Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum-metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system, which is characterized by the Euler characteristic number instead of the Chern number. The work opens up a unique approach to explore the topology of quantum states with the QGT.

Here we report a breakthrough in the fabrication of a long lifetime transmon qubit. We use tantalum films as the base superconductor. By using a dry etching process, we obtained transmon qubits with a best T1 lifetime of 503 μs. As a comparison, we also fabricated transmon qubits with other popular materials, including niobium and aluminum, under the same design and fabrication processes. After characterizing their coherence properties, we found that qubits prepared with tantalum films have the best performance. Since the dry etching process is stable and highly anisotropic, it is much more suitable for fabricating complex scalable quantum circuits, when compared to wet etching. As a result, the current breakthrough indicates that the dry etching process of tantalum film is a promising approach to fabricate medium- or large-scale superconducting quantum circuits with a much longer lifetime, meeting the requirements for building practical quantum computers.

Proximal point algorithms (PPA) are attractive methods for monotone variational inequalities. The approximate versions of PPA are more applicable in practice. A modified approximate proximal point algorithm (APPA) presented by Solodov and Svaiter [Math. Programming, Ser. B 88 (2000) 371-389] relaxes the inexactness criterion significantly. This paper presents an extended version of Solodov-Svaiter's APPA. Building the direction from current iterate to the new iterate obtained by Solodov-Svaiter's APPA, the proposed method improves the profit at each iteration by choosing the optimal step length along this direction. In addition, the inexactness restriction is relaxed further. Numerical example indicates the improvement of the proposed method.  2004 Elsevier Inc. All rights reserved.

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We propose a protocol to realize parametric control of two-qubit coupling, where the amplitude and phase are tuned by a longitudinal field. Based on the tunable Hamiltonian, we demonstrate the superadiabatic two-qubit quantum gate using superconducting quantum circuits. Our experimental results show that the state of qubits evolves adiabatically during the gate operation even though the processing time is close to the quantum limit. In addition, the quantum state transition is insensitive to the variation of control parameters, and the fidelity of a SWAP gate achieved 98.5%. This robust parametric two-qubit gate can alleviate the tension of frequency crowding for quantum computation with multiple qubits.

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Two benzoxazine precursors bearing carborane moiety (1 and 2) were designed and synthesized successfully by the Mannich reaction of corresponding carborane bisphenol (3 and 4) with aniline and formaldehyde in 1,4-dioxane. The obtained precursors were characterized by using multiple spectroscopic techniques including GPC, FTIR, 1 H NMR, 13 C NMR, and 11 B NMR. Nonisothermal DSC studies showed that precursor 1 owned lower apparent activation energies (E a ) than 2. The optimum curing processes of benzoxazine precursors were also obtained on the basis of DSC data. TGA analyses manifested that the incorporation of carborane moiety endowed the obtained benzoxazine resins (cured 1 and 2) with excellent thermal stability and unique thermo-oxidative stability. The T d data showed that the initial degradation of both cured 1 and 2 under nitrogen and air was postponed to some extent owing to the shielding effect of carborane moiety on adjacent organic fragments. At higher temperature three-dimensional polymer networks with B-O-B and B-C linkages were formed as chars by the reaction of carborane cage with atmospheric moisture, degradation products such as phenolic hydroxyl, and oxygen (under air). Under nitrogen this network hindered the motion of radicals formed at elevated temperature and thus inhibited further polymer degradation processes. While under air, the formed boron-rich networks could hardly be further oxidized into carbon dioxide so that the carborane-containing benzoxazine resins also showed very high char yields.Closo-carboranes (C 2 B 10 H 12 ), with an icosahedral geometry, are excellent building blocks for thermally stable polymers. 17 Carboranes could absorb energy like a kind of "power gauge" at high temperature owing to its "superaromatic" electronic structure. Besides, the large volume of three-dimensional cage endows carboranes with strong shielding effect on adjacent segments. Therefore, carboranes were incorporated into many traditional polymers to improve their thermal stability including polysiloxanes, 18-26 epoxy resins, 27,28 phenolic resins, 29,30 aromatic polymers, 31 etc. With the increasing appearance of new polymers, carboranes expanded their application fields such as dendrimers [32][33][34][35][36][37][38] and conjugated polymers with light-emission property. [39][40][41][42][43][44] Additional Supporting Information may be found in the online version of this article.