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.

This paper describes the advantages that the introduction of photonic integration technologies can bring to the development of photonic-enabled wireless communications systems operating in the millimeter wave frequency range. We present two approaches for the development of dual wavelength sources for heterodyne-based millimeter wave generation realized using active/passive photonic integration technology. One approach integrates monolithically two distributed feedback semiconductor lasers along with semiconductor optical amplifiers, wavelength combiners, electro-optic modulators and broad bandwidth photodiodes. The other uses a generic photonic integration platform, developing narrow linewidth dual wavelength lasers based on arrayed waveguide gratings. Moreover, data transmission over a wireless link at a carrier wave frequency above 100 GHz is presented, in which the two lasers are free-running, and the modulation is directly applied to the single photonic chip without the requirement of any additional component.