Publications

Barthe, G, Hsu, J, Ying, M, Yu, N & Zhou, L 2020, 'Relational proofs for quantum programs.', Proc. ACM Program. Lang., vol. 4, no. POPL, pp. 21:1-21:1.
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© 2020 Copyright held by the owner/author(s). Relational verification of quantum programs has many potential applications in quantum and post-quantum security and other domains. We propose a relational program logic for quantum programs. The interpretation of our logic is based on a quantum analogue of probabilistic couplings. We use our logic to verify non-trivial relational properties of quantum programs, including uniformity for samples generated by the quantum Bernoulli factory, reliability of quantum teleportation against noise (bit and phase flip), security of quantum one-time pad and equivalence of quantum walks.

Broadbent, A, Ji, Z, Song, F & Watrous, J 2020, 'Zero-Knowledge Proof Systems for QMA', SIAM Journal on Computing, vol. 49, no. 2, pp. 245-283.
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© 2020 Society for Industrial and Applied Mathematics. Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result representing a further quantum generalization of this fact, which is that every problem in the complexity class QMA has a quantum zero-knowledge proof system. More specifically, assuming the existence of an unconditionally binding and quantum computationally concealing commitment scheme, we prove that every problem in the complexity class QMA has a quantum interactive proof system that is zero-knowledge with respect to efficient quantum computations. Our QMA proof system is sound against arbitrary quantum provers, but only requires an honest prover to perform polynomial-time quantum computations, provided that it holds a quantum witness for a given instance of the QMA problem under consideration. The proof system relies on a new variant of the QMA-complete local Hamiltonian problem in which the local terms are described by Clifford operations and standard basis measurements. We believe that the QMA-completeness of this problem may have other uses in quantum complexity.

Chowdhury, PN, Shivakumara, P, Pal, U, Lu, T & Blumenstein, M 2020, 'A new augmentation-based method for text detection in night and day license plate images', Multimedia Tools and Applications, vol. 79, no. 43-44, pp. 33303-33330.
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Despite a number of methods that have been developed for License Plate Detection (LPD), most of these focus on day images for license plate detection. As a result, license plate detection in night images is still an elusive goal for researchers. This paper presents a new method for LPD based on augmentation and Gradient Vector Flow (GVF) in night and day images. The augmentation involves expanding windows for each pixel in R, G and B color spaces of the input image until the process finds dominant pixels in both night and day license plate images of the respective color spaces. We propose to fuse the dominant pixels in R, G and B color spaces to restore missing pixels. For the results of fusing night and day images, the proposed method explores Gradient Vector Flow (GVF) patterns to eliminate false dominant pixels, which results in candidate pixels. The proposed method explores further GVF arrow patterns to define a unique loop pattern that represents hole in the characters, which gives candidate components. Furthermore, the proposed approach uses a recognition concept to fix the bounding boxes, merging the bounding boxes and eliminating false positives, resulting in text/license plate detection in both night and day images. Experimental results on night images of our dataset and day images of standard license plate datasets, demonstrate that the proposed approach is robust compared to the state-of-the-art methods. To show the effectiveness of the proposed method, we also tested our approach on standard natural scene datasets, namely, ICDAR 2015, MSRA-TD-500, ICDAR 2017-MLT, Total-Text, CTW1500 and MS-COCO datasets, and their results are discussed.

Du, Y, Hsieh, M-H, Liu, T & Tao, D 2020, 'Quantum-inspired algorithm for general minimum conical hull problems', Physical Review Research, vol. 2, no. 3, p. 033199.
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Du, Y, Hsieh, M-H, Liu, T, You, S & Tao, D 2020, 'On the learnability of quantum neural networks'.
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We consider the learnability of the quantum neural network (QNN) built on thevariational hybrid quantum-classical scheme, which remains largely unknown dueto the non-convex optimization landscape, the measurement error, and theunavoidable gate errors introduced by noisy intermediate-scale quantum (NISQ)machines. Our contributions in this paper are multi-fold. First, we derive theutility bounds of QNN towards empirical risk minimization, and show that largegate noise, few quantum measurements, and deep circuit depth will lead to thepoor utility bounds. This result also applies to the variational quantumcircuits with gradient-based classical optimization, and can be of independentinterest. We then prove that QNN can be treated as a differentially private(DP) model. Thirdly, we show that if a concept class can be efficiently learnedby QNN, then it can also be effectively learned by QNN even with gate noise.This result implies the same learnability of QNN whether it is implemented onnoiseless or noisy quantum machines. We last exhibit that the quantumstatistical query (QSQ) model can be effectively simulated by noisy QNN. Sincethe QSQ model can tackle certain tasks with runtime speedup, our resultsuggests that the modified QNN implemented on NISQ devices will retain thequantum advantage. Numerical simulations support the theoretical results.

Du, Y, Hsieh, M-H, Liu, T, You, S & Tao, D 2020, 'Quantum Differentially Private Sparse Regression Learning'.
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The eligibility of various advanced quantum algorithms will be questioned ifthey can not guarantee privacy. To fill this knowledge gap, here we devise anefficient quantum differentially private (QDP) Lasso estimator to solve sparseregression tasks. Concretely, given $N$ $d$-dimensional data points with $N\lld$, we first prove that the optimal classical and quantum non-private Lassorequires $\Omega(N+d)$ and $\Omega(\sqrt{N}+\sqrt{d})$ runtime, respectively.We next prove that the runtime cost of QDP Lasso is \textit{dimensionindependent}, i.e., $O(N^{5/2})$, which implies that the QDP Lasso can befaster than both the optimal classical and quantum non-private Lasso. Last, weexhibit that the QDP Lasso attains a near-optimal utility bound$\tilde{O}(N^{-2/3})$ with privacy guarantees and discuss the chance to realizeit on near-term quantum chips with advantages.

Fang, K, Wang, X, Tomamichel, M & Berta, M 2020, 'Quantum Channel Simulation and the Channel’s Smooth Max-Information', IEEE Transactions on Information Theory, vol. 66, no. 4, pp. 2129-2140.
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Gour, G & Tomamichel, M 2020, 'Entropy and relative entropy from information-theoretic principles', IEEE Trans. Inf. Theory, vol. 67, pp. 6313-6327.
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We introduce an axiomatic approach to entropies and relative entropies thatrelies only on minimal information-theoretic axioms, namely monotonicity undermixing and data-processing as well as additivity for product distributions. Wefind that these axioms induce sufficient structure to establish continuity inthe interior of the probability simplex and meaningful upper and lower bounds,e.g., we find that every relative entropy must lie between the R\'enyidivergences of order $0$ and $\infty$. We further show simple conditions forpositive definiteness of such relative entropies and a characterisation in termof a variant of relative trumping. Our main result is a one-to-onecorrespondence between entropies and relative entropies.

Gour, G & Tomamichel, M 2020, 'Optimal Extensions of Resource Measures and their Applications', Physical Review A, vol. 102, no. 6.
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We develop a framework to extend resource measures from one domain to alarger one. We find that all extensions of resource measures are boundedbetween two quantities that we call the minimal and maximal extensions. Wediscuss various applications of our framework. We show that any relativeentropy (i.e. an additive function on pairs of quantum states that satisfiesthe data processing inequality) must be bounded by the min and max relativeentropies. We prove that the generalized trace distance, the generalizedfidelity, and the purified distance are optimal extensions. And in entanglementtheory we introduce a new technique to extend pure state entanglement measuresto mixed bipartite states.

Hong, X, Zhou, X, Li, S, Feng, Y & Ying, M 2020, 'A Tensor Network based Decision Diagram for Representation of Quantum Circuits.', CoRR, vol. abs/2009.02618.

Jafarzadeh, M, Wu, Y-D, Sanders, YR & Sanders, BC 2020, 'Randomized benchmarking for qudit Clifford gates', New Journal of Physics, vol. 22, no. 6, pp. 063014-063014.
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Abstract We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending single- and multi-qubit URB to single- and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications.

Jain, R, Klauck, H, Kundu, S, Lee, T, Santha, M, Sanyal, S & Vihrovs, J 2020, 'Quadratically Tight Relations for Randomized Query Complexity', Theory of Computing Systems, vol. 64, no. 1, pp. 101-119.
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Ji, Z, Leung, D & Vidick, T 2020, 'A three-player coherent state embezzlement game', Quantum, vol. 4, pp. 349-349.
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We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of1in the game can only be achieved in the limit of strategies using arbitrarily high-dimensional entangled states. Precisely, there exists a constant0<c≤1such that to succeed with probability1−εin the game it is necessary to use an entangled state of at leastΩ(ε−c)qubits, and it is sufficient to use a state of at mostO(ε−1)qubits. The game is based on the coherent state exchange game of Leung et al.\ (CJTCS 2013). In our game, the task of the quantum verifier is delegated to a third player by a classical referee. Our results complement those of Slofstra (arXiv:1703.08618) and Dykema et al.\ (arXiv:1709.05032), who obtained two-player games with similar (though quantitatively weaker) properties based on the representation theory of finitely presented groups andC∗-algebras respectively.

Li, G, Zhou, L, Yu, N, Ding, Y, Ying, M & Xie, Y 2020, 'Projection-based runtime assertions for testing and debugging Quantum programs.', Proc. ACM Program. Lang., vol. 4, no. OOPSLA, pp. 150:1-150:1.
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© 2020 Owner/Author. In this paper, we propose Proq, a runtime assertion scheme for testing and debugging quantum programs on a quantum computer. The predicates in Proq are represented by projections (or equivalently, closed subspaces of the state space), following Birkhoff-von Neumann quantum logic. The satisfaction of a projection by a quantum state can be directly checked upon a small number of projective measurements rather than a large number of repeated executions. On the theory side, we rigorously prove that checking projection-based assertions can help locate bugs or statistically assure that the semantic function of the tested program is close to what we expect, for both exact and approximate quantum programs. On the practice side, we consider hardware constraints and introduce several techniques to transform the assertions, making them directly executable on the measurement-restricted quantum computers. We also propose to achieve simplified assertion implementation using local projection technique with soundness guaranteed. We compare Proq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Proq by its applications to assert two sophisticated quantum algorithms, the Harrow-Hassidim-Lloyd algorithm and Shor's algorithm.

Li, Y & Qiao, Y 2020, 'Group-theoretic generalisations of vertex and edge connectivities', Proceedings of the American Mathematical Society, vol. 148, no. 11, pp. 4679-4693.
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Let p p be an odd prime. Let P P be a finite p p -group of class 2 2 and exponent p p , whose commutator quotient P / [ P , P ] Quantum Science and Technology, vol. 5, no. 3, pp. 035008-035008.
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Abstract We consider testing the ability of quantum network nodes to execute multi-round quantum protocols. Specifically, we examine protocols in which the nodes are capable of performing quantum gates, storing qubits and exchanging said qubits over the network a certain number of times. We propose a simple ping-pong test, which provides a certificate for the capability of the nodes to run certain multi-round protocols. We first show that in the noise-free regime the only way the nodes can pass the test is if they do indeed possess the desired capabilities. We then proceed to consider the case where operations are noisy, and provide an initial analysis showing how our test can be used to estimate parameters that allow us to draw conclusions about the actual performance of such protocols on the tested nodes. Finally, we investigate the tightness of this analysis using example cases in a numerical simulation.

Liu, Y, Lan, C, Blumenstein, M & Li, J 2020, 'Bi-Level Error Correction for PacBio Long Reads', IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 17, no. 3, pp. 899-905.
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IEEE The latest sequencing technologies such as the Pacific Biosciences (PacBio) and Oxford Nanopore machines can generate long reads at the length of thousands of nucleic bases which is much longer than the reads at the length of hundreds generated by Illumina machines. However, these long reads are prone to much higher error rates, for example 15%, making downstream analysis and applications very difficult. Error correction is a process to improve the quality of sequencing data. Hybrid correction strategies have been recently proposed to combine Illumina reads of low error rates to fix sequencing errors in the noisy long reads with good performance. In this paper, we propose a new method named Bicolor, a bi-level framework of hybrid error correction for further improving the quality of PacBio long reads. At the first level, our method uses a de Bruijn graph-based error correction idea to search paths in pairs of solid < formula > < tex > $k$ < /tex > < /formula > -mers iteratively with an increasing length of < formula > < tex > $k$ < /tex > < /formula > -mer. At the second level, we combine the processed results under different parameters from the first level. In particular, a multiple sequence alignment algorithm is used to align those similar long reads, followed by a voting algorithm which determines the final base at each position of the reads. We compare the superior performance of Bicolor with three state-of-the-art methods on three real data sets. Results demonstrate that Bicolor always achieves the highest identity ratio. Bicolor also achieves a higher alignment ratio ( < formula > < tex > $ & #x003E; 1.3\%$ < /tex > < /formula > ) and a higher number of aligned reads than the current methods on two data sets. On the third data set, our method is closely competitive to the current methods in terms of number of aligned reads and genome coverage. The C++ source codes of our algorithm are freely available at https://github.com/yuansliu/Bicolor.

Mann, RL, Mathieson, L & Greenhill, C 2020, 'On the Parameterised Complexity of Induced Multipartite Graph Parameters'.
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We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$ and a given graph $G$, and for natural numbers $k\geq2$ and $\ell$, we must decide whether the maximum value of $p$ over all induced $k$-partite subgraphs of $G$ is at most $\ell$. We prove that this problem is W[1]-hard. Next, we consider a variant of this problem, where we must decide whether the given graph $G$ contains a sufficiently large induced $k$-partite subgraph $H$ such that $p(H)\leq\ell$. We show that for certain parameters this problem is para-NP-hard, while for others it is fixed-parameter tractable.

Mukai, H, Sakata, K, Devitt, SJ, Wang, R, Zhou, Y, Nakajima, Y & Tsai, J-S 2020, 'Pseudo-2D superconducting quantum computing circuit for the surface code: proposal and preliminary tests', New Journal of Physics, vol. 22, no. 4, pp. 043013-043013.
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Abstract Among the major hardware platforms for large-scale quantum computing, one of the leading candidates is superconducting quantum circuits. Current proposed architectures for quantum error-correction with the promising surface code require a two-dimensional layout of superconducting qubits with nearest-neighbor interactions. A major hurdle for the scalability in such an architecture using superconducting systems is the so-called wiring problem, where qubits internal to a chipset become difficult to access by the external control/readout lines. In contrast to the existing approaches which address the problem through intricate three-dimensional wiring and packaging technology, leading to a significant engineering challenge, here we address this problem by presenting a modified microarchitecture in which all the wiring can be realized through a newly introduced pseudo two-dimensional resonator network which provides the inter-qubit connections via airbridges. Our proposal is completely compatible with current standard planar circuit technology. We carried out experiments to examine the feasibility of the new airbridge component. The measured quality factor of the airbridged resonator is below the simulated surface-code threshold required for a coupling resonator, and it should not limit simulated gate fidelity. The measured crosstalk between crossed resonators is at most −49 dB in resonance. Further spatial and frequency separation between the resonators should result in relatively limited crosstalk between them, which would not increase as the size of the chipset increases. This architecture and the preliminary tests indicate the possibility that a large-scale, fully error-corrected quantum computer could be constructed by monolithic integration technologies without additional overhead or special packaging know-how.

Nag, S, Shivakumara, P, Pal, U, Lu, T & Blumenstein, M 2020, 'A new unified method for detecting text from marathon runners and sports players in video (PR-D-19-01078R2)', Pattern Recognition, vol. 107, pp. 107476-107476.
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© 2020 Detecting text located on the torsos of marathon runners and sports players in video is a challenging issue due to poor quality and adverse effects caused by flexible/colorful clothing, and different structures of human bodies or actions. This paper presents a new unified method for tackling the above challenges. The proposed method fuses gradient magnitude and direction coherence of text pixels in a new way for detecting candidate regions. Candidate regions are used for determining the number of temporal frame clusters obtained by K-means clustering on frame differences. This process in turn detects key frames. The proposed method explores Bayesian probability for skin portions using color values at both pixel and component levels of temporal frames, which provides fused images with skin components. Based on skin information, the proposed method then detects faces and torsos by finding structural and spatial coherences between them. We further propose adaptive pixels linking a deep learning model for text detection from torso regions. The proposed method is tested on our own dataset collected from marathon/sports video and three standard datasets, namely, RBNR, MMM and R-ID of marathon images, to evaluate the performance. In addition, the proposed method is also tested on the standard natural scene datasets, namely, CTW1500 and MS-COCO text datasets, to show the objectiveness of the proposed method. A comparative study with the state-of-the-art methods on bib number/text detection of different datasets shows that the proposed method outperforms the existing methods.

Qiao, Y, Sun, X & Yu, N 2020, 'Local Equivalence of Multipartite Entanglement', IEEE Journal on Selected Areas in Communications, vol. 38, no. 3, pp. 568-574.
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© 2020 IEEE. Let R be an invariant polynomial ring of a reductive group acting on a vector space, and let d be the minimum integer such that R is generated by those polynomials in R of degree no more than d. To upper bound such d is a long standing open problem since the very initial study of the invariant theory in the 19th century. Motivated by its significant role in characterizing multipartite entanglement, we study the invariant polynomial rings of local unitary groups-the direct product of unitary groups acting on the tensor product of Hilbert spaces, and local general linear groups-the direct product of general linear groups acting on the tensor product of Hilbert spaces. For these two group actions, we prove explicit upper bounds on the degrees needed to generate the corresponding invariant polynomial rings. On the other hand, systematic methods are provided to construct all homogeneous polynomials that are invariant under these two groups for any fixed degree. Thus, our results can be regarded as a complete characterization of the invariant polynomial rings. As an interesting application, we show that multipartite entanglement is additive in the sense that two multipartite states are local unitary equivalent if and only if r-copies of them are local unitary equivalent for some r.

Rahim, MS, Nguyen, KA, Stewart, RA, Giurco, D & Blumenstein, M 2020, 'Machine Learning and Data Analytic Techniques in Digital Water Metering: A Review', Water, vol. 12, no. 1, pp. 294-294.
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Digital or intelligent water meters are being rolled out globally as a crucial component in improving urban water management. This is because of their ability to frequently send water consumption information electronically and later utilise the information to generate insights or provide feedback to consumers. Recent advances in machine learning (ML) and data analytic (DA) technologies have provided the opportunity to more effectively utilise the vast amount of data generated by these meters. Several studies have been conducted to promote water conservation by analysing the data generated by digital meters and providing feedback to consumers and water utilities. The purpose of this review was to inform scholars and practitioners about the contributions and limitations of ML and DA techniques by critically analysing the relevant literature. We categorised studies into five main themes: (1) water demand forecasting; (2) socioeconomic analysis; (3) behaviour analysis; (4) water event categorisation; and (5) water-use feedback. The review identified significant research gaps in terms of the adoption of advanced ML and DA techniques, which could potentially lead to water savings and more efficient demand management. We concluded that further investigations are required into highly personalised feedback systems, such as recommender systems, to promote water-conscious behaviour. In addition, advanced data management solutions, effective user profiles, and the clustering of consumers based on their profiles require more attention to promote water-conscious behaviours.

Rambach, M, Qaryan, M, Kewming, M, Ferrie, C, White, AG & Romero, J 2020, 'Robust and Efficient High-Dimensional Quantum State Tomography', Physical Review Letters, vol. 126, no. 10.
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Razzak, I, Saris, RA, Blumenstein, M & Xu, G 2020, 'Integrating joint feature selection into subspace learning: A formulation of 2DPCA for outliers robust feature selection', Neural Networks, vol. 121, pp. 441-451.
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© 2019 Elsevier Ltd Since the principal component analysis and its variants are sensitive to outliers that affect their performance and applicability in real world, several variants have been proposed to improve the robustness. However, most of the existing methods are still sensitive to outliers and are unable to select useful features. To overcome the issue of sensitivity of PCA against outliers, in this paper, we introduce two-dimensional outliers-robust principal component analysis (ORPCA) by imposing the joint constraints on the objective function. ORPCA relaxes the orthogonal constraints and penalizes the regression coefficient, thus, it selects important features and ignores the same features that exist in other principal components. It is commonly known that square Frobenius norm is sensitive to outliers. To overcome this issue, we have devised an alternative way to derive objective function. Experimental results on four publicly available benchmark datasets show the effectiveness of joint feature selection and provide better performance as compared to state-of-the-art dimensionality-reduction methods.

Salek, F, Hsieh, M-H & Fonollosa, JR 2020, 'Single-Serving Quantum Broadcast Channel With Common, Individualized, and Confidential Messages', IEEE Transactions on Information Theory, vol. 66, no. 12, pp. 7752-7771.
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Sanders, YR, Berry, DW, Costa, PCS, Tessler, LW, Wiebe, N, Gidney, C, Neven, H & Babbush, R 2020, 'Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization', PRX Quantum, vol. 1, no. 2.
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Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum-accelerated simulated annealing including those using qubitization or Szegedy walks to quantize classical Markov chains and those simulating spectral-gap-amplified Hamiltonians encoding a Gibbs state. We also optimize fault-tolerant realizations of the adiabatic algorithm, quantum-enhanced population transfer, the quantum approximate optimization algorithm, and other approaches. Many of these methods are bottlenecked by calls to the same subroutines; thus, optimized circuits for those primitives should be of interest regardless of which heuristic is most effective in practice. We compile these bottlenecks for several families of optimization problems and report for how long and for what size systems one can perform these heuristics in the surface code given a range of resource budgets. Our results discourage the notion that any quantum optimization heuristic realizing only a quadratic speedup achieves an advantage over classical algorithms on modest superconducting qubit surface code processors without significant improvements in the implementation of the surface code. For instance, under quantum-favorable assumptions (e.g., that the quantum algorithm requires exactly quadratically fewer steps), our analysis suggests that quantum-accelerated simulated annealing requires roughly a day and a million physical qubits to optimize spin glasses that could be solved by classical simulated annealing in about 4 CPU-minutes.

Wang, Q, Huang, Y, Jia, W, He, X, Blumenstein, M, Lyu, S & Lu, Y 2020, 'FACLSTM: ConvLSTM with focused attention for scene text recognition', Science China Information Sciences, vol. 63, no. 2.
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© 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature. Scene text recognition has recently been widely treated as a sequence-to-sequence prediction problem, where traditional fully-connected-LSTM (FC-LSTM) has played a critical role. Owing to the limitation of FC-LSTM, existing methods have to convert 2-D feature maps into 1-D sequential feature vectors, resulting in severe damages of the valuable spatial and structural information of text images. In this paper, we argue that scene text recognition is essentially a spatiotemporal prediction problem for its 2-D image inputs, and propose a convolution LSTM (ConvLSTM)-based scene text recognizer, namely, FACLSTM, i.e., focused attention ConvLSTM, where the spatial correlation of pixels is fully leveraged when performing sequential prediction with LSTM. Particularly, the attention mechanism is properly incorporated into an efficient ConvLSTM structure via the convolutional operations and additional character center masks are generated to help focus attention on right feature areas. The experimental results on benchmark datasets IIIT5K, SVT and CUTE demonstrate that our proposed FACLSTM performs competitively on the regular, low-resolution and noisy text images, and outperforms the state-of-the-art approaches on the curved text images with large margins.

Xu, H, Xu, F, Theurer, T, Egloff, D, Liu, Z-W, Yu, N, Plenio, MB & Zhang, L 2020, 'Experimental Quantification of Coherence of a Tunable Quantum Detector', Physical Review Letters, vol. 125, no. 6, p. 060404.
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Quantum coherence is a fundamental resource that quantum technologies exploit to achieve performance beyond that of classical devices. A necessary prerequisite to achieve this advantage is the ability of measurement devices to detect coherence from the measurement statistics. Based on a recently developed resource theory of quantum operations, here we quantify experimentally the ability of a typical quantum-optical detector, the weak-field homodyne detector, to detect coherence. We derive an improved algorithm for quantum detector tomography and apply it to reconstruct the positive-operator-valued measures of the detector in different configurations. The reconstructed positive-operator-valued measures are then employed to evaluate how well the detector can detect coherence using two computable measures. As the first experimental investigation of quantum measurements from a resource theoretical perspective, our work sheds new light on the rigorous evaluation of the performance of a quantum measurement apparatus.

Xue, M, Shivakumara, P, Wu, X, Lu, T, Pal, U, Blumenstein, M & Lopresti, D 2020, 'Deep invariant texture features for water image classification', SN Applied Sciences, vol. 2, no. 12, p. 2068.
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Detecting potential issues in naturally captured images of water is a challenging task due to visual similarities between clean and polluted water, as well as causes posed by image acquisition with different camera angles and placements. This paper presents novel deep invariant texture features along with a deep network for detecting clean and polluted water images. The proposed method first divides an input image into H, S and V components to extract finer details. For each of the color spaces, the proposed approach generates two directional coherence images based on Eigen value analysis and gradient distribution, which results in enhanced images. Then the proposed method extracts scale invariant gradient orientations based on Gaussian first order derivative filters on different standard deviations to study texture of each smoothed image. To strengthen the above features, we explore the combination of Gabor-wavelet-binary pattern for extracting texture of the input water image. The proposed method integrates merits of aforementioned features and the features extracted by VGG16 deep learning model to obtain a single feature vector. Furthermore, the extracted feature is fed to a gradient boosting decision tree for water image detection. A variety of experimental results on a large dataset containing different types of clean and stagnant water images show that the proposed method outperforms the existing methods in terms of classification rate and accuracy.

Youssry, A, Paz-Silva, GA & Ferrie, C 2020, 'Beyond Quantum Noise Spectroscopy: modelling and mitigating noise with quantum feature engineering', npj Quantum Inf, vol. 6, p. 95.
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The ability to use quantum technology to achieve useful tasks, be theyscientific or industry related, boils down to precise quantum control. Ingeneral it is difficult to assess a proposed solution due to the difficultiesin characterising the quantum system or device. These arise because of theimpossibility to characterise certain components in situ, and are exacerbatedby noise induced by the environment and active controls. Here we present ageneral purpose characterisation and control solution making use of a noveldeep learning framework composed of quantum features. We provide the framework,sample data sets, trained models, and their performance metrics. In addition,we demonstrate how the trained model can be used to extract conventionalindicators, such as noise power spectra.

Yu, N 2020, 'Multipartite Entanglement Certification, With or Without Tomography', IEEE Transactions on Information Theory, vol. 66, no. 10, pp. 6369-6377.
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© 1963-2012 IEEE. Certifying multipartite entanglement is a fundamental task. Since n-qubit state is parameterized by 4n-1 real numbers, it is interesting to design a measurement setup that detects multipartite entanglement with as little effort as possible, and at a minimum without fully revealing the whole information of the state, the so-called 'tomography'. In this paper, we study the relationship between multipartite entanglement certification and tomography, with the constraint that only single-copy measurements are allowed. We show that by using nonadaptive single-copy measurements, universal entanglement detection, among all states, can not be accomplished without full state tomography. Moreover, we show that almost all multipartite correlations, including the genuine entanglement and the entanglement depth, require full state tomography to detect in this measurement setting. We also observe that universal entanglement detection, among pure states, can be accomplished using much fewer measurements than full state tomography even using only local measurements.

Yue, S, Yuan, M, Lu, T, Shivakumara, P, Blumenstein, M, Shi, J & Kumar, GH 2020, 'Rotation invariant angle-density based features for an ice image classification system', Expert Systems with Applications, vol. 162, pp. 113744-113744.
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© 2020 Elsevier Ltd One of the natural disasters which cause economic loss and are a serious threat to society are ice covering phenomena for overhead transmission power lines. This paper presents a new method for ice and non-ice image classification to improve ice detection results. The proposed method uses wavelet decomposition to extract robust features, such as those invariant to rotation, scaling and thickness of ice for classification. The proposed approach estimates the average of the high frequency sub-bands for each level. Then it obtains Canny edge components for the average wavelet image at each level. Our approach studies shape of edge components to identify the presence of ice. To achieve this, the proposed method finds the major and minor axes for each edge component, and then draws parallel lines to the major and minor axes over the edge components. For each parallel line to the major and minor axes, the proposed approach further extracts angle and density-based features for pixels that fall on the parallel lines to the major and minor axes. Next, our method selects features from each average wavelet image and further calculates the mean for the feature vectors corresponding to the level, which results in a feature matrix. Finally, the feature matrix is fed to a Multi-Layer Perceptron Neural Network for classifying ice and non-ice images. Experimental results on a diversified dataset and comparative study with an existing method show that the proposed method is useful for accurate ice detection with better accuracy.

Zhang, K, Hsieh, M-H, Liu, L & Tao, D 2020, 'Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms', Physical Review Research, vol. 3, p. 04395.
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Many quantum algorithms that claim speed-up over their classical counterpartsonly generate quantum states as solutions instead of their final classicaldescription. The additional step to decode quantum states into classicalvectors normally will destroy the quantum advantage in most scenarios becauseall existing tomographic methods require runtime that is polynomial withrespect to the state dimension. In this work, we present an efficient read-outprotocol that yields the classical vector form of the generated state, so itwill achieve the end-to-end advantage for those quantum algorithms. Ourprotocol suits the case that the output state lies in the row space of theinput matrix, of rank $r$, that is stored in the quantum random access memory.The quantum resources for decoding the state in $\ell^2$ norm with $\epsilon$error require $\poly(r,1/\epsilon)$ copies of the output state and $\poly(r,\kappa^r,1/\epsilon)$ queries to the input oracles, where $\kappa$ is thecondition number of the input matrix. With our read-out protocol, we completelycharacterise the end-to-end resources for quantum linear equation solvers andquantum singular value decomposition. One of our technical tools is anefficient quantum algorithm for performing the Gram-Schmidt orthonormalprocedure, which we believe, will be of independent interest.

Zhang, M, Gao, Y, Sun, C & Blumenstein, M 2020, 'A robust matching pursuit algorithm using information theoretic learning', Pattern Recognition, vol. 107, pp. 107415-107415.
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© 2020 Current orthogonal matching pursuit (OMP) algorithms calculate the correlation between two vectors using the inner product operation and minimize the mean square error, which are both suboptimal when there are non-Gaussian noises or outliers in the observation data. To overcome these problems, a new OMP algorithm is developed based on information theoretic learning (ITL), which is built on the following new techniques: (1) an ITL-based correlation (ITL-Correlation) is developed as a new similarity measure which can better exploit higher-order statistics of the data, and is robust against many different types of noise and outliers in a sparse representation framework; (2) a non-second order statistic measurement and minimization method is developed to improve the robustness of OMP by overcoming the limitation of Gaussianity inherent in a cost function based on second-order moments. The experimental results on both simulated and real-world data consistently demonstrate the superiority of the proposed OMP algorithm in data recovery, image reconstruction, and classification.

Zhou, L, Ying, S, Yu, N & Ying, M 2020, 'Strassen's theorem for quantum couplings', THEORETICAL COMPUTER SCIENCE, vol. 802, pp. 67-76.
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Zhou, L, Ying, S, Yu, N & Ying, M 2020, 'Strassen's theorem for quantum couplings.', Theor. Comput. Sci., vol. 802, pp. 67-76.
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© 2019 Elsevier B.V. Strassen's theorem for probabilistic couplings is a fundamental theorem in probability theory that can be used to bound the probability of an event in a distribution by the probability of an event in another distribution coupled with the first. It has been widely applied in computer science for analysis of random algorithms, machine learning and verification of security and privacy protocols. We extend the coupling techniques in probability theory to quantum systems. A quantum generalisation of the notion of lifting, a coupling under certain constraints, is introduced. Several interesting examples and basic properties of quantum couplings and liftings are presented. Finally, a quantum extension of Strassen's theorem is established.

Adak, C, Chaudhuri, BB, Lin, C-T & Blumenstein, M 1970, 'Why Not? Tell us the Reason for Writer Dissimilarity', 2020 International Joint Conference on Neural Networks (IJCNN), 2020 International Joint Conference on Neural Networks (IJCNN), IEEE, pp. 1-7.
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© 2020 IEEE. Writer verification has drawn significant attention over the past few decades due to its extensive applications in forensics and biometrics. In traditional writer verification, handwriting similarity/dissimilarity analysis is mostly performed by extracting two feature vectors from two respective handwritten samples, followed by comparing them in relation to their similarity. In the state-of-the-art writer verification approaches, a distance metric is usually employed in terms of the similarity between two handwritten samples. If the distance between two handwritten samples is greater than a given threshold, then the samples are assumed to be written by two different writers, otherwise, they are considered to be due to the same writer. In this paper, for the very first time, we propose a model that generates English sentences to explain reasons for writer dissimilarity/similarity. First, our proposed model obtains features from handwritten images by employing a convolutional neural network, verifies the writer using a Siamese architecture, and generates English words using a recurrent neural network. Finally, these two networks are merged using an affine transformation to produce an explanatory sentence in support of writer similarity/dissimilarity. We evaluated our model on a handwritten numeral database of 100 writers and obtained promising results.

Barthe, G, Hsu, J, Ying, M, Yu, N & Zhou, L 2020, 'Relational proofs for quantum programs', Proceedings of the ACM on Programming Languages, Association for Computing Machinery (ACM), pp. 1-29.
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Bei, X, Chen, S, Guan, J, Qiao, Y & Sun, X 1970, 'From independent sets and vertex colorings to isotropic spaces and isotropic decompositions: Another bridge between graphs and alternating matrix spaces', Leibniz International Proceedings in Informatics, LIPIcs.
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In the 1970’s, Lovász built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings (FCT 1979). A similar connection between bipartite graphs and matrix spaces plays a key role in the recent resolutions of the non-commutative rank problem (Garg-Gurvits-Oliveira-Wigderson, FOCS 2016; Ivanyos-Qiao-Subrahmanyam, ITCS 2017). In this paper, we lay the foundation for another bridge between graphs and alternating matrix spaces, in the context of independent sets and vertex colorings. The corresponding structures in alternating matrix spaces are isotropic spaces and isotropic decompositions, both useful structures in group theory and manifold theory. We first show that the maximum independent set problem and the vertex c-coloring problem reduce to the maximum isotropic space problem and the isotropic c-decomposition problem, respectively. Next, we show that several topics and results about independent sets and vertex colorings have natural correspondences for isotropic spaces and decompositions. These include algorithmic problems, such as the maximum independent set problem for bipartite graphs, and exact exponential-time algorithms for the chromatic number, as well as mathematical questions, such as the number of maximal independent sets, and the relation between the maximum degree and the chromatic number. These connections lead to new interactions between graph theory and algebra. Some results have concrete applications to group theory and manifold theory, and we initiate a variant of these structures in the context of quantum information theory. Finally, we propose several open questions for further exploration.

Brooksbank, PA, Li, Y, Qiao, Y & Wilson, JB 1970, 'Improved algorithms for alternating matrix space isometry: From theory to practice', Leibniz International Proceedings in Informatics, LIPIcs.
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Motivated by testing isomorphism of p-groups, we study the alternating matrix space isometry problem (AltMatSpIso), which asks to decide whether two m-dimensional subspaces of n × n alternating (skew-symmetric if the field is not of characteristic 2) matrices are the same up to a change of basis. Over a finite field Fp with some prime p 6= 2, solving AltMatSpIso in time pO(n+m) is equivalent to testing isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. The latter problem has long been considered a bottleneck case for the group isomorphism problem. Recently, Li and Qiao presented an average-case algorithm for AltMatSpIso in time pO(n) when n and m are linearly related (FOCS’17). In this paper, we present an average-case algorithm for AltMatSpIso in time pO(n+m). Besides removing the restriction on the relation between n and m, our algorithm is considerably simpler, and the average-case analysis is stronger. We then implement our algorithm, with suitable modifications, in Magma. Our experiments indicate that it improves significantly over default (brute-force) algorithms for this problem.

Chowdhury, PN, Shivakumara, P, Raghavendra, R, Pal, U, Lu, T & Blumenstein, M 1970, 'A New U-Net Based License Plate Enhancement Model in Night and Day Images', Pattern Recognition, ACPR, Springer International Publishing, Auckland, New Zealand, pp. 749-763.
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A new trend of smart city development opens up many challenges. One such issue is that automatic vehicle driving and detection for toll fee payment in night or limited light environments. This paper presents a new work for enhancing license plates captured in limited or low light conditions such that license plate detection methods can be expanded to detect images at night. Due to the popularity of Convolutional Neural Network (CNN) in solving complex issues, we explore U-Net-CNN for enhancing contrast of license plate pixels. Since the difference between pixels that represent license plates and pixels that represent background is too due to low light effect, the special property of U-Net that extracts context and symmetric of license plate pixels to separate them from background pixels irrespective of content. This process results in image enhancement. To validate the enhancement results, we use text detection methods and based on text detection results we validate the proposed system. Experimental results on our newly constructed dataset which includes images captured in night/low light/limited light conditions and the benchmark dataset, namely, UCSD, which includes very poor quality and high quality images captured in day, show that the proposed method outperforms the existing methods. In addition, the results on text detection by different methods show that the proposed enhancement is effective and robust for license plate detection.

Das, A, Suwanwiwat, H, Pal, U & Blumenstein, M 1970, 'ICFHR 2020 Competition on Short answer ASsessment and Thai student SIGnature and Name COMponents Recognition and Verification (SASIGCOM 2020)', 2020 17th International Conference on Frontiers in Handwriting Recognition (ICFHR), 2020 17th International Conference on Frontiers in Handwriting Recognition (ICFHR), IEEE, Dortmund, Germany, pp. 222-227.
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This paper describes the results of the competition on Short answer ASsessment and Thai student SIGnature and Name COMponents Recognition and Verification (SASIGCOM 2020) in conjunction with the 17th International Conference on Frontiers in Handwriting Recognition (ICFHR 2020). The competition was aimed to automate the evaluation process short answer-based examination and record the development and gain attention to such system. The proposed competition contains three elements which are short answer assessment (recognition and marking the answers to short-answer questions derived from examination papers), student name components (first and last names) and signature verification and recognition. Signatures and name components data were collected from 100 volunteers. For the Thai signature dataset, there are 30 genuine signatures, 12 skilled and 12 simple forgeries for each writer. With Thai name components dataset, there are 30 genuine and 12 skilfully forged name components for each writer. There are 104 exam papers in the short answer assessment dataset, 52 of which were written with cursive handwriting; the rest of 52 papers were written with printed handwriting. The exam papers contain ten questions, and the answers to the questions were designed to be a few words per question. Three teams from distinguished labs submitted their systems. For short answer assessment, word spotting task was also performed. This paper analysed the results produced by their algorithms using a performance measure and defines a way forward for this subject of research. Both the datasets, along with some of the accompanying ground truth/baseline mask will be made freely available for research purposes via the TC10/TC11.

Kundu, S, Shivakumara, P, Grouver, A, Pal, U, Lu, T & Blumenstein, M 1970, 'A New Forged Handwriting Detection Method Based on Fourier Spectral Density and Variation', Pattern Recognition, Asian Conference on Pattern Recognition, Springer International Publishing, Auckland, New Zealand, pp. 136-150.
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Use of handwriting words for person identification in contrast to biometric features is gaining importance in the field of forensic applications. As a result, forging handwriting is a part of crime applications and hence is challenging for the researchers. This paper presents a new work for detecting forged handwriting words because width and amplitude of spectral distributions have the ability to exhibit unique properties for forged handwriting words compared to blurred, noisy and normal handwriting words. The proposed method studies spectral density and variation of input handwriting images through clustering of high and low frequency coefficients. The extracted features, which are invariant to rotation and scaling, are passed to a neural network classifier for the classification for forged handwriting words from other types of handwriting words (like blurred, noisy and normal handwriting words). Experimental results on our own dataset, which consists of four handwriting word classes, and two benchmark datasets, namely, caption and scene text classification and forged IMEI number dataset, show that the proposed method outperforms the existing methods in terms of classification rate.

Mathieson, L & Moscato, P 1970, 'The Unexpected Virtue of Problem Reductions or How to Solve Problems Being Lazy but Wise', 2020 IEEE Symposium Series on Computational Intelligence (SSCI), 2020 IEEE Symposium Series on Computational Intelligence (SSCI), IEEE.
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Mittal, A, Shivakumara, P, Pal, U, Lu, T, Blumenstein, M & Lopresti, D 1970, 'A New Context-Based Method for Restoring Occluded Text in Natural Scene Images', Document Analysis Systems, International Workshop on Document Analysis Systems, Springer International Publishing, Wuhan, China, pp. 466-480.
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Text recognition from natural scene images is an active research area because of its important real world applications, including multimedia search and retrieval, and scene understanding through computer vision. It is often the case that portions of text in images are missed due to occlusion with objects in the background. Therefore, this paper presents a method for restoring occluded text to improve text recognition performance. The proposed method uses the GOOGLE Vision API for obtaining labels for input images. We propose to use PixelLink-E2E methods for detecting text and obtaining recognition results. Using these results, the proposed method generates candidate words based on distance measures employing lexicons created through natural scene text recognition. We extract the semantic similarity between labels and recognition results, which results in a Global Context Score (GCS). Next, we use the Natural Language Processing (NLP) system known as BERT for extracting semantics between candidate words, which results in a Local Context Score (LCS). Global and local context scores are then fused for estimating the ranking for each candidate word. The word that gets the highest ranking is taken as the correction for text which is occluded in the image. Experimental results on a dataset assembled from standard natural scene datasets and our resources show that our approach helps to improve the text recognition performance significantly.

Nalamati, M, Sharma, N, Saqib, M & Blumenstein, M 1970, 'Automated Monitoring in Maritime Video Surveillance System', 2020 35th International Conference on Image and Vision Computing New Zealand (IVCNZ), 2020 35th International Conference on Image and Vision Computing New Zealand (IVCNZ), IEEE, New Zealand, pp. 1-6.
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Maritime surveillance for intruders/illegal activities requires monitoring of a large area of the coastline. This task being manually exhaustive, would benefit immensely by application of object detection techniques to surveillance videos. However, object detection models trained on general objects datasets cannot be expected to give best performance for this scenario as marine vessels are only a small subset of these huge datasets and also do not classify the specific type of sea vehicle. Hence, their benchmarks are not appropriate for maritime surveillance. Some studies have been done with applications of Convolutional Neural Networks (CNN) for ship/boat detection on private and publicly available sea vessels datasets. This paper presents a summary of the benchmarks so far and presents our experiments of the latest object detection techniques for combined marine vessels dataset. A survey of the currently available datasets is also given. Results of our experiments in terms of mean Average Precision (mAP) and Frames Per Second (FPS) are presented.

Nandanwar, L, Shivakumara, P, Manna, S, Pal, U, Lu, T & Blumenstein, M 1970, 'A New DCT-FFT Fusion Based Method for Caption and Scene Text Classification in Action Video Images', Pattern Recognition and Artificial Intelligence, International Conference on Pattern Recognition and Artificial Intelligence, Springer International Publishing, Zhongshan, China, pp. 80-92.
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Achieving better recognition rate for text in video action images is challenging due to multi-type texts with unpredictable backgrounds. We propose a new method for the classification of captions (which is edited text) and scene texts (which is part of an image in video images of Yoga, Concert, Teleshopping, Craft, and Recipe classes). The proposed method introduces a new fusion criterion-based on DCT and Fourier coefficients to extract features that represent good clarity and visibility of captions to separate them from scene texts. The variances for coefficients of corresponding pixels of DCT and Fourier images are computed to derive the respective weights. The weights and coefficients are further used to generate a fused image. Furthermore, the proposed method estimates sparsity in Canny edge image of each fused image to derive rules for classifying caption and scene texts. Lastly, the proposed method is evaluated on images of five above-mentioned action image classes to validate the derived rules. Comparative studies with the state-of-the-art methods on the standard databases show that the proposed method outperforms the existing methods in terms of classification. The recognition experiments before and after classification show that the recognition performance rate improves significantly after classification.

Pelchen, T, Mathieson, L & Lister, R 1970, 'On the Evidence for a Learning Hierarchy in Data Structures Exams', Proceedings of the Twenty-Second Australasian Computing Education Conference, ACE'20: Twenty-Second Australasian Computing Education Conference, ACM, pp. 122-131.
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© 2020 Association for Computing Machinery. ACM ISBN 978-1-4503-7686-0/20/02...$15.00 Several previous research studies have found a relationship between the ability of novices to trace and explain code, and the ability to write code. Harrington and Cheng refer to that relationship as the Learning Hierarchy. However, almost all of those studies examined students at the end of their first semester of learning to program (i.e. CS1). This paper is only the third paper to describe a study of explain in plain English questions on students at the end of an introductory data structures course. The preceding two papers reached contradictory conclusions. Corney et al. presented results consistent with the Learning Hierarchy identified in the CS1 studies. However, Harrington and Cheng presented results for data structures students suggesting that the hierarchy reversed by the time students had progressed to the level of learning about data structures; that is, tracing and explaining were skills that followed writing. In our study of data structures students, we present results that are consistent with the Learning Hierarchy derived from the CS1 students. We believe that the reversal identified by Harrington and Cheng can occur, but only as a consequence of a mismatch in the relative difficulty of tracing, explaining and writing questions.

Ramakrishnan, RK, Ravichandran, AB, Talabattula, S, Vijayan, MK, Lund, AP & Rohde, PP 1970, 'Photonic Quantum Error Correction of Qudits Using W-state Encoding', 14th Pacific Rim Conference on Lasers and Electro-Optics (CLEO PR 2020), Conference on Lasers and Electro-Optics/Pacific Rim, Optica Publishing Group.
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In this paper, we present a passive linear optics error correction scheme for qudits using W-state encoding, based on post selection, which reduces the effects of dephasing noise in photonic quantum communication.

Roy, S, Shivakumara, P, Pal, U, Lu, T & Blumenstein, M 1970, 'New Moments Based Fuzzy Similarity Measure for Text Detection in Distorted Social Media Images', Pattern Recognition, Asian Conference on Pattern Recognition, Springer International Publishing, New Zealand, pp. 720-734.
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A trend towards capturing or filming images using cellphone and sharing images on social media is a part and parcel of day to day activities of humans. When an image is forwarded several times in social media it may be distorted a lot due to several different devices. This work deals with text detection from such distorted images. In this work, we consider images pass through three mobile devices on WhatsApp social media, which results in four images (including the original image) Unlike the existing methods that aim at developing new ways, we utilize the results detected by the existing ones to improve performances. The proposed method extracts Hu moments and fuzzy logic from detected texts of images. The similarity between text detection results given by three existing text detection methods is studied for determining the best pair of texts. The same similarity estimation is then used in a novel way to remove extra background or non-texts and restoring missing text information. Experimental results on own dataset and benchmark datasets of natural scene images, namely, MSRA-TD500, ICDAR2017-MLT, Total-Text, CTW1500 dataset and COCO datasets, show that the proposed method outperforms the existing methods.

Wakakuwa, E, Nakata, Y & Hsieh, M-H 1970, 'One-Shot Trade-Off Bounds for State Redistribution of Classical-Quantum Sources', 2020 IEEE International Symposium on Information Theory (ISIT), 2020 IEEE International Symposium on Information Theory (ISIT), IEEE.
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Apers, S & Lee, T 2020, 'Quantum complexity of minimum cut'.

Béjanin, JH, Earnest, CT, Sanders, YR & Mariantoni, M 2020, 'Resonant Coupling Parameter Estimation with Superconducting Qubits'.

Belovs, A & Lee, T 2020, 'The quantum query complexity of composition with a relation'.
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The negative weight adversary method, $\mathrm{ADV}^\pm(g)$, is known to characterize the bounded-error quantum query complexity of any Boolean function $g$, and also obeys a perfect composition theorem $\mathrm{ADV}^\pm(f \circ g^n) = \mathrm{ADV}^\pm(f) \mathrm{ADV}^\pm(g)$. Belovs gave a modified version of the negative weight adversary method, $\mathrm{ADV}_{rel}^\pm(f)$, that characterizes the bounded-error quantum query complexity of a relation $f \subseteq \{0,1\}^n \times [K]$, provided the relation is efficiently verifiable. A relation is efficiently verifiable if $\mathrm{ADV}^\pm(f_a) = o(\mathrm{ADV}_{rel}^\pm(f))$ for every $a \in [K]$, where $f_a$ is the Boolean function defined as $f_a(x) = 1$ if and only if $(x,a) \in f$. In this note we show a perfect composition theorem for the composition of a relation $f$ with a Boolean function $g$ \[ \mathrm{ADV}_{rel}^\pm(f \circ g^n) = \mathrm{ADV}_{rel}^\pm(f) \mathrm{ADV}^\pm(g) \enspace . \] For an efficiently verifiable relation $f$ this means $Q(f \circ g^n) = \Theta( \mathrm{ADV}_{rel}^\pm(f) \mathrm{ADV}^\pm(g) )$.

Du, Y, Hsieh, M-H, Liu, T, Tao, D & Liu, N 2020, 'Quantum noise protects quantum classifiers against adversaries', p. 023153.
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Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies. However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy. It is then natural to ask, can we harness the power of quantum noise that is beneficial to quantum computing? An important current direction for quantum computing is its application to machine learning, such as classification problems. One outstanding problem in machine learning for classification is its sensitivity to adversarial examples. These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers. They can also be considered as `worst-case' perturbations by unknown noise sources. We show that by taking advantage of depolarisation noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise. This robustness property is intimately connected with an important security concept called differential privacy which can be extended to quantum differential privacy. For the protection of quantum data, this is the first quantum protocol that can be used against the most general adversaries. Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of classification model are absent, thus also providing a potential quantum advantage for classical data that is independent of quantum speedups. This opens the opportunity to explore other ways in which quantum noise can be used in our favour, as well as identifying other ways quantum algorithms can be helpful that is independent of quantum speedups.

Du, Y, Huang, T, You, S, Hsieh, M-H & Tao, D 2020, 'Quantum circuit architecture search for variational quantum algorithms', npj Quantum Information, p. 62.
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Variational quantum algorithms (VQAs) are expected to be a path to quantum advantages on noisy intermediate-scale quantum devices. However, both empirical and theoretical results exhibit that the deployed ansatz heavily affects the performance of VQAs such that an ansatz with a larger number of quantum gates enables a stronger expressivity, while the accumulated noise may render a poor trainability. To maximally improve the robustness and trainability of VQAs, here we devise a resource and runtime efficient scheme termed quantum architecture search (QAS). In particular, given a learning task, QAS automatically seeks a near-optimal ansatz (i.e., circuit architecture) to balance benefits and side-effects brought by adding more noisy quantum gates to achieve a good performance. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. In the problems studied, numerical and experimental results show that QAS can not only alleviate the influence of quantum noise and barren plateaus, but also outperforms VQAs with pre-selected ansatze.

Fan, J, Li, J, Wang, J, Wei, Z & Hsieh, M-H 2020, 'Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances'.

Lee, T, Li, T, Santha, M & Zhang, S 2020, 'On the cut dimension of a graph'.

Lee, T, Santha, M & Zhang, S 2020, 'Quantum algorithms for graph problems with cut queries'.
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Let $G$ be an $n$-vertex graph with $m$ edges. When asked a subset $S$ of vertices, a cut query on $G$ returns the number of edges of $G$ that have exactly one endpoint in $S$. We show that there is a bounded-error quantum algorithm that determines all connected components of $G$ after making $O(\log(n)^6)$ many cut queries. In contrast, it follows from results in communication complexity that any randomized algorithm even just to decide whether the graph is connected or not must make at least $\Omega(n/\log(n))$ many cut queries. We further show that with $O(\log(n)^8)$ many cut queries a quantum algorithm can with high probability output a spanning forest for $G$. En route to proving these results, we design quantum algorithms for learning a graph using cut queries. We show that a quantum algorithm can learn a graph with maximum degree $d$ after $O(d \log(n)^2)$ many cut queries, and can learn a general graph with $O(\sqrt{m} \log(n)^{3/2})$ many cut queries. These two upper bounds are tight up to the poly-logarithmic factors, and compare to $\Omega(dn)$ and $\Omega(m/\log(n))$ lower bounds on the number of cut queries needed by a randomized algorithm for the same problems, respectively. The key ingredients in our results are the Bernstein-Vazirani algorithm, approximate counting with "OR queries", and learning sparse vectors from inner products as in compressed sensing.

Li, S, Zhou, X & Feng, Y 2020, 'Qubit Mapping Based on Subgraph Isomorphism and Filtered Depth-Limited Search'.

Sanders, YR, Berry, DW, Costa, PCS, Tessler, LW, Wiebe, N, Gidney, C, Neven, H & Babbush, R 2020, 'Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization'.

Zhang, W-W, Sanders, YR & Sanders, BC 2020, 'Channel Discord and Distortion'.