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Earlier sources: Science
Science investigates the natural world through observation, experiments, and mathematical models. Explore papers and developments in biology, medicine, materials, neuroscience, physics, climate, and mathematics; a reported finding is not necessarily established consensus.
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Open in the map ↗1419 classified signals in the fourteen-day window. Recent momentum: steady. These counts include signals awaiting readable evidence.
Earlier sources
Up to ten sources with readable evidence, ordered by their feed timestamp. These archive sources can be older than the live fourteen-day window. This list is a sample, not a measure of total activity. Dates distinguish paper publication, repository creation, model/dataset activity, Hacker News posts, and KEV catalog additions. “First archived” records when SYMTRI first stored the signal.
- arXiv · Published · First archived
Universal Bounds for Out-of-Distribution Unitary Learning ↗
How much can the action of an unknown unitary dynamics on one family of states reveal about its action elsewhere? We develop a general framework for out-of-distribution quantum dynamics learning based on the first and second moments of the input distribution. These define a notion of the bias and expressivity of an ensemble, which together control generalization between arbitrary pure-state training and testing distributions. Our framework shows that only studying the action of a unitary on random real states can learn its action on random complex states, that tensor products of unbiased pure-…
- arXiv · Published · First archived
Efficient Block Encoding of Structured Hamiltonians by Separating Where and What ↗
Fault-tolerant block encodings of structured Hamiltonians can reduce their non-Clifford cost in SELECT by selecting where an operator acts separately from what is applied. We construct permute-act-unpermute circuits whose CSWAP networks exploit the support geometry: a selected support is brought to a fixed target register, a shared local circuit acts there, and the permutation is undone. For supports of fixed size, the $T$ count of SELECT then grows with the system size rather than with the number of terms, without requiring translational symmetry or factorised coefficients. For two-site suppo…
- arXiv · Published · First archived
Single-Shot Error Correction at Optimal Spacetime Cost ↗
Recent work established that, for independent erasures, storing $K$ logical qubits for $S$ time steps with error at most $\varepsilon$ requires a spacetime cost of $Ω(S(K+\log(S/\varepsilon)))$. A matching construction was also given, but assumes ideal error correction. Here we show that the same scaling can be achieved with an explicit noisy error-correction circuit and efficient decoding, counting all state-preparation, gate, measurement, and wait locations, provided that the hardware supports long-range qubit connectivity and fast, reliable classical processing. Thus, reliability adds only…
- arXiv · Published · First archived
Modified logarithmic Sobolev inequality for 1D non-commuting Hamiltonians ↗
Given a finite-range, non-commuting Hamiltonian on a 1D chain of finite spins, we prove a modified logarithmic Sobolev inequality with constant $Ω(1/\log n)$ for the heat-bath dynamics, a quasi-local Gibbs sampler, and for the regularised heat-bath dynamics. This implies rapid mixing of both samplers towards the Gibbs state in relative entropy and trace norm, with mixing times of order $\mathcal{O}(\log n\cdot \log(n/ε))$. The interactions may be spatially inhomogeneous. The proof combines weak quasi-factorisation of relative entropy, decay-of-correlation estimates, a uniform conditional local…
- arXiv · Published · First archived
Low-Overhead Quantum Error Correction with Boundary-Connected Planar Modules ↗
Realizing practical quantum computers requires quantum error correction, but the most widely implemented approach, the planar surface code, demands a substantial physical qubit overhead. Here, we demonstrate that partitioning quantum processors into manageable, flat modules with non-local inter-module connections provides a natural solution. By wiring sparse, static boundary connections between Euclidean planar modules, we construct modular hyperbolic surface and color codes, based on new families of semi-hyperbolic codes. Using modular syndrome extraction circuits and efficient neural network…
- arXiv · Published · First archived
Exact Recovery for Non-Abelian Surface Codes ↗
We study exact recovery for non-Abelian topological surface codes based on the quantum double $D(G)$ of any finite group $G$. We determine an orthogonal error basis, that is comprised of group multiplication and irreducible representation operators. Whenever the errors are supported on closed loops on the lattice or dual lattice, there is a redundancy in the basis, due to stabilizers. To remedy this, we introduce a gauge-fixing that results in a complete and orthogonal error basis on the code space. Assuming as input predetermined, neutral correctable error clusters, we construct charge and fl…
- arXiv · Published · First archived
How I Learned to Stop Worrying and Love the Redfield Equation: Completely-Positive Resummation of Non-Markovian Dynamics ↗
The Redfield equation with time-dependent coefficients (or TCL2 equation) gives one of the simplest perturbative descriptions of open quantum system dynamics derived from a microscopic theory. Its status as an approximation is nevertheless subtle: while perturbation theory fixes the reduced dynamics order-by-order in the system-environment coupling, solving the Redfield equation yields a particular resummation that need not preserve complete positivity. Here we compare Redfield evolution with an exponentiated (Magnus) resummation of the same second-order perturbative map, which is completely p…
- arXiv · Published · First archived
Efficient capacity-achieving entanglement generation with application to pure-loss Bosonic channels ↗
While the ultimate limits on the rate of quantum communication over noisy channels are well-established, very few efficient coding schemes achieving these limits are known. This contrasts sharply with transmitting classical data over classical channels, where polar codes and low-density parity-check codes both efficiently achieve the classical capacity of any noisy channel. In this work we construct an efficient entanglement generation scheme which achieves the coherent information for a broad class of channels. For degradable channels in the class, which includes truncated versions of the pur…
- arXiv · Published · First archived
Quantum Simulation on Riemannian Manifolds ↗
We investigate algorithms for the quantum simulation of the Schrödinger equation on a Riemannian manifold, where the kinetic operator is defined by the Laplace--Beltrami operator corresponding to the metric. Our first algorithms are based on a global spectral method based on the identification of an efficient transform to the eigenbasis of the Laplace--Beltrami operator. We use this method to provide explicit, efficient, quantum simulation algorithms for the Riemannian Schrödinger equation on tori and spheres with their standard metrics, simplices with the Wright--Fisher metric, truncated posi…
- arXiv · Published · First archived
Ordering-Aware Theory of Trotter Error ↗
Product formulas are a basic tool for simulating quantum many-body dynamics, but a fundamental degree of freedom in their application---the ordering of Hamiltonian terms---has remained largely unexplored. Here we systematically study such ordering effects, quantifying their impact on simulation accuracy and exploiting them to design more accurate product-formula simulations. We develop an efficiently computable, ordering-sensitive bound on the finite-step-size Trotter error for geometrically local Hamiltonians for arbitrarily high-order product formulas. For translation-invariant one-dimension…
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