Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

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.

Stable quantum-correlated many-body states through engineered dissipation

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.

Measurement-induced entanglement and teleportation on a noisy quantum processor

Measurement has a special role in quantum theory1: by collapsing the wavefunction, it can enable phenomena such as teleportation2 and thereby alter the 'arrow of time' that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space-time3-10 that go beyond the established paradigms for characterizing phases, either in or out of equilibrium11-13. For present-day noisy intermediate-scale quantum (NISQ) processors14, the experimental realization of such physics can be problematic because of hardware limitations and the stochastic nature of quantum measurement. Here we address these experimental challenges and study measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping9,15-17 to avoid mid-circuit measurement and access different manifestations of the underlying phases, from entanglement scaling3,4 to measurement-induced teleportation18. We obtain finite-sized signatures of a phase transition with a decoding protocol that correlates the experimental measurement with classical simulation data. The phases display remarkably different sensitivity to noise, and we use this disparity to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realizing measurement-induced physics at scales that are at the limits of current NISQ processors.

Non-Abelian braiding of graph vertices in a superconducting processor

Indistinguishability of particles is a fundamental principle of quantum mechanics¹. For all elementary and quasiparticles observed to date-including fermions, bosons and Abelian anyons-this principle guarantees that the braiding of identical particles leaves the system unchanged^2,3. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions^4-8. Hence, it can change the observables of the system without violating the principle of indistinguishability. Despite the well-developed mathematical description of non-Abelian anyons and numerous theoretical proposals^9-22, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. Whereas efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasiparticles, superconducting quantum processors allow for directly manipulating the many-body wavefunction by means of unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons^9,10, we implement a generalized stabilizer code and unitary protocol²³ to create and braid them. This allows us to experimentally verify the fusion rules of the anyons and braid them to realize their statistics. We then study the prospect of using the anyons for quantum computation and use braiding to create an entangled state of anyons encoding three logical qubits. Our work provides new insights about non-Abelian braiding and, through the future inclusion of error correction to achieve topological protection, could open a path towards fault-tolerant quantum computing.

Formation of robust bound states of interacting microwave photons

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.

Noise-resilient edge modes on a chain of superconducting qubits

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 ℤ 2 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.

Realizing topologically ordered states on a quantum processor

[Figure: see text].

Time-Crystalline Eigenstate Order on a Quantum Processor

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states¹. 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.

A study establishes a scalable approach to engineer and characterize a many-body-localized discrete time crystal phase on a superconducting quantum processor.

Information scrambling in quantum circuits

[Figure: see text].

Hartree-Fock on a superconducting qubit quantum computer

The simulation of fermionic systems is among the most anticipated applications of quantum computing. We performed several quantum simulations of chemistry with up to one dozen qubits, including modeling the isomerization mechanism of diazene. We also demonstrated error-mitigation strategies based on N-representability that dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realized the Givens rotation approach to noninteracting fermion evolution, which we variationally optimized to prepare the Hartree-Fock wave function. This ubiquitous algorithmic primitive is classically tractable to simulate yet still generates highly entangled states over the computational basis, which allowed us to assess the performance of our hardware and establish a foundation for scaling up correlated quantum chemistry simulations.

Higgs physics at the CLIC electron-positron linear collider

The Compact Linear Collider (CLIC) is an option for a future [Formula: see text] collider operating at centre-of-mass energies up to [Formula: see text], providing sensitivity to a wide range of new physics phenomena and precision physics measurements at the energy frontier. This paper is the first comprehensive presentation of the Higgs physics reach of CLIC operating at three energy stages: [Formula: see text], 1.4 and [Formula: see text]. The initial stage of operation allows the study of Higgs boson production in Higgsstrahlung ([Formula: see text]) and [Formula: see text]-fusion ([Formula: see text]), resulting in precise measurements of the production cross sections, the Higgs total decay width [Formula: see text], and model-independent determinations of the Higgs couplings. Operation at [Formula: see text] provides high-statistics samples of Higgs bosons produced through [Formula: see text]-fusion, enabling tight constraints on the Higgs boson couplings. Studies of the rarer processes [Formula: see text] and [Formula: see text] allow measurements of the top Yukawa coupling and the Higgs boson self-coupling. This paper presents detailed studies of the precision achievable with Higgs measurements at CLIC and describes the interpretation of these measurements in a global fit.

In vivo administration of monoclonal antibodies to the CD3 T cell receptor complex induces cell death (apoptosis) in immature thymocytes

Some thymocytes, upon activation via the TCR complex in vitro, undergo apoptotic cell death. In this report, we examine the cell death induced in the thymus after administration of anti-CD3 or anti-TCR antibodies. We found that shortly after antibody injection, cortical thymocytes undergo apoptosis as characterized by morphologic changes and DNA fragmentation. Anti-CD3 administration led to depletion of nearly all CD4+CD8+ thymocytes, and approximately 50% of CD4+CD8- thymocytes. This depletion predominantly affected cells bearing low levels of CD3, although some depletion also occurred among cells expressing intermediate and high levels. Administration of an anti-TCR antibody also induced apoptosis, but affected significantly fewer thymocytes than anti-CD3. This effect was probably not due to different binding affinities for the two antibodies, because both antibodies show similar dose response effects in an in vitro model of activation-induced apoptosis. This work demonstrates that findings on activation-induced apoptosis in vitro can be extended to the in vivo situation, and further, that the activation of cortical thymocytes, in situ, results in apoptosis and removal of the activated cells. The possible relationships between this activation-induced cell death in immature thymocytes and the process of negative selection of autoreactive T cells is discussed.

In vivo administration of monoclonal antibodies to the CD3 T cell receptor complex induces cell death (apoptosis) in immature thymocytes

Some thymocytes, upon activation via the TCR complex in vitro, undergo apoptotic cell death. In this report, we examine the cell death induced in the thymus after administration of anti-CD3 or anti-TCR antibodies. We found that shortly after antibody injection, cortical thymocytes undergo apoptosis as characterized by morphologic changes and DNA fragmentation. Anti-CD3 administration led to depletion of nearly all CD4+CD8+ thymocytes, and approximately 50% of CD4+CD8- thymocytes. This depletion predominantly affected cells bearing low levels of CD3, although some depletion also occurred among cells expressing intermediate and high levels. Administration of an anti-TCR antibody also induced apoptosis, but affected significantly fewer thymocytes than anti-CD3. This effect was probably not due to different binding affinities for the two antibodies, because both antibodies show similar dose response effects in an in vitro model of activation-induced apoptosis. This work demonstrates that findings on activation-induced apoptosis in vitro can be extended to the in vivo situation, and further, that the activation of cortical thymocytes, in situ, results in apoptosis and removal of the activated cells. The possible relationships between this activation-induced cell death in immature thymocytes and the process of negative selection of autoreactive T cells is discussed.

[A myasthenic episode following intake of large amounts of a beta blocker]

A transient myasthenic syndrome confirmed by EMG after taking large doses of beta blocking agent is reported. Data on similar complications have not been found in the literature. Theories trying to explain the myasthenic, myopathic effect of the beta-blocking agents are reviewed. In the opinion of the authors the quinidine-like membrane stabilising effect played a role in their case, although the possibility of the direct effect of the drug on the neurotransmitters cannot be excluded either.

Trigonal catalase crystals: a new molecular packing assignment obtained from sections preserved with tannic acid

The molecular packing of a trigonal crystal form of catalase initially studied by Longley [1] has been re-evaluated. Sections of crystals fixed and preserved with tannic acid were obtained parallel to the (001) and (100) planes. Specimens prepared by either conventional or low temperature embedding maintained 20 A resolution after sectioning. The space group of the crystals is either P3(1)21 or P3(2)21 and the observed unit cell parameters for (001) and (100) are a = b = 174 A, gamma = 119 degrees and b = 189 A, c = 248 A with alpha = 89.5 degrees. Computer-based reconstructions of two principal projections coupled with crystal density measurements allowed the deduction that there is one catalase tetramer per asymmetric unit. The crystal structure consists of 6 molecules packed closely about a common triad screw axis. This interpretation differs from that proposed by Longley [J. Mol. Biol. 30 (1967) 323], because thin sections of embedded crystals were assumed a priori to be positively stained in the early work; in actuality the sections were negatively stained. We also demonstrate that tannic acid fixation can lead to well preserved, positively stained crystal sections under certain conditions.

Acute retention of urine due to isolated sacral myeloradiculitis

Two cases of isolated sacral myeloradiculitis are described with retention of urine, sensory disorders in sacral segments and pleocytosis in the CSF. The patients were treated with steroids and recovered after 30 days of treatment. The differential diagnosis and literature are reviewed.

Growth control of prostatic carcinoma cells in serum-free media: interrelationship of hormone response, cell density, and nutrient media

Two established prostatic carcinoma cell lines have been grown in long-term culture in a defined medium (PFMR-4) free of serum, hormones, or growth factors. Growth of both lines in serum-free medium was population dependent. This cell-density requirement could be replaced by mitomycin C-inactivated feeder cells, homologous conditioned medium, or fetal bovine serum, but not by hormones or growth factors. The cells responded to these factors only at high density. The nature of this hormonal response was dependent on the kind of basal nutrient medium used. Growth in PFMR-4 with added insulin was more rapid than that in DME/F12 medium with any combination of hormones or growth factors and was substantially greater than growth in DME/F12 medium with insulin alone. The results demonstrate that whereas these two prostatic carcinoma lines (PC-3 and DU 145) do not require hormones for survival or growth, they do respond to certain hormones under appropriate conditions. These conditions include both the type of basal nutrient medium used and the population density.

Sickle cell hemoglobin fiber structure altered by alpha-chain mutation

Hybrid hemoglobin molecules prepared with beta chains from hemoglobin S (beta 6 Glu leads to Val) and alpha chains from hemoglobin Sealy (alpha 47 Asp leads to His) form fibers with a novel structure. In contrast to the typical fibers of hemoglobin S with an average diameter of 22 nm and a solid cross section composed of 10 outer filaments surrounding a 4-filament core, the fibers of the alpha Sealy2 beta S2 hybrid are much larger, with a mean diameter of 32 nm and a unique double-hollow arrangement of filaments. Sealy--S fibers can be described by a model in which the two pairs of filaments most readily lost from fibers of hemoglobin S are missing to form the hollow regions, with an additional sheath of filaments added to form the overall larger structure.

[A disease pattern simulating a cubitocarpal "double-tunnel" syndrome due to anastomosis after Martin-Gruber (author's transl)]

The article reports on a case which appeared as though two tunnel syndromes were present simultaneously, namely, the cubital and the carpal tunnel syndromes. Thorough electrophysiological examination revealed, however, that this simulated pattern was due to the presence of an anastomosis after Martin-Gruber. Three months after surgery the patient was free from symptoms. Intraoperative neurography had established the compression and its resolution. Anastomosis of Riche-Canieu was an additional, secondary finding.