Quantum computing has the potential to realize powerful and revolutionary applications. A quantum computer can, in theory, solve certain problems exponentially faster than its classical counterparts. The current state of the art devices, however, are too small and noisy to practically realize this goal. An important tool for the advancement of quantum hardware, called model-based characterization, seeks to learn what types of noise are exhibited in a quantum processor. This technique, however, is notoriously difficult to scale up to even modest numbers of qubit, and has been limited to just 2 qubits until now. In this report, we present a novel method for performing model-based characterization, or tomography, on a many-qubit quantum processor. We consider up to 10 qubits, but the technique is expected to scale to even larger systems.
Benchmarking methods that can be adapted to multiqubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which measures a single error rate that quantifies overall performance. But, scaling Clifford RB to many qubits is surprisingly hard. It has only been performed on one, two, and three qubits as of this writing. This reflects a fundamental inefficiency in Clifford RB: the n-qubit Clifford gates at its core have to be compiled into large circuits over the one- and two-qubit gates native to a device. As n grows, the quality of these Clifford gates quickly degrades, making Clifford RB impractical at relatively low n. In this Letter, we propose a direct RB protocol that mostly avoids compiling. Instead, it uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization. We demonstrate this protocol experimentally on two to five qubits using the publicly available ibmqx5. We believe this to be the greatest number of qubits holistically benchmarked, and this was achieved on a freely available device without any special tuning up. Our protocol retains the simplicity and convenient properties of Clifford RB: it estimates an error rate from an exponential decay. But, it can be extended to processors with more qubits - we present simulations on 10+ qubits - and it reports a more directly informative and flexible error rate than the one reported by Clifford RB. We show how to use this flexibility to measure separate error rates for distinct sets of gates, and we use this method to estimate the average error rate of a set of cnot gates.
Despite their ubiquity in nanoscale electronic devices, the physics of tunnel barriers has not been developed to the extent necessary for the engineering of devices in the few-electron regime. This problem is of urgent interest, as this is the specific regime into which current extreme-scale electronics fall. Here, we propose theoretically and validate experimentally a compact model for multielectrode tunnel barriers, suitable for design-rules-based engineering of tunnel junctions in quantum devices. We perform transport spectroscopy at approximately T=4 K, extracting effective barrier heights and widths for a wide range of biases, using an efficient Landauer-Büttiker tunneling model to perform the analysis. We find that the barrier height shows several regimes of voltage dependence, either linear or approximately exponential. Effects on threshold, such as metal-insulator transition and lateral confinement, are included because they influence parameters that determine barrier height and width (e.g., the Fermi energy and local electric fields). We compare these results to semiclassical solutions of Poisson's equation and find them to agree qualitatively. Finally, this characterization technique is applied to an efficient lateral tunnel barrier design that does not require an electrode directly above the barrier region in order to estimate barrier heights and widths.