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By implementing random circuit sampling, experimental and theoretical results establish the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors.

Profiling assays measure thousands of features to uncover biological insights but lack reliable methods for quality evaluation. Here, the authors develop a versatile information retrieval framework to robustly quantify sample activity and similarity in large-scale profiling data.

Generalized measurements that do not correspond to conventional basis projections of the quantum wavefunction are a part of several important protocols in quantum information. These measurements can be certifiably performed on higher-dimensional systems using optical fibre technology.

Closed-loop brain stimulation of the human hippocampal theta rhythm produces lasting enhancement of network communication. This implicates theta rhythms in human hippocampal network communication and provides a possible route to memory modulation.

An ultra-low-loss integrated photonic chip fabricated on a customized multilayer silicon nitride 300-mm wafer platform, coupled over fibre with high-efficiency photon number resolving detectors, is used to generate Gottesman–Kitaev–Preskill qubit states.

The pathogen Pseudomonas aeruginosa uses a membrane complex, PelBC, to produce exopolysaccharides for biofilm formation. Here the authors combine structural analysis, simulations and single-channel recordings of PelBC to provide a detailed view on its unique architecture and dynamics, and reveal the export route for the polysaccharide.

The electrodynamics of superconducting devices make them suitable for applications as detectors, amplifiers, and qubits. Here the authors show that resonators made from granular aluminum, which naturally realizes a network of Josephson junctions, have practically useful impedances and nonlinearities.

A violation of Bell's inequality, which is a direct proof of entanglement, can be observed in the solid state using the electron and nuclear spins of a single phosphorus atom in silicon.

Cavity QED systems which can be used for quantum information processing can absorb or emit signals with specific frequencies and temporal envelops. Here, the authors show that the temporal and spectral content of microwave signals can be manipulated with a flexible aluminium drumhead embedded in a circuit.

The orbital angular momentum of light is a promising degree of freedom for long-distance information transportation. To create high-dimensional entanglement for pairs of photons, Fickler et al.use an optical mode sorter in reverse to transfer entanglement between the path into the orbital angular momentum.

Superconducting quantum processors need to balance intentional disorder (to protect qubits) and nonlinear resonator coupling (to manipulate qubits), while avoiding chaotic instabilities. Berke et al. use the techniques of many-body localization theory to study the stability of current platforms against quantum chaos.

Molecular electron spins are promising qubit candidates, however physical implementation of quantum gates is challenging. Little et al. explore the implementation of two-qubit entangling gates between nitroxide spin centres by pulsed electron paramagnetic resonance, building on NMR quantum computing protocols.

Circadian clocks enable organisms to anticipate daily cycles, while being robust to molecular and environmental noise. Here, Eremina et al. show how the cyanobacterial clock buffers genetic and environmental perturbations through its core phosphorylation loop, and demonstrate that known clock regulators are dispensable for clock robustness.

Recently topological phases have been generalized to amorphous materials, but demonstrations have been limited to non-interacting particles. Cassella et al. show the emergence of chiral amorphous quantum spin liquid in an exactly soluble model by extending the Kitaev honeycomb model to random lattices.

GABAB receptors contribute to complex inhibition that regulates cortical neurons in a translationally relevant manner over adult life. Here, authors show stronger presynaptic inhibition in humans than rats, and a role for GABAB receptors in the anti-seizure profile of levetiracetam.

Entanglement between photons is easily destroyed by losses in optical systems as light propagates through it. For entanglement of orbital angular momentum, McLaren et al.show that losses caused by obstructions in the beam path can be overcome if measurements are made in the Bessel basis.

The kernel method in machine learning can be implemented on near-term quantum computers. A 27-qubit device has now been used to solve learning problems using kernels that have the potential to be practically useful.

Quantum computing platforms allowing quantum error correction usually rely on complex redundant encoding within multiple two-level systems. Here, instead, the authors realize a CNOT gate between two qubits encoded in the multiphoton states of two microwave cavities nonlinearly coupled by a transmon.

The variational quantum unsampling protocol provides a way to realize verification and inference of near-term quantum circuit outputs. This protocol is then experimentally verified on a quantum photonic processor.

The role of the human claustrum during slow wave sleep is unknown. Here the authors characterize the spiking activity of claustrum neurons in humans and demonstrate that claustrum neurons track slow waves during NREM sleep.

The memory function of sleep relies on the coordination of slow oscillations and spindles. Here the authors show that respiration is associated with the emergence and interplay of these sleep rhythms, and that this coupling is linked to memory reactivation.

Waves are ubiquitous in nature and occur across various scales and settings. In this Primer, Jafarzadeh et al. discuss techniques for preprocessing and analysing waves, including information on choosing the appropriate methods based on wave properties, and present worked examples using synthetic datasets.

Future quantum computers will employ error correction to protect quantum data from decoherence and faulty hardware. Here, using a quantum processor with five superconducting qubits, the authors demonstrate how to protect one logical qubit from bitflip errors using multi-qubit, stabilizer measurements.

Multimodal results (iEEG, fMRI and MEG) of predictions from integrated information theory and global neuronal workspace theory align with some predictions of both theories on visual consciousness, but also critically challenge key tenets of both theories.

The segmentation motor activity of the small intestine is believed to be a result of alternating inhibitory and excitatory neural activity. Huizinga et al.show that the segmentation motor pattern is in fact a result of phase–amplitude interactions of slow-wave activities generated by two networks of interstitial cells of Cajal.

Here, the authors show that reactivating motor memories during sleep at moments of high (vs. low) neuronal excitability (up vs. down phases of slow oscillations) enhances their consolidation. Up-reactivation strengthens sleep markers of plasticity and the neural responses supporting memory consolidation.

Estimating the quantum capacity allows one to assess the performance of quantum memories, communication channels, repeaters as well as error correction schemes. Here, the authors show how to estimate and verify one-shot quantum capacity in the most general case of arbitrarily correlated errors.

Photo-excitation in strongly correlated materials is usually modelled as an increase of electronic energy that is then transferred to other degrees of freedom. Contrarily, Novelli et al.show that in a charge-transfer insulator, sub-gap excitation forms electrons that are suddenly dressed by the boson field.

In quantum mechanics, the uncertainty principle is considered a limiting factor forbidding a system from being in a state where all possible measurements have perfectly predictable outcomes. Here, Dahlsten et al. show its positive role as the enabler of non-classical dynamics in an interferometer.

Optical rotation in a medium, which is typically small, can be enhanced by harnessing spin-orbit interaction in fiber modes. Here the authors use this effect to develop a fiber-based wavelength-measurement technique with high resolution.

Quantum supremacy is demonstrated using a programmable superconducting processor known as Sycamore, taking approximately 200 seconds to sample one instance of a quantum circuit a million times, which would take a state-of-the-art supercomputer around ten thousand years to compute.

Hippocampal theta–gamma phase–amplitude coupling integrates cognitive control and working memory storage across brain areas in humans.

Wave breaking mechanisms relevant for modelling of ocean-atmosphere interaction and rogue waves, remain computationally challenging. The authors propose a machine learning framework for prediction of breaking and its effects on wave evolution that can be applied for forecasting of real world sea states.

Is it possible to deduce the number of dimensions of a completely unknown system only from the results of measurements performed on it? So-called dimension witnesses allow such an estimation, and are now experimentally demonstrated using pairs of entangled photons.

Quantum communications operate with shared multipartite entangled states, and this has to be certified in a setting where not all parties are trusted in the same way. Here the authors propose a method to certify multipartite entanglement in asymmetric scenarios and demonstrate it in an optical experiment.

The Feynman-Vernon Path Integral and the Generalized Quantum Master Equation are the two main and oldest approaches to open quantum system dynamics modelling. Here, the authors discover a formal link between them, and use it to find a Hamiltonian learning method that can extract environmental spectral densities from the dynamics of the reduced system.

Untrustworthy sources or detectors mean that quantum entanglement cannot always be ensured, but quantum steering inequalities can verify its presence. Using a highly efficient system, Smithet al. are able to close the detection loophole and clearly demonstrate steering between two parties.

Sequential neural spiking activity is a potential substrate for learning and memory across species. Here, the authors showed spiking in the human cortex forms an average backbone sequence, and flexibility around this backbone is associated with cognition.

Organic semiconductors employed in light-emitting diodes (OLEDs) allow for magnetic resonance studies that explore light-matter interactions in the ultrastrong-drive regime, where the Rabi frequency exceeds the Larmor frequency. The authors report the formation of Floquet spin states in OLEDs.

Understanding the spin dynamics in magnetic nanostructures is important for spintronics, but so far it has been impossible to probe the spin dynamics directly. A neutron-scattering technique providing direct information about dynamical two-spin correlations in a molecular nanomagnet has now been demonstrated.

Here, the authors show that beta oscillations in the frontal and parietal lobes of monkeys propagate as traveling waves. The strength of these signals increases after rewards, suggesting a role for traveling waves in memory for recent events.

Experiments with a trapped-ion quantum simulator observe Stark many-body localization, in which the quantum system evades thermalization despite having no disorder.