Quantum computers promise computational advantages for many important problems across various application domains. Unfortunately, physical quantum devices are highly susceptible to errors that limit us from running most of these quantum applications. Quantum Error Correction (QEC) codes are required to implement Fault-Tolerant Quantum Computers (FTQC) on which computations can be performed without encountering errors. Error decoding is a critical component of quantum error correction and is responsible for transforming a set of qubit measurements generated by the QEC code, called the syndrome, into error locations and error types. For the feasibility of implementation, error decoders must not only identify errors with high accuracy, but also be fast and scalable to a large number of qubits. Unfortunately, most of the prior works on error decoding have focused primarily only on the accuracy and have relied on software implementations that are too slow to be of practical use. Furthermore, these studies only look at designing a single decoder and do not analyze the challenges involved in scaling the storage and bandwidth requirements when performing error correction in large systems with thousands of qubits.In this paper, we present AFS, an accurate, fast, and scalable decoder architecture that is designed to operate in the context of systems with hundreds of logical qubits. We present the hardware implementation of AFS, which is based on the Union Find decoding algorithm and employs a three-stage pipelined design. AFS provides orders of magnitude higher accuracy compared to recent SFQ-based hardware decoders (logical error rate of 6×10−10for physical error rate of 10−3) and low decoding latency (42ns on average), while being robust to measurement errors introduced while extracting syndromes during the QEC cycles. We also reduce the amount of decoding hardware required to perform QEC simultaneously on all the logical qubits by co-designing the micro-architecture across multiple decoding units. Our proposed Conjoined-Decoder Architecture (CDA) reduces the storage overhead by 70% (10MB to 2.8MB). Finally, we reduce the bandwidth overheads required to transmit syndromes from the qubits to the decoders by exploiting the sparsity in the syndromes and compressing the data. Our proposed Syndrome Compression reduces the bandwidth requirement by 30x, on an average.

Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return incorrect outcomes or inject additional faults into the qubits. To achieve fault-tolerant error correction, Shor proposed to repeat the sequence of parity check measurements until the same outcome is observed sufficiently many times. Then, one can use this information to perform error correction. A basic implementation of this fault tolerance strategy requires$\Omega (r d^{2})$parity check measurements for a distance-$d$code defined by$r$parity checks. For some specific highly structured quantum codes, Bombin has shown that single-shot fault-tolerant quantum error correction is possible using only$r$measurements. In this work, we consider a phenomenological noise model for parity check measurements assuming that each bit of a codeword and the measurement outcome suffer from independent bit flips with some error rate$p$. For this model, we demonstrate that fault-tolerant quantum error correction can be achieved using$O(d \log (d))$measurements for any code with distance$d \geq \Omega (n^\alpha)$for some constant$\alpha > 0$. Moreover, we prove the existence of a sub-single-shot fault-tolerant quantum error correction scheme using fewer than$r$measurements. In some cases, the number of parity check measurements required for fault-tolerant quantum error correction is exponentially smaller than the number of parity checks defining the code. The short measurement sequences constructed generally have high weight and our phenomenological noise model is not realistic in this regime. Our error correction strategy could find applications to small codes and LDPC codes if one can manage to keep the weight of the measured parity checks low.

Quantum computing harnesses quantum laws of nature to enable new types of algorithms, not efficiently possible on traditional computers, that may lead to breakthroughs in crucial areas like materials science and chemistry. There is rapidly growing demand for a quantum workforce educated in the basics of quantum computing, in particular in quantum programming. However, there are few offerings for non-specialists and little information on best practices for training computer science and engineering students. In this report we describe our experience teaching an undergraduate course on quantum computing using a practical, software-driven approach. We centered our course around teaching quantum algorithms through hands-on programming, reducing the significance of traditional written assignments and relying instead on self-paced programming exercises ("Quantum Katas''), a variety of programming assignments, and a final project. We observed that the programming sections of the course helped students internalize theoretical material presented during the lectures. In the survey results, students indicated that the programming exercises and the final project contributed the most to their learning process. We describe the motivation for centering the course around quantum programming, discuss major artifacts used in this course, and present our lessons learned and best practices for a future improved course offering. We hope that our experience will help guide instructors who want to adopt a practical approach to teaching quantum computing and will enable more undergraduate programs to offer quantum programming as an elective.

In 1981, Richard Feynman proposed a device called a 'quantum computer' to take advantage of the laws of quantum physics to achieve computational speed-ups over classical methods. Quantum computing promises to revolutionize how and what we compute. Over the course of three decades, quantum algorithms have been developed that offer fast solutions to problems in a variety of fields including number theory, optimization, chemistry, physics, and materials science. Quantum devices have also significantly advanced such that components of a scalable quantum computer have been demonstrated; the promise of implementing quantum algorithms is in our near future. I will attempt to explain some of the mysteries of this disruptive, revolutionary computational paradigm and how it will transform our digital age.

We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with m constraint matrices, each of dimension n, rank at most r, and sparsity s. The first algorithm assumes an input model where one is given access to an oracle to the entries of the matrices at unit cost. We show that it has run time O~(s^2 (sqrt{m} epsilon^{-10} + sqrt{n} epsilon^{-12})), with epsilon the error of the solution. This gives an optimal dependence in terms of m, n and quadratic improvement over previous quantum algorithms (when m ~~ n). The second algorithm assumes a fully quantum input model in which the input matrices are given as quantum states. We show that its run time is O~(sqrt{m}+poly(r))*poly(log m,log n,B,epsilon^{-1}), with B an upper bound on the trace-norm of all input matrices. In particular the complexity depends only polylogarithmically in n and polynomially in r. We apply the second SDP solver to learn a good description of a quantum state with respect to a set of measurements: Given m measurements and a supply of copies of an unknown state rho with rank at most r, we show we can find in time sqrt{m}*poly(log m,log n,r,epsilon^{-1}) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as rho on the m measurements, up to error epsilon. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes' principle from statistical mechanics. As in previous work, we obtain our algorithm by "quantizing" classical SDP solvers based on the matrix multiplicative weight update method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians, given quantum states encoding these Hamiltonians, with a poly-logarithmic dependence on its dimension, which is based on ideas developed in quantum principal component analysis. We also develop a "fast" quantum OR lemma with a quadratic improvement in gate complexity over the construction of Harrow et al. [Harrow et al., 2017]. We believe both techniques might be of independent interest.

We survey recent strides made towards building a software framework that is capable of compiling quantum algorithms from a high-level description down to physical gates that can be implemented on a fault-tolerant quantum computer. We discuss why compilation and design automation tools such as the ones in our framework are key for tackling the grand challenge of building a scalable quantum computer. We then describe specialized libraries that have been developed using the LIQUi|〉 programming language. This includes reversible circuits for arithmetic as well as new, truly quantum approaches that rely on quantum computer architectures that allow the probabilistic execution of gates, a model that can reduce time and space overheads in some cases. We highlight why these libraries are useful for the implementation of many quantum algorithms. Finally, we survey the tool Revs that facilitate resource efficient compilation of higher-level irreversible programs into lower-level reversible circuits while trying to optimize the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future.

We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst-case running time n1/2m1/2s2poly(log(n), log(m), R, r, 1/δ), with n and s the dimension and row-sparsity of the input matrices, respectively, m the number of constraints, δ the accuracy of the solution, and R, r upper bounds on the size of the optimal primal and dual solutions, respectively. This gives a square-root unconditional speed-up over any classical method for solving SDPs both in n and m. We prove the algorithm cannot be substantially improved (in terms of n and m) giving a Ω(n1/2+ m2) quantum lower bound for solving semidefinite programs with constant s, R, r and δ. The quantum algorithm is constructed by a combination of quantum Gibbs sampling and the multiplicative weight method. In particular it is based on a classical algorithm of Arora and Kale for approximately solving SDPs. We present a modification of their algorithm to eliminate the need for solving an inner linear program which may be of independent interest.

In 1981, Richard Feynman proposed a device called a "quantum computer" to take advantage of the laws of quantum physics to achieve computational speed-ups over classical methods. Quantum computing promises to revolutionize how and what we compute. Over the course of three decades, quantum algorithms have been developed that offer fast solutions to problems in a variety of fields including number theory, optimization, chemistry, physics, and materials science. Quantum devices have also significantly advanced such that components of a scalable quantum computer have been demonstrated; the promise of implementing quantum algorithms is in our near future. I will attempt to explain some of the mysteries of this disruptive, revolutionary computational paradigm and how it will transform our digital age.

We demonstrate how quantum computation can provide non-trivial improvements in the computational and statistical complexity of the perceptron model. We develop two quantum algorithms for perceptron learning. The first algorithm exploits quantum information processing to determine a separating hyperplane using a number of steps sublinear in the number of data points $N$, namely $O(\sqrt{N})$. The second algorithm illustrates how the classical mistake bound of $O(\frac{1}{\gamma^2})$ can be further improved to $O(\frac{1}{\sqrt{\gamma}})$ through quantum means, where $\gamma$ denotes the margin. Such improvements are achieved through the application of quantum amplitude amplification to the version space interpretation of the perceptron model.

The queries people issue to a search engine and the results clicked following a query change over time. For example, after the earthquake in Japan in March 2011, the query japan spiked in popularity and people issuing the query were more likely to click government-related results than they would prior to the earthquake. We explore the modeling and prediction of such temporal patterns in Web search behavior. We develop a temporal modeling framework adapted from physics and signal processing and harness it to predict temporal patterns in search behavior using smoothing, trends, periodicities, and surprises. Using current and past behavioral data, we develop a learning procedure that can be used to construct models of users' Web search activities. We also develop a novel methodology that learns to select the best prediction model from a family of predictive models for a given query or a class of queries. Experimental results indicate that the predictive models significantly outperform baseline models that weight historical evidence the same for all queries. We present two applications where new methods introduced for the temporal modeling of user behavior significantly improve upon the state of the art. Finally, we discuss opportunities for using models of temporal dynamics to enhance other areas of Web search and information retrieval.

Many learning algorithms generate complex models that are difficult for a human to interpret, debug, and extend. In this paper, we address this challenge by proposing a new learning paradigm called correctable learning, where the learning algorithm receives external feedback about which data examples are incorrectly learned. We define a set of metrics which measure the correctability of a learning algorithm. We then propose a simple and efficient correctable learning algorithm which learns local models for different regions of the data space. Given an incorrect example, our method samples data in the neighborhood of that example and learns a new, more correct local model over that region. Experiments over multiple classification and ranking datasets show that our correctable learning algorithm offers significant improvements over the state-of-the-art techniques.

Content on the Internet is always changing. We explore the value of biasing search result snippets towards new webpage content. We present results from a user study comparing traditional query-focused snippets with snippets that emphasize new page content for two query types: general and trending. Our results indicate that searchers prefer the inclusion of temporal information for trending queries but not for general queries, and that this is particularly valuable for pages that have not been recently crawled.

User behavior on the Web changes over time. For example, the queries that people issue to search engines, and the underlying informational goals behind the queries vary over time. In this paper, we examine how to model and predict this temporal user behavior. We develop a temporal modeling framework adapted from physics and signal processing that can be used to predict time-varying user behavior using smoothing and trends. We also explore other dynamics of Web behaviors, such as the detection of periodicities and surprises. We develop a learning procedure that can be used to construct models of users' activities based on features of current and historical behaviors. The results of experiments indicate that by using our framework to predict user behavior, we can achieve significant improvements in prediction compared to baseline models that weight historical evidence the same for all queries. We also develop a novel learning algorithm that explicitly learns when to apply a given prediction model among a set of such models. Our improved temporal modeling of user behavior can be used to enhance query suggestions, crawling policies, and result ranking.

Web search is strongly influenced by time. The queries people issue change over time, with some queries occasionally spiking in popularity (e.g., earthquake) and others remaining relatively constant (e.g., youtube). The documents indexed by the search engine also change, with some documents always being about a particular query (e.g., the Wikipedia page on earthquakes is about the query earthquake) and others being about the query only at a particular point in time (e.g., the New York Times is only about earthquakes following a major seismic activity). The relationship between documents and queries can also change as people's intent changes (e.g., people sought different content for the query earthquake before the Haitian earthquake than they did after). In this paper, we explore how queries, their associated documents, and the query intent change over the course of 10 weeks by analyzing query log data, a daily Web crawl, and periodic human relevance judgments. We identify several interesting features by which changes to query popularity can be classified, and show that presence of these features, when accompanied by changes in result content, can be a good indicator of change in query intent.

We investigate the problem of learning to rank with document retrieval from the perspective of learning for multiple objective functions. We present solutions to two open problems in learning to rank: first, we show how multiple measures can be combined into a single graded measure that can be learned. This solves the problem of learning from a 'scorecard' of measures by making such scorecards comparable, and we show results where a standard web relevance measure (NDCG) is used for the top-tier measure, and a relevance measure derived from click data is used for the second-tier measure; the second-tier measure is shown to significantly improve while leaving the top-tier measure largely unchanged. Second, we note that the learning-to-rank problem can itself be viewed as changing as the ranking model learns: for example, early in learning, adjusting the rank of all documents can be advantageous, but later during training, it becomes more desirable to concentrate on correcting the top few documents for each query. We show how an analysis of these problems leads to an improved, iteration-dependent cost function that interpolates between a cost function that is more appropriate for early learning, with one that is more appropriate for late-stage learning. The approach results in a significant improvement in accuracy with the same size models. We investigate these ideas using LambdaMART, a state-of-the-art ranking algorithm.

Ranking search results is a fundamental problem in information retrieval. In this paper we explore whether the use of proximity and phrase information can improve web retrieval accuracy. We build on existing research by incorporating novel ranking features based on flexible proximity terms with recent state-of-the-art machine learning ranking models. We introduce a method of determining the goodness of a set of proximity terms that takes advantage of the structured nature of web documents, document metadata, and phrasal information from search engine user query logs. We perform experiments on a large real-world Web data collection and show that using the goodness score of flexible proximity terms can improve ranking accuracy over state-of-the-art ranking methods by as much as 13%. We also show that we can improve accuracy on the hardest queries by as much as 9% relative to state-of-the-art approaches.

This paper studies quality of human labels used to train search engines' rankers. Our specific focus is performance improvements obtained by using overlapping relevance labels, which is by collecting multiple human judgments for each training sample. The paper explores whether, when, and for which samples one should obtain overlapping training labels, as well as how many labels per sample are needed. The proposed selective labeling scheme collects additional labels only for a subset of training samples, specifically for those that are labeled relevant by a judge. Our experiments show that this labeling scheme improves the NDCG of two Web search rankers on several real-world test sets, with a low labeling overhead of around 1.4 labels per sample. This labeling scheme also outperforms several methods of using overlapping labels, such as simple k-overlap, majority vote, the highest labels, etc. Finally, the paper presents a study of how many overlapping labels are needed to get the best improvement in retrieval accuracy.

Many have speculated that classifying web pages can improve a search engine's ranking of results. Intuitively results should be more relevant when they match the class of a query. We present a simple framework for classification-enhanced ranking that uses clicks in combination with the classification of web pages to derive a class distribution for the query. We then go on to define a variety of features that capture the match between the class distributions of a web page and a query, the ambiguity of a query, and the coverage of a retrieved result relative to a query's set of classes. Experimental results demonstrate that a ranker learned with these features significantly improves ranking over a competitive baseline. Furthermore, our methodology is agnostic with respect to the classification space and can be used to derive query classes for a variety of different taxonomies.

Despite the widespread use of BM25, there have been few studies examining its effectiveness on a document description over single and multiple field combinations. We determine the effectiveness of BM25 on various document fields. We find that BM25 models relevance on popularity fields such as anchor text and query click information no better than a linear function of the field attributes. We also find query click information to be the single most important field for retrieval. In response, we develop a machine learning approach to BM25-style retrieval that learns, using LambdaRank, from the input attributes of BM25. Our model significantly improves retrieval effectiveness over BM25 and BM25F. Our data-driven approach is fast, effective, avoids the problem of parameter tuning, and can directly optimize for several common information retrieval measures. We demonstrate the advantages of our model on a very large real-world Web data collection.

A machine learning approach to learning to rank trains a model to optimize a target evaluation measure with repect to training data. Currently, existing information retrieval measures are impossible to optimize directly except for models with a very small number of parameters. The IR community thus faces a major challenge: how to optimize IR measures of interest directly. In this paper, we present a solution. Specifically, we show that LambdaRank, which smoothly approximates the gradient of the target measure, can be adapted to work with four popular IR target evaluation measures using the same underlying gradient construction. It is likely, therefore, that this construction is extendable to other evaluation measures. We empirically show that LambdaRank finds a locally optimal solution for mean [email protected], mean NDCG, MAP and MRR with a 99% confidence rate. We also show that the amount of effective training data varies with IR measure and that with a sufficiently large training set size, matching the training optimization measure to the target evaluation measure yields the best accuracy.

We present a component anomaly detector for a host-based intrusion detection system (IDS) for Microsoft Windows. The core of the detector is a learning-based anomaly detection algorithm that detects attacks on a host machine by looking for anomalous