Ultrathin epitaxial graphite was grown on single-crystal silicon carbide by vacuum graphitization. The material can be patterned using standard nanolithography methods. The transport properties, which are closely related to those of carbon nanotubes, are dominated by the single epitaxial graphene layer at the silicon carbide interface and reveal the Dirac nature of the charge carriers. Patterned structures show quantum confinement of electrons and phase coherence lengths beyond 1 micrometer at 4 kelvin, with mobilities exceeding 2.5 square meters per volt-second. All-graphene electronically coherent devices and device architectures are envisaged.

We have produced ultrathin epitaxial graphite films which show remarkable 2D electron gas (2DEG) behavior. The films, composed of typically 3 graphene sheets, were grown by thermal decomposition on the (0001) surface of 6H-SiC, and characterized by surface-science techniques. The low-temperature conductance spans a range of localization regimes according to the structural state (square resistance 1.5 kΩ to 225 kΩ at 4 K, with positive magnetoconductance). Low resistance samples show characteristics of weak-localization in two dimensions, from which we estimate elastic and inelastic mean free paths. At low field, the Hall resistance is linear up to 4.5 T, which is well-explained by n-type carriers of density 10 12 cm −2 per graphene sheet. The most highlyordered sample exhibits Shubnikov -de Haas oscillations which correspond to nonlinearities observed in the Hall resistance, indicating a potential new quantum Hall system. We show that the high-mobility films can be patterned via conventional lithographic techniques, and we demonstrate modulation of the film conductance using a top-gate electrode. These key elements suggest electronic device applications based on nano-patterned epitaxial graphene (NPEG), with the potential for large-scale integration.

We describe and implement a family of entangling gates activated by radio-frequency flux modulation applied to a tunable transmon that is statically coupled to a neighboring transmon. The effect of this modulation is the resonant exchange of photons directly between levels of the two-transmon system, obviating the need for mediating qubits or resonator modes and allowing for the full utilization of all qubits in a scalable architecture. The resonance condition is selective in both the frequency and amplitude of modulation and thus alleviates frequency crowding. We demonstrate the use of three such resonances to produce entangling gates that enable universal quantum computation: one iSWAP gate and two distinct controlled Z gates. We report interleaved randomized benchmarking results indicating gate error rates of 6% for the iSWAP (duration 135ns) and 9% for the controlled Z gates (durations 175 ns and 270 ns), limited largely by qubit coherence.A central challenge in building a scalable quantum computer with superconducting qubits is the execution of high-fidelity, two-qubit gates within an architecture containing many resonant elements. As more elements are added, or as the multiplicity of couplings between elements is increased, the frequency space of the design becomes crowded and device performance suffers. In architectures composed of transmon qubits [1], there are two main approaches to implementing two-qubit gates. The first utilizes fixed-frequency qubits with static couplings where the two-qubit operations are activated by applying transverse microwave drives [2][3][4][5][6][7][8]. While fixedfrequency qubits generally have long coherence times, this architecture requires satisfying stringent constraints on qubit frequencies and anharmonicities [5,6,8] which requires some tunability to scale to many qubits [9]. The second approach relies on frequency-tunable transmons, and two-qubit gates are activated by tuning qubits into and out of resonance with a particular transition [10][11][12][13][14][15][16]. However, tunability comes at the cost of additional decoherence channels, thus significantly limiting coherence times [17]. In this approach the delivery of shaped unbalanced control signals poses a challenge [15]. Such gates are furthermore sensitive to frequency crowdingavoiding unwanted crossings with neighboring qubit energy levels during gate operations limits the flexibility and connectivity of the architecture.An alternative to these approaches is to modulate a circuit's couplings or energy levels at a frequency corresponding to the detuning between particular energy levels of interest [18][19][20][21][22][23][24][25][26]. This enables an entangling gate between a qubit and a single resonator [21,22], a qubit and many resonator modes [26], two transmon qubits coupled by a tunable mediating qubit [16,25], or two tunable transmons coupled to a mediating resonator [23,24].Building on these earlier results, we implement two entangling gates, iSWAP and controlled Z (CZ), between a flux-tunable transmon an...

We have discovered new features of the current-phase relation, I͑f͒, in superfluid 3 He weak links. Firstly, we find that at any given temperature there are two distinct I͑f͒ functions that characterize the weak link. Secondly, both functions continuously develop an unusual form that ultimately leads to the previously reported p state. The observed form of I͑f͒ has recently been predicted for unconventional quantum fluids such as 3 He, high-T c superconductors, and Bose-Einstein condensates. The two distinct states are likely to originate from the textural degree of freedom in superfluid 3 He. PACS numbers: 67.57. -z, 74.50. + r At temperatures not too far below the superfluid transition ͑T c 0.93 mK͒, the current-phase relation for 3 He aperture-array weak links is given by the dc-Josephson expression, I͑f͒ I c sinf, where I c is referred to as the link's critical current [1,2]. In this regime experiments have revealed several dynamic phenomena which are analogous to known effects in superconducting weak links: Josephson oscillations [3], plasma mode motion [4], homodyne current spikes [5], and Shapiro steps [6].The experiments also revealed a new phenomenon: the existence at lower temperatures of a metastable state, characterized by a p phase difference across the link [7]. The appearance of such a state implies that the system's energy has a local minimum at f min p, a feature not yet observed experimentally for conventional superconductors.Several theories have been advanced to explain the physics that gives rise to such minimum [8][9][10]. To test these theories it is necessary to determine the I͑f͒ function of the weak links with better precision. In order to improve on our earlier measurements we have built an elaborate acoustic shield surrounding our experiment in order to decrease noise caused by acoustical disturbances in the environment. Pressure driven fluctuations have been reduced (relative to our earlier work) by at least 1 order of magnitude, and important properties heretofore hidden, particularly near f p, have now become visible.We use a double diaphragm cell (which is described more completely elsewhere [3]) to study the dynamics of the weak links. This cell consists of a flat cylindrical container bounded on the top and bottom with metallized flexible plastic membranes of known stiffness. The weak link (a square array of 65 3 65 holes, each nominally 100 nm diameter separated by 3 mm, in a 50 nm thick SiN wall [11]) is mounted in the lower membrane. The top membrane's position is monitored with a SQUID-based displacement transducer [12]. This cell is immersed into liquid 3 He-B (at zero ambient pressure) which also fills the inside region.By applying a step voltage between the bottom diaphragm and the adjacent rigid electrode we create an initial pressure head across the weak link which eventually relaxes due to dissipation. A sufficiently large impulse sends the system into the Josephson oscillation regime; i.e., the phase is winding through angles greater than 2p and the average pressure he...