Here we report on the production and tomography of genuinely entangled Greenberger-Horne-Zeilinger states with up to ten qubits connecting to a bus resonator in a superconducting circuit, where the resonator-mediated qubit-qubit interactions are used to controllably entangle multiple qubits and to operate on different pairs of qubits in parallel. The resulting 10-qubit density matrix is probed by quantum state tomography, with a fidelity of 0.668±0.025. Our results demonstrate the largest entanglement created so far in solid-state architectures and pave the way to large-scale quantum computation.

The development of meaningful ways to transfer biomass into useful materials, more efficient energy carriers, and/or carbon storage deposits is a profound challenge of our days. Herein, an ionothermal carbonization (ITC) method, via treating natural resources (glucose, cellulose, and sugar cane bagesse) in nonmetal ionic liquids (ILs) at ∼200 °C, is established for the fabrication of porous heteroatom-doped carbon materials with high yield. Commercial ILs with bulky bis(trifluoromethylsulfonyl)imide anion or cross-linkable nitrile group were found to be efficient and recyclable templates for porosity control, leading to exciting nanoarchitectures with promising performance in oxygen reduction reaction. The optimized ILs (12 mL) can dissolve and directly convert up to 15 g of glucose into porous carbon materials (SBET: 272 m(2)/g) one time. This ITC method relies on the synergistic use of structure-directing effect, good biomass solubility, and excellent thermal stability of ILs, and provides a sustainable strategy for exploiting biomass.

Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a paradigm, where quantum logic operations are realized through geometric phase manipulation that has some intrinsic noise-resilient advantages and may enable simplified implementation of multi-qubit gates compared to the dynamical approach. Here we report observation of a continuous-variable geometric phase and demonstrate a quantum gate protocol based on this phase in a superconducting circuit, where five qubits are controllably coupled to a resonator. Our geometric approach allows for one-step implementation of n-qubit controlled-phase gates, which represents a remarkable advantage compared to gate decomposition methods, where the number of required steps dramatically increases with n. Following this approach, we realize these gates with n up to 4, verifying the high efficiency of this geometric manipulation for quantum computation.

Anyons are quasiparticles occurring in two dimensions, whose topological properties are believed to be robust against local perturbations and may hold promise for fault tolerant quantum computing. Here we present an experiment of demonstrating the path independent nature of anyonic braiding statistics with a superconducting quantum circuit, which represents a 7-qubit version of the toric code model. We dynamically create the ground state of the model, achieving a state fidelity of 0.688±0.015 as verified by quantum state tomography. Anyonic excitations and braiding operations are subsequently implemented with single-qubit rotations. The braiding robustness is witnessed by looping an anyonic excitation around another one along two distinct, but topologically equivalent paths: Both reveal the nontrivial π-phase shift, the hallmark of Abelian 1/2 anyons, with a phase accuracy of ∼99% in the Ramsey-type interference measurement.