Ru0.05Ce0.95Ox is an active catalyst for methanation of CO2 with H2. Under reaction conditions one expects that oxygen vacancies are present on the oxide catalyst surface and that their steady-state concentration depends upon the relative ratio of the oxidant (CO2) to the reductant (H2). We show that the activity of the catalyst is sensitive to the degree of surface reduction: a surface that is too reduced or too oxidized loses activity. Exposing the oxidized surface to CO2 and then to H2 produces no methane, while on a reduced surface methane is produced by exposure to CO2 followed by H2. If the reaction is carried out at the steady state, purged, and then exposed to only hydrogen, methane is produced. Methane is formed through the reaction of hydrogen with surface species, whose infrared spectrum is associated with a variety of surface carbonates, and not through CO or a formate intermediate.

Two types of Ru-ceria catalysts were investigated, one prepared by combustion to create an atomically doped metal oxide, and the other, prepared by impregnation, as supported Ru oxide. They have different physical properties (as measured by X-ray photoelectron spectroscopy, X-ray diffraction, and Infrared spectra of adsorbed CO) but identical catalytic activity for dry reforming of methane. We show that the catalyst for dry reforming is partially reduced using XPS and IR spectroscopy. Furthermore, transient oxidation reaction spectroscopy with oxygen pulses confirms partial reduction of the catalyst is necessary for dry reforming activity. © 2013 Springer Science+Business Media New York.

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.

Realizing the potential of quantum computing requires sufficiently low logical error rates¹. Many applications call for error rates as low as 10^-15 (refs. ^2-9), but state-of-the-art quantum platforms typically have physical error rates near 10^-3 (refs. ^10-14). Quantum error correction^15-17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device^18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.