Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester

Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity $Q(f)$, and show that $B(f)=\Theta(Q(f)^2)$. This result gives a new method to upper bound the quantum query complexity: we give a method of finding bomb query algorithms from classical algorithms, which then provide nonconstructive upper bounds on $Q(f)=\Theta(\sqrt{B(f)})$. We subsequently were able to give explicit quantum algorithms matching our upper bound method. We apply this method on the single-source shortest paths problem on unweighted graphs, obtaining an algorithm with $O(n^{1.5})$ quantum query complexity, improving the best known algorithm of $O(n^{1.5}\sqrt{\log n})$ [arXiv:quant-ph/0606127]. Applying this method to the maximum bipartite matching problem gives an $O(n^{1.75})$ algorithm, improving the best known trivial $O(n^2)$ upper bound.Comment: 32 pages. Minor revisions and corrections. Regev and Schiff's proof that P(OR) = \Omega(N) remove

Nonparametric modeling and forecasting electricity demand: an empirical study

This paper uses half-hourly electricity demand data in South Australia as an empirical study of nonparametric modeling and forecasting methods for prediction from half-hour ahead to one year ahead. A notable feature of the univariate time series of electricity demand is the presence of both intraweek and intraday seasonalities. An intraday seasonal cycle is apparent from the similarity of the demand from one day to the next, and an intraweek seasonal cycle is evident from comparing the demand on the corresponding day of adjacent weeks. There is a strong appeal in using forecasting methods that are able to capture both seasonalities. In this paper, the forecasting methods slice a seasonal univariate time series into a time series of curves. The forecasting methods reduce the dimensionality by applying functional principal component analysis to the observed data, and then utilize an univariate time series forecasting method and functional principal component regression techniques. When data points in the most recent curve are sequentially observed, updating methods can improve the point and interval forecast accuracy. We also revisit a nonparametric approach to construct prediction intervals of updated forecasts, and evaluate the interval forecast accuracy.Functional principal component analysis; functional time series; multivariate time series, ordinary least squares, penalized least squares; ridge regression; seasonal time series

Fluctuation-induced tunneling conduction through RuO2_2 nanowire contacts

A good understanding of the electronic conduction processes through nanocontacts is a crucial step for the implementation of functional nanoelectronic devices. We have studied the current-voltage ($I$-$V$) characteristics of nanocontacts between single metallic RuO$_2$ nanowires (NWs) and contacting Au electrodes which were pre-patterned by simple photolithography. Both the temperature behavior of contact resistance in the low-bias voltage ohmic regime and the $I$-$V$ curves in the high-bias voltage non-ohmic regime have been investigated. We found that the electronic conduction processes in the wide temperature interval 1--300 K can be well described by the fluctuation-induced tunneling (FIT) conduction theory. Taken together with our previous work (Lin {\it et al.}, Nanotechnology {\bf 19}, 365201 (2008)) where the nanocontacts were fabricated by delicate electron-beam lithography, our study demonstrates the general validity of the FIT model in characterizing electronic nanocontacts.Comment: 6 pages, 5 figure

HAQ: Hardware-Aware Automated Quantization with Mixed Precision

Model quantization is a widely used technique to compress and accelerate deep neural network (DNN) inference. Emergent DNN hardware accelerators begin to support mixed precision (1-8 bits) to further improve the computation efficiency, which raises a great challenge to find the optimal bitwidth for each layer: it requires domain experts to explore the vast design space trading off among accuracy, latency, energy, and model size, which is both time-consuming and sub-optimal. Conventional quantization algorithm ignores the different hardware architectures and quantizes all the layers in a uniform way. In this paper, we introduce the Hardware-Aware Automated Quantization (HAQ) framework which leverages the reinforcement learning to automatically determine the quantization policy, and we take the hardware accelerator's feedback in the design loop. Rather than relying on proxy signals such as FLOPs and model size, we employ a hardware simulator to generate direct feedback signals (latency and energy) to the RL agent. Compared with conventional methods, our framework is fully automated and can specialize the quantization policy for different neural network architectures and hardware architectures. Our framework effectively reduced the latency by 1.4-1.95x and the energy consumption by 1.9x with negligible loss of accuracy compared with the fixed bitwidth (8 bits) quantization. Our framework reveals that the optimal policies on different hardware architectures (i.e., edge and cloud architectures) under different resource constraints (i.e., latency, energy and model size) are drastically different. We interpreted the implication of different quantization policies, which offer insights for both neural network architecture design and hardware architecture design.Comment: CVPR 2019. The first three authors contributed equally to this work. Project page: https://hanlab.mit.edu/projects/haq