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Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit superconducting transmon device and demonstrate fault-tolerant state preparation. We characterize the resulting code words through quantum process tomography and study the free evolution of the logical observables. Our results are consistent with fault-tolerant state preparation in a protected qubit subspace.

We present the first measurements of cyclotron resonance of electrons and holes in bilayer graphene. In magnetic fields up to B = 18 T we observe four distinct intraband transitions in both the conduction and valence bands. The transition energies are roughly linear in B between the lowest Landau levels, whereas they follow \sqrt{B} for the higher transitions. This highly unusual behavior represents a change from a parabolic to a linear energy dispersion. The density of states derived from our data generally agrees with the existing lowest order tight binding calculation for bilayer graphene. However in comparing data to theory, a single set of fitting parameters fails to describe the experimental results., Comment: to appear in Phys. Rev. Lett. Updated version with two added references and minor text editing