Digital zero noise extrapolation for quantum error mitigation

Zero-noise extrapolation (ZNE) is an increasingly popular technique for mitigating errors in noisy quantum computations without using additional quantum resources. We review the fundamentals of ZNE and propose several improvements to noise scaling and extrapolation, the two key components in the technique. We introduce unitary folding and parameterized noise scaling. These are digital noise scaling frameworks, i.e. one can apply them using only gate-level access common to most quantum instruction sets. We also study different extrapolation methods, including a new adaptive protocol that uses a statistical inference framework. Benchmarks of our techniques show error reductions of 18X to 24X over non-mitigated circuits and demonstrate ZNE effectiveness at larger qubit numbers than have been tested previously. In addition to presenting new results, this work is a self-contained introduction to the practical use of ZNE by quantum programmers.Comment: 11 pages, 7 figure

High level cognitive information processing in neural networks

Two related research efforts were addressed: (1) high-level connectionist cognitive modeling; and (2) local neural circuit modeling. The goals of the first effort were to develop connectionist models of high-level cognitive processes such as problem solving or natural language understanding, and to understand the computational requirements of such models. The goals of the second effort were to develop biologically-realistic model of local neural circuits, and to understand the computational behavior of such models. In keeping with the nature of NASA's Innovative Research Program, all the work conducted under the grant was highly innovative. For instance, the following ideas, all summarized, are contributions to the study of connectionist/neural networks: (1) the temporal-winner-take-all, relative-position encoding, and pattern-similarity association techniques; (2) the importation of logical combinators into connection; (3) the use of analogy-based reasoning as a bridge across the gap between the traditional symbolic paradigm and the connectionist paradigm; and (4) the application of connectionism to the domain of belief representation/reasoning. The work on local neural circuit modeling also departs significantly from the work of related researchers. In particular, its concentration on low-level neural phenomena that could support high-level cognitive processing is unusual within the area of biological local circuit modeling, and also serves to expand the horizons of the artificial neural net field

A Framework for Program Development Based on Schematic Proof

Often, calculi for manipulating and reasoning about programs can be recast as calculi for synthesizing programs. The difference involves often only a slight shift of perspective: admitting metavariables into proofs. We propose that such calculi should be implemented in logical frameworks that support this kind of proof construction and that such an implementation can unify program verification and synthesis. Our proposal is illustrated with a worked example developed in Paulson's Isabelle system. We also give examples of existent calculi that are closely related to the methodology we are proposing and others that can be profitably recast using our approach

Large-Scale Optical Neural Networks based on Photoelectric Multiplication

Recent success in deep neural networks has generated strong interest in hardware accelerators to improve speed and energy consumption. This paper presents a new type of photonic accelerator based on coherent detection that is scalable to large ($N \gtrsim 10^6$) networks and can be operated at high (GHz) speeds and very low (sub-aJ) energies per multiply-and-accumulate (MAC), using the massive spatial multiplexing enabled by standard free-space optical components. In contrast to previous approaches, both weights and inputs are optically encoded so that the network can be reprogrammed and trained on the fly. Simulations of the network using models for digit- and image-classification reveal a "standard quantum limit" for optical neural networks, set by photodetector shot noise. This bound, which can be as low as 50 zJ/MAC, suggests performance below the thermodynamic (Landauer) limit for digital irreversible computation is theoretically possible in this device. The proposed accelerator can implement both fully-connected and convolutional networks. We also present a scheme for back-propagation and training that can be performed in the same hardware. This architecture will enable a new class of ultra-low-energy processors for deep learning.Comment: Text: 10 pages, 5 figures, 1 table. Supplementary: 8 pages, 5, figures, 2 table

Cascadable all-optical NAND gates using diffractive networks

Owing to its potential advantages such as scalability, low latency and power efficiency, optical computing has seen rapid advances over the last decades. A core unit of a potential all-optical processor would be the NAND gate, which can be cascaded to perform an arbitrary logical operation. Here, we present the design and analysis of cascadable all-optical NAND gates using diffractive neural networks. We encoded the logical values at the input and output planes of a diffractive NAND gate using the relative optical power of two spatially-separated apertures. Based on this architecture, we numerically optimized the design of a diffractive neural network composed of 4 passive layers to all-optically perform NAND operation using the diffraction of light, and cascaded these diffractive NAND gates to perform complex logical functions by successively feeding the output of one diffractive NAND gate into another. We demonstrated the cascadability of our diffractive NAND gates by using identical diffractive designs to all-optically perform AND and OR operations, as well as a half-adder. Cascadable all-optical NAND gates composed of spatially-engineered passive diffractive layers can serve as a core component of various optical computing platforms.Comment: 24 Pages, 5 Figure