Non-Abelian braiding of graph vertices in a superconducting processor

Indistinguishability of particles is a fundamental principle of quantum mechanics. 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. However, in two spatial dimensions, an intriguing possibility exists: braiding of non-Abelian anyons causes rotations in a space of topologically degenerate wavefunctions. 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, 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. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates. Building on predictions that stabilizer codes can host projective non-Abelian Ising anyons, we implement a generalized stabilizer code and unitary protocol 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 employing the anyons for quantum computation and utilize 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 toward fault-tolerant quantum computing

Evaluating the Solvent Stark Effect from Temperature-Dependent Solvatochromic Shifts of Anthracene

The solvent Stark effect on the spectral shifts of anthracene is studied with temperature‐dependent solvatochromic measurements. The Stark contribution ΔvStark to the absorption shift Δvp in polar solvents is measured to be ΔvStark=(53±35) cm−1, in reasonable agreement with dielectric continuum theory estimate of 28 cm−1, whereas the major shift Δvp∼300 cm−1 presumably originates from the solute quadrupole. We pay attention to the accurate correction of Δvp for the nonpolar contribution that is crucial when the shifts are modest in magnitude.Peer Reviewe

Multistate Multiconfiguration Quantum Chemical Computation of the Two-Photon Absorption Spectra of Bovine Rhodopsin

Recently, progress in IR sources has led to the discovery that humans can detect infrared (IR) light. This is hypothesized to be due to the two-photon absorption (TPA) events promoting the retina dim-light rod photoreceptor rhodopsin to the same excited state populated via one-photon absorption (OPA). Here, we combine quantum mechanics/molecular mechanics and extended multiconfiguration quasi-degenerate perturbation theory calculations to simulate the TPA spectrum of bovine rhodopsin (Rh) as a model for the human photoreceptor. The results show that the TPA spectrum of Rh has an intense S-0 -> S-1 band but shows also S-0 -> S-2 and S-0 -> S-3 transitions whose intensities, relative to the S-0 -> S-1 band, are significantly increased when compared to the corresponding bands of the OPA spectrum. In conclusion, we show that IR light in the 950 nm region can be perceived by rod photoreceptors, thus supporting the two-photon origin of the IR perception. We also found that the same photoreceptor can perceive red (i.e., close to 680 nm) light provided that TPA induces population of S-2

Trifluoromethylation of Fullerenes: Kinetic and Thermodynamic Control

We present a survey and theoretical interpretation of the experimental results on trifluoromethylation of fullerenes. A thermodynamic model has been developed to describe the C_60/70(CF₃)_<i>n</i> condensed phase mixtures capable of free exchange of addends and, consequently, of isomerization and changing the degrees of addition. It was found that the purely thermodynamic model affords at least satisfactory prediction of composition of products even for apparently nonequilibrium syntheses. Special cases can be identified by means of detailed kinetic modeling based on the BEP approach, which includes stepwise energetic analysis of the possible trifluoromethylation sequences. This analysis reveals two types of reactions with remarkable difference in rates: direct trifluoromethylation and rearrangements of the CF₃ groups. Whenever a particular group of compounds is interrelated through direct addition/abstraction of CF₃ groups, it is more or less safe to assume that the said group is in equilibrium describable by the thermodynamic model. In the same time, the slower migration of addends is controlled kinetically, and interference of the sublimation processes frequently prevents its equilibration. Among the most illustrative examples of hindered formation via rearrangements in absence of sufficiently favorable direct trifluoromethylation pathways are certain isomers of the <i>C</i>_3<i>v</i>–C₆₀(CF₃)₁₈, C₇₀(CF₃)₁₈, and C₇₀(CF₃)₂₀ compounds

Anion Radicals of Isomeric [5,6] and [6,6] Benzoadducts of Sc₃N@C₈₀: Remarkable Differences in Endohedral Cluster Spin Density and Dynamics

The anion radicals of isomeric [5,6] and [6,6] Sc₃N@C₈₀ benzoadducts were studied by electron spin resonance spectroscopy, density functional theory computations, and molecular dynamics. In both compounds the rotation of the Sc₃N cluster is frozen and the spin density distribution of the cluster is highly anisotropic, with hyperfine coupling constants of 9.1 and 2 × 33.3 G for the [5,6] adduct and ∼0.6 and 2 × 47.9 G for the [6,6] adduct. Remarkably, the subtle variation of the position of the exohedral group on the surface of the cage results in very pronounced changes in the spin density distribution and the dynamics of the encapsulated Sc₃N cluster

Cage Shrinkage of Fullerene via a C₂ Loss: from IPR C₉₀(28)Cl₂₄ to Nonclassical, Heptagon-Containing C₈₈Cl_22/24

A new case of chlorination-promoted fullerene cage shrinkage is reported. Chlorination of C₉₀ (isolated pentagon rule isomer no. 28) with VCl₄ afforded C₈₈Cl₂₂ with a nonclassic carbon cage (NCC) containing 1 heptagon and 13 pentagons including 2 fused pairs flanking the heptagon. The pathway of C₂ abstraction from the C₉₀ cage is suggested on the basis of density functional theory calculations

Skeletal Transformation of Isolated Pentagon Rule (IPR) Fullerene C₈₂ into Non-IPR C₈₂Cl₂₈ with Notably Low Activation Barriers

A novel case of chlorination-promoted skeletal transformation in higher fullerenes is reported. Chlorination of C₈₂ [isolated pentagon rule (IPR) isomer no. 3] with SbCl₅ results in two consecutive Stone–Wales rearrangements into non-IPR C₈₂Cl₂₈ with one pair of fused pentagons. An extensive theoretical study of the transformation pathways in C₈₂ revealed that the thermodynamically favorable rearrangement into non-IPR C₈₂Cl₂₈ needs a comparatively low activation energy