Fragile topology in line-graph lattices with two, three, or four gapped flat bands

The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: their lowest energy bands are perfectly flat, and here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.Comment: 8+25 pages, 3+19 figures, 2+3 table

Spin-Orbit-Induced Topological Flat Bands in Line and Split Graphs of Bipartite Lattices

Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to construct two-dimensional (2D) topological quasi-flat bands from line graphs and split graphs of bipartite lattices. A line graph or split graph of a bipartite lattice exhibits a set of flat bands and a set of dispersive bands. The flat band connects to the dispersive bands through a degenerate state at some momentum. We find that, with spin-orbit coupling (SOC), the flat band becomes quasi-flat and gapped from the dispersive bands. By studying a series of specific line graphs and split graphs of bipartite lattices, we find that (i) if the flat band (without SOC) has inversion or $C_2$ symmetry and is non-degenerate, then the resulting quasi-flat band must be topologically nontrivial, and (ii) if the flat band (without SOC) is degenerate, then there exists an SOC potential such that the resulting quasi-flat band is topologically nontrivial. This generic mechanism serves as a paradigm for finding topological quasi-flat bands in 2D crystalline materials and meta-materials

The Gas Consumption History to z ~ 4

Using the observations of the star formation rate and HI densities to z ~ 4, with measurements of the Molecular Gas Depletion Rate (MGDR) and local density of H_2 at z = 0, we derive the history of the gas consumption by star formation to z ~ 4. We find that closed-box models in which H_2 is not replenished by HI require improbably large increases in rho(H_2) and a decrease in the MGDR with lookback time that is inconsistent with observations. Allowing the H_2 used in star formation to be replenished by HI does not alleviate the problem because observations show that there is very little evolution of rho(HI) from z = 0 to z = 4. We show that to be consistent with observational constraints, star formation on cosmic timescales must be fueled by intergalactic ionized gas, which may come from either accretion of gas through cold (but ionized) flows or from ionized gas associated with accretion of dark matter halos. We constrain the rate at which the extraglactic ionized gas must be converted into HI and ultimately into H_2. The ionized gas inflow rate roughly traces the SFRD: about 1 - 2 x 10^8 M_sun Gyr^-1 Mpc^-3 from z ~ 1 - 4, decreasing by about an order of magnitude from z=1 to z=0 with details depending largely on MGDR(t). All models considered require the volume averaged density of rho(H_2) to increase by a factor of 1.5 - 10 to z ~ 1.5 over the currently measured value. Because the molecular gas must reside in galaxies, it implies that galaxies at high z must, on average, be more molecule rich than they are at the present epoch, which is consistent with observations. These quantitative results, derived solely from observations, agree well with cosmological simulations.Comment: 11 pages, 6 figures. Accepted for publication in the Astrophysical Journal

Aggregation-induced emission poly(meth)acrylates for photopatterning via wavelength-dependent visible-light-regulated controlled radical polymerization in batch and flow conditions

A robust wavelength-dependent visible-light-regulated reversible-deactivation radical polymerization protocol is first reported for the batch preparation of >20 aggregation-induced emission (AIE)-active polyacrylates and polymethacrylates. The resulting polymers possess narrow molar mass distributions (Đ ≈ 1.09–1.25) and high end-group fidelity at high monomer conversions (mostly >95%). This demonstrated control provides facile access to the in situ generation of complex sequence-defined tetrablock copolymers in one reactor, even while chain extending from less reactive monomers. Polymerizations can be successfully carried out under various irradiation conditions, including using UV, blue, green, and red LED light with more disperse polymers obtained at the longer, less energetic, wavelengths. We observe a red shift and wavelength dependence for the most efficient polymerization using LED illumination in a polymerization reaction. We find that the absorption of the copper(II) complex is not a reliable guide to reaction conditions. Moreover, the reported protocol is readily translated to a flow setup. The prepared AIE-active polymers are demonstrated to exhibit good photopatterning, making them promising materials for applications in advanced optoelectronic devices

Tunable inductive coupler for high fidelity gates between fluxonium qubits

The fluxonium qubit is a promising candidate for quantum computation due to its long coherence times and large anharmonicity. We present a tunable coupler that realizes strong inductive coupling between two heavy-fluxonium qubits, each with $\sim50$MHz frequencies and $\sim5$ GHz anharmonicities. The coupler enables the qubits to have a large tuning range of $\textit{XX}$ coupling strengths ($-35$ to $75$ MHz). The $\textit{ZZ}$ coupling strength is $<3$kHz across the entire coupler bias range, and $<100$Hz at the coupler off-position. These qualities lead to fast, high-fidelity single- and two-qubit gates. By driving at the difference frequency of the two qubits, we realize a $\sqrt{i\mathrm{SWAP}}$ gate in $258$ns with fidelity $99.72\%$, and by driving at the sum frequency of the two qubits, we achieve a $\sqrt{b\mathrm{SWAP}}$ gate in $102$ns with fidelity $99.91\%$. This latter gate is only 5 qubit Larmor periods in length. We run cross-entropy benchmarking for over $20$ consecutive hours and measure stable gate fidelities, with $\sqrt{b\mathrm{SWAP}}$ drift ($2 \sigma$) $< 0.02\%$ and $\sqrt{i\mathrm{SWAP}}$ drift $< 0.08\%$.Comment: 16 pages, 14 figure

State Transfer Between a Mechanical Oscillator and Microwave Fields in the Quantum Regime

Recently, macroscopic mechanical oscillators have been coaxed into a regime of quantum behavior, by direct refrigeration [1] or a combination of refrigeration and laser-like cooling [2, 3]. This exciting result has encouraged notions that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits [1, 4-7], either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems [8, 9]. As yet, the transfer of an itinerant state or propagating mode of a microwave field to and from a mechanical oscillator has not been demonstrated owing to the inability to agilely turn on and off the interaction between microwave electricity and mechanical motion. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in, and retrieved from a mechanical oscillator with amplitudes at the single quanta level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mechanical oscillator. In this quantum regime, the mechanical oscillator can both store and transduce quantum information

Measurements of the Correlation Function of a Microwave Frequency Single Photon Source

At optical frequencies the radiation produced by a source, such as a laser, a black body or a single photon source, is frequently characterized by analyzing the temporal correlations of emitted photons using single photon counters. At microwave frequencies, however, there are no efficient single photon counters yet. Instead, well developed linear amplifiers allow for efficient measurement of the amplitude of an electromagnetic field. Here, we demonstrate how the properties of a microwave single photon source can be characterized using correlation measurements of the emitted radiation with such detectors. We also demonstrate the cooling of a thermal field stored in a cavity, an effect which we detect using a cross-correlation measurement of the radiation emitted at the two ends of the cavity.Comment: 5 pages, 4 figure

Circuit Quantum Electrodynamics with a Spin Qubit

Circuit quantum electrodynamics allows spatially separated superconducting qubits to interact via a "quantum bus", enabling two-qubit entanglement and the implementation of simple quantum algorithms. We combine the circuit quantum electrodynamics architecture with spin qubits by coupling an InAs nanowire double quantum dot to a superconducting cavity. We drive single spin rotations using electric dipole spin resonance and demonstrate that photons trapped in the cavity are sensitive to single spin dynamics. The hybrid quantum system allows measurements of the spin lifetime and the observation of coherent spin rotations. Our results demonstrate that a spin-cavity coupling strength of 1 MHz is feasible.Comment: Related papers at http://pettagroup.princeton.edu

Preparation and Measurement of Three-Qubit Entanglement in a Superconducting Circuit

Traditionally, quantum entanglement has played a central role in foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can exhibit results at odds with classical behavior. These discrepancies increase exponentially with the number of entangled particles. When entanglement is extended from just two quantum bits (qubits) to three, the incompatibilities between classical and quantum correlation properties can change from a violation of inequalities involving statistical averages to sign differences in deterministic observations. With the ample confirmation of quantum mechanical predictions by experiments, entanglement has evolved from a philosophical conundrum to a key resource for quantum-based technologies, like quantum cryptography and computation. In particular, maximal entanglement of more than two qubits is crucial to the implementation of quantum error correction protocols. While entanglement of up to 3, 5, and 8 qubits has been demonstrated among spins, photons, and ions, respectively, entanglement in engineered solid-state systems has been limited to two qubits. Here, we demonstrate three-qubit entanglement in a superconducting circuit, creating Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88%, measured with quantum state tomography. Several entanglement witnesses show violation of bi-separable bounds by 830\pm80%. Our entangling sequence realizes the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of encoding, decoding and error-correcting steps in a feedback loop will be the next milestone for quantum computing with integrated circuits.Comment: 7 pages, 4 figures, and Supplementary Information (4 figures)

Quantum Simulation of Tunneling in Small Systems

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution. We show that physically interesting simulations of tunneling using 2 qubits (i.e. on 4 lattice point grids) may be performed with 40 single and two-qubit gates. Approximately 70 to 140 gates are needed to see interesting tunneling dynamics in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure