The effect of noise correlations on randomized benchmarking

Among the most popular and well studied quantum characterization, verification and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in "Pauli space." Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a gamma distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes -- consistent with existing experimental data -- highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the Filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation.Comment: Updated and expanded to include full derivation. Related papers available from http://www.physics.usyd.edu.au/~mbiercuk/Publications.htm

Comparing Experiments to the Fault-Tolerance Threshold

Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between measured error rates and thresholds is complicated by the fact that benchmarking estimates average error rates while thresholds reflect worst-case behavior when a gate is used as part of a large computation. These two measures of error can differ by orders of magnitude in the regime of interest. Here we facilitate comparison between the experimentally accessible average error rates and the worst-case quantities that arise in current threshold theorems by deriving relations between the two for a variety of physical noise sources. Our results indicate that it is coherent errors that lead to an enormous mismatch between average and worst case, and we quantify how well these errors must be controlled to ensure fair comparison between average error probabilities and fault-tolerance thresholds.Comment: 5 pages, 2 figures, 13 page appendi

Ultracompact Generation of Continuous-Variable Cluster States

We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs, which can be engineered into a single optical parametric oscillator (OPO). The desired CV cluster state is produced directly from a joint squeezing operation on the vacuum using a multi-frequency pump beam. This method has potential for ultracompact experimental implementation. As an illustration, we detail an experimental proposal for creating a four-mode square CV cluster state with a single OPO.Comment: 4 pages, 1 figure; v2 improved discussion of the implications of our result; added discussion of finite squeezing effect

Substrate induced proximity effect in superconducting niobium nanofilms

Structural and superconducting properties of high quality Niobium nanofilms with different thicknesses are investigated on silicon oxide and sapphire substrates. The role played by the different substrates and the superconducting properties of the Nb films are discussed based on the defectivity of the films and on the presence of an interfacial oxide layer between the Nb film and the substrate. The X-ray absorption spectroscopy is employed to uncover the structure of the interfacial layer. We show that this interfacial layer leads to a strong proximity effect, specially in films deposited on a SiO$_2$ substrate, altering the superconducting properties of the Nb films. Our results establish that the critical temperature is determined by an interplay between quantum-size effects, due to the reduction of the Nb film thicknesses, and proximity effects

Generalized Limits for Single-Parameter Quantum Estimation

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the quantum limit scales as $1/N^k$ where $N$ is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.Comment: 4 pages, 1 figure. v2 typos correcte

NASA/DOD Aerospace Knowledge Diffusion Research Project. Paper 28: The technical communication practices of Russian and US aerospace engineers and scientists

As part of Phase 4 of the NASA/DoD Aerospace Knowledge Diffusion Research Project, two studies were conducted that investigated the technical communication practices of Russian and U.S. aerospace engineers and scientists. Both studies had the same five objectives: first, to solicit the opinions of aerospace engineers and scientists regarding the importance of technical communication to their professions; second, to determine the use and production of technical communication by aerospace engineers and scientists; third, to seek their views about the appropriate content of the undergraduate course in technical communication; fourth, to determine aerospace engineers' and scientists' use of libraries, technical information centers, and on-line databases; and fifth, to determine the use and importance of computer and information technology to them. A self administered questionnaire was distributed to Russian aerospace engineers and scientists at the Central Aero-Hydrodynamic Institute (TsAGI) and to their U.S. counterparts at the NASA Ames Research Center and the NASA Langley Research Center. The completion rates for the Russian and U.S. surveys were 64 and 61 percent, respectively. Responses of the Russian and U.S. participants to selected questions are presented in this paper

Graphical calculus for Gaussian pure states

We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semi-local Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term "CV graph state" currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the "closest" CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this new graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.Comment: (v3) shortened title, very minor corrections (v2) minor corrections, reference added, new figures for CZ gate and beamsplitter graph rules; (v1) 25 pages, 11 figures (made with TikZ

Entanglement and the Power of One Qubit

The "Power of One Qubit" refers to a computational model that has access to only one pure bit of quantum information, along with n qubits in the totally mixed state. This model, though not as powerful as a pure-state quantum computer, is capable of performing some computational tasks exponentially faster than any known classical algorithm. One such task is to estimate with fixed accuracy the normalized trace of a unitary operator that can be implemented efficiently in a quantum circuit. We show that circuits of this type generally lead to entangled states, and we investigate the amount of entanglement possible in such circuits, as measured by the multiplicative negativity. We show that the multiplicative negativity is bounded by a constant, independent of n, for all bipartite divisions of the n+1 qubits, and so becomes, when n is large, a vanishingly small fraction of the maximum possible multiplicative negativity for roughly equal divisions. This suggests that the global nature of entanglement is a more important resource for quantum computation than the magnitude of the entanglement.Comment: 22 pages, 4 figure

Quantum metrology with Bose-Einstein condensates

We show how a generalized quantum metrology protocol can be implemented in a two-mode Bose-Einstein condensate of n atoms, achieving a sensitivity that scales better than 1/n and approaches 1/n^(3/2) for appropriate design of the condensate