-theoretic setting, a family of
quantum states is not classicalizable if and only if it is unclonable. Indeed, these recent works also explicitly highlight the unclonability of their
quantum proofs as a key mechanism behind their separations, and their arguments crucially rely on this property. This raises the question of whether unclonability is necessary for
quantum proofs to be more powerful than classical ones. In this work, we show that even clonable
quantum proofs can be more powerful than classical ones relative to a classical oracle by constructing a classical oracle O such that QCMA^O != ClonableQMA^O. This resolves the open question of Nehoran and Zhandry (ITCS '24), who established the analogous separation relative to a
quantum oracle. We also show a classical-oracle separation between BQP/clonableqpoly and BQP/poly, and give applications of our results to
quantum cryptography.
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All authors Alper Cakan, Kai-Min Chung, Wei-Hsiang Hung, Tzu-Yi Yang
High Energy Physics (Phenomenology)
Novel dependence between neutrino mass splittings strongly supported by initial JUNO results
I. Alikhanov
In the standard three-
flavor paradigm, two of the three
neutrino mass-squared differences are independent. The existence of an additional dependence between these oscillation parameters was recently predicted on empirical grounds, taking the form $$\frac{\sqrt{\Delta m^2_{31}}+\sqrt{\Delta m^2_{21}}}{\sqrt{\Delta m^2_{31}}-\sqrt{\Delta m^2_{21}}}=\sqrt{2}.$$ The JUNO Collaboration has now reported the most precise measurements to date of both $\Delta m^2_{21}$ and $\Delta m^2_{31}$. We demonstrate that this relation is in excellent agreement with the experimental data, which yield $1.4143_{-0.0038}^{+0.0036}$ corresponding to a relative precision of $0.27\%$. Remarkably, the central value differs by less than $0.03$ standard deviations from the prediction ($\sqrt{2}\approx1.4142$). This provides strong experimental support for the novel constraint and thereby suggests an underlying
symmetry governing the
neutrino mass spectrum, rather than purely independent parameters.
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Quantum Physics
Anti-symmetrization is cheap and useful
Adam Bene Watts, John Bostanci, Matthias C. Caro et al. (+3 more)
We consider the computational task of anti-symmetrization of an unknown mixed
quantum state: Given iid copies of a rank-$r$ qudit state $\rho=\sum_{i=1}^r \lambda_i |\varphi_i\rangle\!\langle\varphi_i|$, prepare a copy of the state proportional to $\Pi_{\mathrm{anti}}^r (|\varphi_1\rangle\otimes \ldots\otimes|\varphi_r\rangle)$, with $\Pi_{\mathrm{anti}}^r$ the anti-symmetric subspace projector. We first give a simple
algorithm for anti-symmetrization that uses $\widetilde{O}(r / \lambda_{\min})$ copies of $\rho$, where $\lambda_{\min}$ is the minimum non-zero
eigenvalue of $\rho$. This
algorithm works even in the streaming setting with small working
memory, and it uses only simple
quantum operations like controlled-SWAPs and constantly many layers of single-
qubit gates. As an application of this streaming anti-symmetrization procedure, we give a reduction from gapped mixed-state one-way state generators to pure-state one-way state generators. Then, using tools from Schur-Weyl duality, we give and analyze a second (non-streaming) anti-symmetrization procedure that uses $O(r / \lambda_{\min})$ copies of $\rho$, which then serves as a building block in new
algorithms for weak Schur sampling and
unitary Schur sampling, outperforming existing approaches in some regimes of number of copies $n$ and local dimension $d$, as well as in an
algorithm for optimal purity amplification for qudit states.
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All authors Adam Bene Watts, John Bostanci, Matthias C. Caro, Daniel Grier, Sihan Liu, Gaurav Mahajan
Quantum Physics
Characterizing Photonic Partial Distinguishability Through Gram Matrix Tomography
Marcin Kotowski, Marco Robbio, Oliver Reardon-Smith et al. (+4 more)
Partial distinguishability affects multiphoton interference, which is central to large-scale photonic experiments such as
Boson Sampling and to applications of multiphoton states across
quantum technologies. Characterizing the internal degrees of freedom responsible for this behavior is challenging: in many scenarios they cannot be accessed directly and even their dimension or physical nature may be unknown a priori. Here we introduce Gram-
matrix tomography for independently prepared
photons with pure or nearly pure internal states. For pure states, the Gram
matrix contains all information required to predict the statistics of experiments that are insensitive to the internal degrees of freedom. We reconstruct this
matrix, up to physically irrelevant phase choices, from a quadratic number of measurable Bargmann invariants (quantities encoding overlap magnitudes and collective phases). We access these quantities using two complementary approaches: targeted
Fourier interferometers and two- and three-body
photon-number correlations measured in a single random interferometer. We derive explicit error bounds that control the total-variation distance between predicted and actual outcome distributions for any subsequent experiment that is insensitive to the internal states. These guarantees account for finite sampling and deviations from purity. Crucially, the total sample complexity of the protocol is independent of the internal
Hilbert-space dimension and
polynomial under mild assumptions on overlaps of internal states. Our protocol uses standard interferometric measurements and turns them into a robust and operationally grounded characterization of partially distinguishable
photons.
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All authors Marcin Kotowski, Marco Robbio, Oliver Reardon-Smith, Benoit Seron, Leonardo Novo, Ernesto F. Galvão, Michał Oszmaniec
High Energy Physics (Phenomenology)
Two-loop RI/SMOM-$\overline{\text{MS}}$ matching factors for the renormalization of bi-local operators contributing to $\epsilon_K$
Erik Lundstrum
The measure of indirect CP violation in the neutral kaon system, $\epsilon_K$, is an important precision test of the Standard Model. A first-principles Standard Model prediction of $\epsilon_K$ requires evaluating the long-distance contribution in which the $\Delta S = 2$ process proceeds via two $\Delta S = 1$ operators. The non-perturbative nature of QCD in the relevant energy regimes requires a
lattice QCD simulation. In this paper we present the two-loop, $O(\alpha_s)$ RI/SMOM - $\overline{\text{MS}}$ matching factors required to renormalize a
lattice QCD calculation of the long-distance contribution to $\epsilon_K$.
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