Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources [1]. Finding exact numerical solutions to these interacting fermion problems has exponential cost, while Monte Carlo methods are plagued by the fermionic sign problem. These limitations of classical computational methods have made even few-atom molecular structures problems of practical interest for medium-sized quantum computers.Yet, thus far experimental implementations have been restricted to molecules involving only Period I elements [2][3][4][5][6][7][8]. Here, we demonstrate the experimental optimization of up to six-qubit Hamiltonian problems with over a hundred Pauli terms, determining the ground state energy for molecules of increasing size, up to BeH 2 . This is enabled by a hardware-efficient variational quantum eigensolver with trial states specifically tailored to the available interactions in our quantum processor, combined with a compact encoding of fermionic Hamiltonians [9] and a robust stochastic optimization routine [10]. We further demonstrate the flexibility of our approach by applying the technique to a problem of quantum magnetism [11]. Across all studied problems, we find agreement between experiment and numerical simulations with a noisy model of the device. These results help elucidate the requirements for scaling the method to larger systems, and aim at bridging the gap between problems at the forefront of high-performance computing and their implementation on quantum hardware.The fundamental goal of addressing molecular structure problems is to solve for the ground state energy of many-body interacting fermionic Hamiltonians. Solving this problem on a quantum computer relies on a mapping between fermionic and qubit operators [12]. This restates it as a specific instance of a local Hamiltonian problem on a set of qubits. Given a k-local Hamiltonian H, composed of terms that act on at most k qubits, the solution to the local Hamiltonian problem amounts to finding its * These authors contributed equally to this work.smallest eigenvalue E G ,To date, no efficient algorithm is known that can solve this problem in full generality. For k ≥ 2 the problem is known to be QMA-complete [13]. However, it is expected that physical systems have Hamiltonians that do not constitute hard instances of this problem, and can be solved efficiently on a quantum computer, while remaining hard to solve classically. Following Feynman's idea for quantum simulation, a quantum algorithm for the ground state problem of interacting fermions was proposed in [14] and [15]. The approach relies on a good initial state that has a large overlap with the ground state and then solves the problem using the quantum phase estimation algorithm (PEA) [16]. While PEA has been demonstrated to achieve extremely accurate energy estimates for quantum chemistry [2, 3, 5, 8], it applies stringent requirements on quantum coherence.An a...

The integration of materials having a high dielectric constant (high-kappa) into carbon-nanotube transistors promises to push the performance limit for molecular electronics. Here, high-kappa (approximately 25) zirconium oxide thin-films (approximately 8 nm) are formed on top of individual single-walled carbon nanotubes by atomic-layer deposition and used as gate dielectrics for nanotube field-effect transistors. The p-type transistors exhibit subthreshold swings of S approximately 70 mV per decade, approaching the room-temperature theoretical limit for field-effect transistors. Key transistor performance parameters, transconductance and carrier mobility reach 6,000 S x m(-1) (12 microS per tube) and 3,000 cm2 x V(-1) x s(-1) respectively. N-type field-effect transistors obtained by annealing the devices in hydrogen exhibit S approximately 90 mV per decade. High voltage gains of up to 60 are obtained for complementary nanotube-based inverters. The atomic-layer deposition process affords gate insulators with high capacitance while being chemically benign to nanotubes, a key to the integration of advanced dielectrics into molecular electronics.

We show that the band structure of a carbon nanotube (NT) can be dramatically altered by mechanical strain. We employ an atomic force microscope tip to simultaneously vary the NT strain and to electrostatically gate the tube. We show that strain can open a bandgap in a metallic NT and modify the bandgap in a semiconducting NT. Theoretical work predicts that bandgap changes can range between ± 100 meV per 1% stretch, depending on NT chirality, and our measurements are consistent with this predicted range. PACS numbers: 62.25.+g, 71.20.Tx, 73.63.Fg, 81.07.De, 85.35.Kt The electronic and mechanical properties of carbon NTs make them interesting for both technological applications and basic science. A NT can be either metallic or semiconducting depending on the orientation between the atomic lattice and the tube axis [1,2]. NTs can accommodate very large mechanical strains [3] and have an extremely high Young's modulus [4]. Both theory and experiment indicate that NTs also have interesting electromechanical properties [5][6][7][8][9][10][11][12]. A pioneering experiment [10] showed that the conductance of a metallic NT could decrease by orders of magnitude when strained by an atomic force microscope (AFM) tip. The authors suggest that a local distortion of the sp 2 bonding where the NT is touched by the AFM tip causes the drop in conductance. In Ref.[12], however, it is argued that the observed drop in conductance is due to a bandgap induced in the NT as it is axially stretched [5,8,11] as illustrated in Fig. 1(a). Evidence for the effect of strain on NT bandgap also comes from recent STM work on semiconducting NTs containing encapsulated metallofullerenes [13]. The authors found a bandgap reduction of 60% at the expected positions of the metallofullerenes and postulated that strain could account for this change.Here we present measurements to demonstrate conclusively that strain modulates the band structure of NTs. We employ an AFM tip to simultaneously vary the NT strain and to electrostatically gate the tube. We find that, under strain, the conductance of the NT can increase or decrease, depending on the tube. By using the tip as a gate, we show that this is related to the increase or decrease in the bandgap of a NT under strain. The magnitude of the effect and its dependence on strain are consistent with theoretical expectations.The samples consist of NTs suspended over a trench and clamped at both ends by electrical contacts [10,[14][15][16][17]. CVD growth is utilized to grow NTs with diameters between 1 and 10 nm at lithographically defined catalyst sites [18] on a Si substrate with a 500nm oxide. Metal contacts (5nm Cr and 50-80nm gold) are made using photolithography, as described previously [19]. An ashing step (400°C for 10 minutes in Ar atmosphere) removes photoresist residue and improves contact resistances. An HF etch (3 minutes in 6:1 BHF, etch rate 80 nm/min) followed by critical point drying is used to suspend the NTs [16]. Device conductances are not changed significantly by the etching/drying p...

Deterministic lateral displacement (DLD) pillar arrays are an efficient technology to sort, separate and enrich micrometre-scale particles, which include parasites, bacteria, blood cells and circulating tumour cells in blood. However, this technology has not been translated to the true nanoscale, where it could function on biocolloids, such as exosomes. Exosomes, a key target of 'liquid biopsies', are secreted by cells and contain nucleic acid and protein information about their originating tissue. One challenge in the study of exosome biology is to sort exosomes by size and surface markers. We use manufacturable silicon processes to produce nanoscale DLD (nano-DLD) arrays of uniform gap sizes ranging from 25 to 235 nm. We show that at low Péclet (Pe) numbers, at which diffusion and deterministic displacement compete, nano-DLD arrays separate particles between 20 to 110 nm based on size with sharp resolution. Further, we demonstrate the size-based displacement of exosomes, and so open up the potential for on-chip sorting and quantification of these important biocolloids.

We improve the quality of quantum circuits on superconducting quantum computing systems, as measured by the quantum volume (QV), with a combination of dynamical decoupling, compiler optimizations, shorter two-qubit gates, and excited state promoted readout. This result shows that the path to larger QV systems requires the simultaneous increase of coherence, control gate fidelities, measurement fidelities, and smarter software which takes into account hardware details, thereby demonstrating the need to continue to co-design the software and hardware stack for the foreseeable future.

We perform low-temperature electrical transport measurements on gated, quasi-2D graphite quantum dots. In devices with low contact resistances, we use longitudinal and Hall resistances to extract carrier densities of 9.2-13 x 10(12) cm(-2) and mobilities of 200-1900 cm(2)/V.s. In devices with high resistance contacts, we observe Coulomb blockade phenomena and infer the charging energies and capacitive couplings. These experiments demonstrate that electrons in mesoscopic graphite pieces are delocalized over nearly the whole graphite piece down to low temperatures.

We present parity measurements on a five-qubit lattice with connectivity amenable to the surface code quantum error correction architecture. Using all-microwave controls of superconducting qubits coupled via resonators, we encode the parities of four data qubit states in either the X-or the Z-basis. Given the connectivity of the lattice, we perform full characterization of the static Zinteractions within the set of five qubits, as well as dynamical Z-interactions brought along by single-and two-qubit microwave drives. The parity measurements are significantly improved by modifying the microwave two-qubit gates to dynamically remove non-ideal Z errors.The fragile nature of quantum information means that the success of large-scale quantum computing hinges upon the successful implementation of quantum error correction (QEC) on physical qubit systems. Typically QEC protocols function through encoding of physical qubit information onto larger subspaces, which are subsequently protected against particular quantum errors [1, 2]. Amongst the many proposed QEC codes, the topological surface code [3,4] has gathered a large amount of interest by experimental implementations [5,6] due to its use of short-range nearest-neighbor interactions between physical qubits and its relatively high error thresholds.Building up a physical quantum network with the complete functionality of the surface code brings along a number of experimental challenges, some of which have yet to be explored. However, in the particular case of superconducting qubits, recent advances in coherence times [7][8][9] and in the understanding of environmental constraints [10,11] have triggered important experimental demonstrations on increasingly larger systems, including correction of bit-flip errors on linear qubit arrays [6,12], the detection of arbitrary quantum errors [13], and state preservation via encoding in cavity coherent states [14]. With gate fidelities continuing to improve [15,16], it becomes critical to demonstrate the ability to perform these operations in systems with the degree of connectivity required by the surface code. Furthermore, exploring higher-order errors in such nontrivially arranged networks of qubits are necessary for outlining the proper route towards larger numbers of interconnected qubits for QEC.In this Letter we demonstrate a plaquette of the surface code QEC protocol with an interconnected network of five superconducting transmon qubits. This network consists of four data qubits each explicitly coupled to a single syndrome qubit, through which single-shot highfidelity readout is used to measure weight-four checks of both the bit-flip and phase-flip data qubit parity. The geometrical arrangement of the network permits a systematic calibration of crosstalk noise within the plaquette, and we specifically look for errors in non-participating, or "spectator" qubits, during two-qubit gates. To make The five specific qubits used for the plaquette experiment are highlighted and labeled as data qubits (Di, i ∈ [1, 4]) and syndrome ...

We use an atomic force microscope (AFM) tip to locally probe the electronic properties of semiconducting carbon nanotube transistors. A gold-coated AFM tip serves as a voltage or current probe in three-probe measurement setup. Using the tip as a movable current probe, we investigate the scaling of the device properties with channel length. Using the tip as a voltage probe, we study the properties of the contacts. We find that Au makes an excellent contact in the p region, with no Schottky barrier. In the n region, large contact resistances were found which dominate the transport properties.