Stabilizer states are central to quantum computing, underlying quantum error correction, benchmarking, and efficient classical simulation. Yet their learnability exhibits a striking gap: an $n$-qubit stabilizer state can be learned from $Θ(n)$ copies using two-copy Bell measurements, whereas non-adaptive single-copy measurements require $Ω(n^2)$ copies. Here we show that adaptivity completely closes this gap. We giv…
Maximum-likelihood decoding provides an optimal decoding strategy for quantum error correction under stochastic Pauli noise. However, computing logical-class probabilities is challenging, and the leading exact tensor-network contraction requires time exponential in treewidth. In this work, we introduce a new decoding algorithm based on rank-decomposition dynamic programming (Rank DP). We express decoding partition f…
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, lea…
Reliable multistep quantum lattice-Boltzmann evolution requires controlling computational faults. When ideal collision preserves encoded mass and momentum exactly, changes in those charges can provide syndromes for selected faults at the post-collision checkpoint. A fault that shifts one population then leaves a unique mass-momentum residual labeled by the lattice velocity. A coherent reference register stores the e…
Scientific code generation can produce executable programs that fail to compute the intended scientific object. We study this problem in language-model synthesis of Clifford circuits, which prepare the stabilizer states used in quantum error correction and admit exact classical verification. In our target-conditioned framework, each target is given as compact signed stabilizer generators, and an exact verifier check…
Nature Physics, Published online: 30 September 2026; doi:10.1038/s41567-026-03471-5 Graph states entangle many photons in a special structure that is useful for several quantum protocols. Making graph states is often probabilistic and inefficient, but now a deterministic approach using superconducting qubits has been demonstrated.
A Clifford template is a finite ordered family of repeatable Clifford operations, and an instantiation specifies how many times each operation is applied. The Clifford template compilation problem asks how to choose these repetition numbers so that the template realizes a target transformation of Pauli operators. This problem arises, for example, when searching for logical operations in quantum error correction usin…
Nature Physics, Published online: 30 September 2026; doi:10.1038/s41567-026-03408-y The continuous energy injection in active fluids leads to active turbulence. Now, geometric and mechanical analyses reveal a phase transition that leads to fully developed active turbulence.
We establish sufficient conditions for preparing quantum thermal states of noncommuting local Hamiltonians with polylogarithmic circuit depth in arbitrary fixed spatial dimension. Our conditions combine locality and stability bounds on the effective interactions of reduced density matrices of a Gibbs state with a quantitative high-temperature condition and access to coarse classical reference Hamiltonians. When thes…
Nature Physics, Published online: 29 September 2026; doi:10.1038/s41567-026-03475-1 Complex fluids display unusual flow behaviour that originates from their microstructure, but observing this structure has been challenging. Now, X-ray scattering microscopy is fast enough to follow the tumbling of nanoparticles.
Quantum Computing (QC) has evolved into a computational model that can potentially solve problems of classes that cannot be solved by classical systems. This review gives a discussion on the innovation of software frameworks, experimental platforms and quantum computing tools used to compute quantum algorithm development, simulation and implementation. It concentrates on widely used programming environments, which c…
Coherent uncomputation can be as costly as the computation itself, creating substantial spacetime overheads that can be prohibitive on early fault-tolerant quantum computers. We develop an algebraic framework for measurement-based uncomputation (MBU) through a quantum error-correction picture: measurements of the garbage register induce relative phases analogous to errors causing non-trivial syndromes. Accepting onl…
Nature Physics, Published online: 29 September 2026; doi:10.1038/s41567-026-03467-1 The trajectories of embedded particles provide a route for probing fluid flow dynamics. An X-ray scatter microscopy approach that enables precise monitoring of non-sphericalnanoparticles now reveals multiscale dynamics in complex fluids.
Nature Physics, Published online: 28 September 2026; doi:10.1038/s41567-026-03459-1 Topological phases of matter have long been studied in idealized pure states at absolute zero. Two experiments now show how controlled disorder can give mixed states measurable topological features in quantum simulators.
Nature Physics, Published online: 28 September 2026; doi:10.1038/s41567-026-03453-7 Wave propagation in irregular cavities made from conventional isotropic media is typically chaotic. Now odd-shaped cavities made from hyperbolic metamaterials are shown to suppress chaotic wave dynamics and produce stable geometric wave patterns.
