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.

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.

Differential stimulation of hepatic and brain metallothioneins by ethanol

Administration of ethanol induces the synthesis of hepatic metallothionein and metallothionein mRNA in the liver but not in the brain. Furthermore, ethyl alcohol, methyl alcohol and isopropyl alcohol enhance the synthesis of metallothionein in Chang cells but not in neuroblastoma IMR-32 cells in culture. The results of this study are interpreted to suggest that the mechanisms of synthesis of metallothionein and the utilization of essential metal nutrients in the brain and peripheral tissues are not identical.

Accumulation of Chlorophyll, Chloroplastic Proteins, and Thylakoid Membranes during Reversion of Chromoplasts to Chloroplasts in Citrus sinensis Epicarp

In vitro culture of pericarp segments from fruit of Citrus sinensis (L.) Osbeck cv Valencia was used to determine the temporal sequence in development of chloroplasts from chromoplasts during regreening of the epicarp. Regreening of chromoplasts closely resembled greening of etioplasts, except that regreening proceeded much more slowly. Chlorophyll, the light-harvesting chlorophyll a/b binding protein of photosystem II, the chlorophyll a binding protein of reaction center P-700 of photosystem I, thylakoid membranes, and adenosine triphosphate synthetase were all detected at very low levels in degreened epicarp. All of these increased in parallel during regreening of the epicarp. Ribulose 1,5-bisphosphate carboxylase (RuBPCase) levels were high in degreened epicarp and declined for the first 10 days of culture before reaccumulating in the regreening segments. Light was necessary for the accumulation of all of the chloroplastic components. A lack of exogenous nitrogen did not prevent the accumulation of any chloroplastic component except Ru-BPCase, although accumulation of the other components was reduced. Sucrose at 150 millimolar in media lacking nitrogen markedly inhibited the accumulation of chlorophyll and light-harvesting chlorophyll a/b-protein.

Sugar regulation of plastid interconversions in epicarp of citrus fruit

Seasonal transformations between chloroplasts and chromoplasts, as measured by changes in chlorophyll content, in the epicarp of degreening and regreening Citrus sinensis (L.) Osbeck cv Valencia fruit closely parallelled the accumulation and later loss of soluble sugars. At any stage of development, reversing the relative soluble sugar content in the epicarp by culturing pericarp segments on agar media with low (15 millimolar) or high (150 millimolar) sucrose concentrations reversed the direction of change in chlorophyll content. Fruit of C. madurensis Lour., which mature year around and do not regreen, also accumulated soluble sugars in the pericarp as degreening was initiated.The epicarp of C. sinensis fruit accumulated nitrogen, but total nitrogen concentrations and amino acid concentrations changed little, during degreening and regreening of C. sinensis fruit. Cessation of nitrogen fertilization reduced the tendency of pericarp segments to regreen in vitro during subsequent years, but regreening tendency was restored by inclusion of KNO(3) in the media.It is concluded that chloroplasts become chromoplasts and citrus fruit degreen partially in response to the accumulation of sugars in the epicarp and that the reverse transformation accompanying regreening of certain citrus species occurs when accumulated sugars disappear. Change in nitrogen flux to the fruit is probably not a factor in regulating seasonal transformations, but an abundance of nitrogen in the epicarp diminishes the effects of high sugar concentrations in inducing transformation of chloroplasts to chromoplasts, thereby retarding degreening and promoting regreening.

Nutritional control of regreening and degreening in citrus peel segments

A method for reversibly regreening and degreening citrus epicarp in vitro using peel segments was developed.Peel segments from mature degreened fruit promptly regreened when kept in light upon agar medium containing low (15 millimolar) concentrations of sucrose. Higher concentrations of sucrose inhibited this regreening, but NO(3) (-) and certain amino acids included in the media overcame the inhibition by sucrose. However, l-serine strongly inhibited regreening. In the presence of nitrogen, sucrose promoted regreening.Peel segments from green fruit remained green on media with low concentrations of sucrose and on media with high concentrations of sucrose and 60 millimolar KNO(3), but degreened in response to high concentrations of sucrose in the absence of nitrogen. Nitrate overcame the degreening effects of high sucrose concentrations in both light and dark. Peel segments were reversibly degreened and regreened by transferring the segments between appropriate media.Nitrate in the media markedly reduced the levels of endogenous sugars in the epicarp and increased endogenous amino acid levels. Sucrose in the media increased endogenous sugar levels and, in the presence of nitrate, increased endogenous amino acid levels. In the absence of nitrogen, high sucrose concentrations reduced endogenous amino acid concentrations.