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.

Selenium bioaccumulation in stocked fish as an indicator of fishery potential in pit lakes on reclaimed coal mines in Alberta, Canada

Pit lakes are a common reclamation strategy for open pit mines; however, there is a concern about their water quality and suitability as fish habitat because they are often contaminated by metals or metalloids. This study assessed the exposure of fish and invertebrates to selenium (Se) and other metals and metalloids in pit lakes formed by open pit coal mining in Tertiary (thermal coal) and in Cretaceous (metallurgical coal) bedrock. Juvenile hatchery rainbow trout, Oncorhynchus mykiss, and brook trout, Salvelinus fontinalis, were stocked into two thermal coal pit lakes (water Se < 2 μg/L, low water Se) and two metallurgical coal pit lakes (water Se > 15 μg/L, high water Se). Se accumulation in stocked fish and concentrations in invertebrates were characterized over a period of 2 years. In the metallurgical pits, invertebrates had higher Se concentrations and fish accumulated Se to higher levels (exceeding USEPA tissue Se guidelines) than biota in the thermal pits. Rainbow and brook trout accumulated similar concentrations of Se in their muscle and exhibited a similar relationship between whole-body and muscle Se concentrations. These results may be used by resource managers to assess compliance with whole-body tissue Se guidelines and to determine if pit lakes in coal mining areas pose a significant Se risk to wildlife or human health. The high Se exposure in metallurgical coal pits indicates that under the current mining and reclamation strategy, these lakes are not suitable for management as recreational "put and take" fisheries.

Chondroblastoma of the talus: a case report

Chondroblastoma of bone is an uncommon condition that has a predilection for secondary ossification centers, particularly of the humerus, tibia, and femur. Treatment usually involves surgical curettage and autogenous bone graft. This article reports the case of a chondroblastoma affecting the talus of a young man and a minimally invasive surgical approach for the treatment of this lesion. The patient presented with an 18-month history of right ankle pain and swelling. The lesion involved most of the talar body, with 2.5-cm cortical erosion inferiorly at the posterior talocalcaneal facet. A lateral approach was made to the talus and a window was fashioned at the distal end of the sinus tarsi under fluoroscopic guidance to allow access to the lesion. This was curetted and the defect was filled with autogenous bone graft taken from the ipsilateral iliac crest. The patient underwent an uneventful recovery, and was asymptomatic at follow-up 24 months postsurgery. He had 75% movement at the subtalar joint, when compared with the contralateral foot.

A statewide system to track medical students' careers: the Pennsylvania model

In 1994 the Commonwealth of Pennsylvania announced a statewide Generalist Physician Initiative (GPI) modeled after The Robert Wood Johnson Foundation's GPI. Three-year grants totaling more than $9 million were awarded to seven of Pennsylvania's medical schools, including two that had already received GPI grants from the foundation. Stimulated by these initiatives, the state's six allopathic and two osteopathic medical schools decided to work together to develop a collaborative longitudinal tracking system to follow the careers of all their students from matriculation into their professional careers. This statewide data system, which includes information for more than 18,000 students and graduates beginning with the entering class of 1982, can be used to evaluate the impact of the Pennsylvania GPI, and it also yielded a local longitudinal tracking system for each medical school. This paper outlines the concept of the system, its technical implementation, and the corresponding implications for other medical schools considering the development of similar outcomes assessment systems.

Ultrasonography in developmental hip dysplasia

With the evolving use of ultrasonography, there has been an increasing emphasis on the technically oriented diagnosis of developmental hip dysplasia. Graf's alpha and beta angles and Harcke's bony rim percentage are two of the more common criteria, but their repeatability and reliability have not been well documented. Fifty-eight hip ultrasounds of 29 infants were measured independently by three physicians, and statistical analysis was performed. It was concluded that Graf's and Harcke's methods could be repeatable with training and frequent use of ultrasonography. Harcke's guidelines have a large equivocal zone, which limited their clinical usefulness. Graf's angles gave a better classification, but their clinical relevance has not been proven.

Phytophotodermatitis: a visit to Margaritaville

Phytophotodermatitis is a phototoxic eruption following contact with photosensitizing compounds and long-wave ultraviolet light. The most common phototoxic compounds are the furocoumarins contained in a wide variety of plants, especially of the Umbelliferae, Rutaceae, and Moracea families. Commonly occurring photosensitizing plants include citrus fruits such as limes and oranges and many vegetables, notably celery, parsnip, parsley, carrots, and dill.

Esterase and malate dehydrogenase isozyme polymorphisms in 15 Artemia populations

1. Starch gel electrophoresis of adult brine shrimps from 15 populations revealed little intrapopulation polymorphism in NAD-dependent malate dehydrogenase (MDH) isozymes or in the two fastest esterases (demonstrated with alpha-naphthyl propionate as substrate). 2. Interpopulation differences could be summarized as three different electrophoresis band patterns for the five- to seven-banded MDH isozymes and another three patterns for the two fastest esterases. 3. These differences in electrophoresis patterns divide the 15 Artemia populations into four categories (each containing one to seven populations) which may be distinguished by isozyme content and which are congruent with categories established by the criterion of reproductive isolation in an earlier study.

The hemoglobins of Artemia salina. IV. A model for genetic control of hemoglobin 1, hemoglobin 2, and hemoglobin X

Two loci account for all genetic variation resulting in difference in electrophoretic mobility in three hemoglobins (Hb1, Hb2, and HbX) in the hemolymph of the brine shrimp. Four alpha alleles and nine beta alleles have been studied. In shrimps of all genotypes and in electrophoresis in media with varying degrees of molecular sieving, Hb2 is approximately equidistant from Hb1 and HbX. A shrimp heterozygous at both loci has a three-banded Hb1, a four-banded Hb2, and a three-banded BbX. We conclude that Hb2 contains n alpha-polypeptides and n beta-polypeptides. Hb1 contains 2n alpha-polypeptides. HbX contains 2n beta-polypeptides. During electrophoresis, the three native hemoglobins undergo reversible dissociation to n subunits. Subunits with the same charge reassemble to migrate as molecules of the same size as the native molecules. Although there is no evidence for an additional polypeptide in the three hemoglobins, we cannot exclude such a possibility. If it exists, it is under three constraints: (1) it must be present in equal amounts in each of the three hemoglobins; (2) it must have the same molecular weight as the alpha- and beta-polypeptides; and (3) it must be free of genetic variation (detectable by electrophoresis).

The hemoglobins of Artemia salina. V. Genetic variation in hemoglobin 1, hemoglobin 2, and hemoglobin 3

Electrophoretic mobilities of three hemoglobins (Hb1, Hb2, and Hb3) were studied in 15 populations of brine shrimps. Genetic segregation data support the model that Hb2 contains n alpha-polypeptides and n beta-polypeptides; Hb1 contains 2n alpha-polypeptides- Hb3 contains neither alpha- nor beta-polypeptides. There is no evidence of linkage of alpha and beta loci with each other or with the locus (or loci) which governs Hb3 or with the nonhomologous portion of the sex chromosomes. Hemoglobins of different populations may be hybridized in vitro by incubation at high temperature. Reversible dissociation to subunits which contain only one (alpha or beta) polypeptide occurs at 40 C (for Hb1) and at 50 C (for Hb2).