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Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

Functional neuroimaging methods hold promise for the identification of cognitive function and communication capacity in some severely brain-injured patients who may not retain sufficient motor function to demonstrate their abilities. We studied seven severely brain-injured patients and a control group of 14 subjects using a novel hierarchical functional magnetic resonance imaging assessment utilizing mental imagery responses. Whereas the control group showed consistent and accurate (for communication) blood-oxygen-level-dependent responses without exception, the brain-injured subjects showed a wide variation in the correlation of blood-oxygen-level-dependent responses and overt behavioural responses. Specifically, the brain-injured subjects dissociated bedside and functional magnetic resonance imaging-based command following and communication capabilities. These observations reveal significant challenges in developing validated functional magnetic resonance imaging-based methods for clinical use and raise interesting questions about underlying brain function assayed using these methods in brain-injured subjects. [ABSTRACT FROM AUTHOR]

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators 1,2 . Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble-Zurek scaling predictions 3 in the XY model, as well as signatures of the classical Kosterlitz-Thouless phase transition 4 . Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis 5-7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue-digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics., Competing Interests: Competing interests: A provisional patent application has been submitted for the analogue calibration scheme, titled ‘High-accuracy calibration of an analog quantum simulator’ (application number 63/639,509). The listed inventors are T.I.A., J.A.G., D.A.A. and X.M. The other authors declare no competing interests., (© 2025. The Author(s).)

Undesired coupling to the surrounding environment destroys long-range correlations in quantum processors and hinders coherent evolution in the nominally available computational space. This noise is an outstanding challenge when leveraging the computation power of near-term quantum processors 1 . It has been shown that benchmarking random circuit sampling with cross-entropy benchmarking can provide an estimate of the effective size of the Hilbert space coherently available 2-8 . Nevertheless, quantum algorithms' outputs can be trivialized by noise, making them susceptible to classical computation spoofing. Here, by implementing an algorithm for random circuit sampling, we demonstrate experimentally that two phase transitions are observable with cross-entropy benchmarking, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak-link model, which allows us to vary the strength of the noise versus coherent evolution. Furthermore, by presenting a random circuit sampling experiment in the weak-noise phase with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers. Our experimental and theoretical work establishes the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors., (© 2024. The Author(s).)

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain's center, [Formula: see text]. The first two moments of [Formula: see text] show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.

Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.

Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with [Formula: see text] parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states 1 . However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases 2-8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC) 7,9-15 . Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order 7,16,17 . In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states 7,9,10 . Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors., (© 2021. The Author(s).)

Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error–correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of –ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.

Quantum information processing systems rely on a broad range of microwave technologies and have spurred development of microwave devices and methods in new operating regimes. Here we review the use of microwave signals and systems in quantum computing, with specific reference to three leading quantum computing platforms: trapped atomic ion qubits, spin qubits in semiconductors, and superconducting qubits. We highlight some key results and progress in quantum computing achieved through the use of microwave systems, and discuss how quantum computing applications have pushed the frontiers of microwave technology in some areas. We also describe open microwave engineering challenges for the construction of large-scale, fault-tolerant quantum computers.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform 1-4 . However, the accuracy needed to outperform classical methods has not been achieved so far. Here, using 18 superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to investigate fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors, and measure the energy eigenvalues of this wire with an error of approximately 0.01 rad, whereas typical energy scales are of the order of 1 rad. Insight into the fidelity of this algorithm is gained by highlighting the robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 10 -4 rad. We also synthesize magnetic flux and disordered local potentials, which are two key tenets of a condensed-matter system. When sweeping the magnetic flux we observe avoided level crossings in the spectrum, providing a detailed fingerprint of the spatial distribution of local disorder. By combining these methods we reconstruct electronic properties of the eigenstates, observing persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation 5,6 and paves the way to study new quantum materials with superconducting qubits.

Quantum algorithms offer a dramatic speedup for computational problems in material science and chemistry. However, any near-term realizations of these algorithms will need to be optimized to fit within the finite resources offered by existing noisy hardware. Here, taking advantage of the adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a threefold reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an imaginary swap-like (iSWAP-like) gate to attain an arbitrary swap angle, θ, and a controlled-phase gate that generates an arbitrary conditional phase, ϕ. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic simulation (fSim) gate set. We benchmark the fidelity of the iSWAP-like and controlled-phase gate families as well as 525 other fSim gates spread evenly across the entire fSim(θ,ϕ) parameter space, achieving a purity-limited average two-qubit Pauli error of 3.8×10^{-3} per fSim gate.

Superconducting nanowire single photon detectors are typically biased using a constant current source and shunted in a conductance that is over an order of magnitude larger than the peak normal domain conductance of the detector. While this design choice is required to ensure quenching of the normal domain, the use of a small load resistor limits the pulse amplitude, rising-edge slew rate, and recovery time of the detector. Here, we explore the possibility of actively quenching the normal domain, thereby removing the need to shunt the detector in a small resistance. We first consider the theoretical performance of an actively quenched superconducting nanowire single photon detector and, in comparison to a passively quenched device, we predict roughly an order of magnitude improvement in the slew rate and peak voltage achieved in this configuration. The experimental performance of actively and passively quenched superconducting nanowire single photon detectors are then compared. It is shown that, in comparison to a passively quenched device, the actively quenched detectors simultaneously exhibited improved count rates, dark count rates, and timing jitter.

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor 1 . A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits 2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2 53 (about 10 16 ). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy 8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

Graphene, a single atomic layer of covalently bonded carbon atoms, has been investigated intensively for optoelectronics and represents a promising candidate for high-speed electronics. Here, we present a microwave mixer constructed as an asymmetrically contacted two-terminal graphene device based on the thermoelectric effect. We report a 50 GHz (minimum) mixer bandwidth as well as 130 V/W (163 mA/W) extrinsic direct-detection responsivity. Anomalous second-harmonic generation due to self-mixing in our graphene detector is also observed. Careful investigation of the responsivity from four different approaches gives consistent results, confirming the exceptional performance of our zero-bias device operating at room temperature. The 50 GHz bandwidth indicates an extremely fast response time and our experimental results represent an encouraging advance toward practical graphene microwave devices with anticipated future applications extended through millimeter wave and terahertz frequencies.

Radiofrequency switches are critical components in wireless communication systems and consumer electronics. Emerging devices include switches based on microelectromechanical systems and phase-change materials. However, these devices suffer from disadvantages such as large physical dimensions and high actuation voltages. Here we propose and demonstrate a nanoscale radiofrequency switch based on a memristive device. The device can be programmed with a voltage as low as 0.4 V and has an ON/OFF conductance ratio up to 10(12) with long state retention. We measure the radiofrequency performance of the switch up to 110 GHz and demonstrate low insertion loss (0.3 dB at 40 GHz), high isolation (30 dB at 40 GHz), an average cutoff frequency of 35 THz and competitive linearity and power-handling capability. Our results suggest that, in addition to their application in memory and computing, memristive devices are also a leading contender for radiofrequency switch applications.

Background: Recent neuroimaging investigations have explored the use of mental imagery tasks as proxies for an overt motor response, in which patients are asked to imagine performing a task, such as "Imagine yourself swimming.", Objectives: To detect covert volitional brain activity in patients with severe brain injury using pattern classification of the blood oxygenation level-dependent (BOLD) response during mental imagery and to compare these results with those of a univariate functional magnetic resonance imaging analysis., Design: Case-control study., Setting: Academic research., Participants: Experiments were performed in 8 healthy control subjects and in 5 patients with severe brain injury. The patients with severe brain injury constituted a convenience sample., Main Outcome Measures: Functional magnetic resonance imaging data were acquired as the patients were asked to follow commands or to answer questions using motor imagery as a proxy response., Results: In the controls, the responses were accurately classified. In the patient group, the responses of 3 of 5 patients were correctly classified. The remaining 2 patients showed no significant BOLD response in a standard univariate analysis, suggesting that they did not perform the task. In addition, we showed that a classifier trained on command-following data can be used to evaluate a later communication run. This technique was used to successfully disambiguate 2 potential BOLD responses to a single question., Conclusions: Pattern classification in functional magnetic resonance imaging is a promising technique for advancing the understanding of volitional brain responses in patients with severe brain injury and may serve as a powerful complement to traditional general linear model-based univariate analysis methods.

Objective: To determine whether EEG spectral analysis could be used to demonstrate awareness in patients with severe brain injury., Methods: We recorded EEG from healthy controls and three patients with severe brain injury, ranging from minimally conscious state (MCS) to locked-in-state (LIS), while they were asked to imagine motor and spatial navigation tasks. We assessed EEG spectral differences from 4 to 24 Hz with univariate comparisons (individual frequencies) and multivariate comparisons (patterns across the frequency range)., Results: In controls, EEG spectral power differed at multiple frequency bands and channels during performance of both tasks compared to a resting baseline. As patterns of signal change were inconsistent between controls, we defined a positive response in patient subjects as consistent spectral changes across task performances. One patient in MCS and one in LIS showed evidence of motor imagery task performance, though with patterns of spectral change different from the controls., Conclusions: EEG power spectral analysis demonstrates evidence for performance of mental imagery tasks in healthy controls and patients with severe brain injury., Significance: EEG power spectral analysis can be used as a flexible bedside tool to demonstrate awareness in brain-injured patients who are otherwise unable to communicate., (Copyright © 2011 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.)