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We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the context of quantum computing, it corresponds to the least possible amount of data to define and describe a quantum circuit or quantum computer program. Our Kolmogorov complexity of unitary transformation is built upon Kolmogorov "qubit complexity" of Berthiaume, W. Van Dam and S. Laplante via mapping from unitary transformations to unnormalized density operators, which are subsequently "purified" into unnormalized vectors in Hilbert space. We discuss the optimality of our notion of Kolmogorov complexity in a broad sense. [ABSTRACT FROM AUTHOR]

Quantum computers promise exponential speed ups over classical computers for various tasks. This emerging technology is expected to have its first huge impact in High Performance Computing (HPC), as it can solve problems beyond the reach of HPC. To that end, HPC will require quantum accelerators, which will enable applications to run on both classical and quantum devices, via hybrid quantum-classical nodes. Hybrid quantum-HPC applications should be scalable, executable on Quantum Error Corrected (QEC) devices, and could use quantum-classical primitives. However, the lack of scalability, poor performances, and inability to insert classical schemes within quantum applications has prevented current quantum frameworks from being adopted by the HPC community. This paper specifies the requirements of a hybrid quantum-classical framework compatible with HPC environments, and introduces a novel hardware-agnostic framework called Q-Pragma. This framework extends the classical programming language C++ heavily used in HPC via the addition of pragma directives to manage quantum computations. [ABSTRACT FROM AUTHOR]

Despite the great promises and potential of quantum computing, the full range of possibilities and practical applications is not yet clear. In this contribution, we highlight the potential for quantum theories and computation to reignite the art and science of expert systems and knowledge engineering. With their grounding in uncertainty and unpredictability, quantum concepts are able to expand theoretical and practical boundaries of research and exploration. We demonstrate the advantages of using quantum logic and computation when applying expert knowledge such as the ability to ask imprecise (inherently probabalistic) queries and do so efficiently through large and complicated computational spaces by leveraging quantum concepts such as superposition, entanglement, parallelism, and interference to sustain and manipulate networks of quantum qubits. This, we argue, can provide non-insignificant computational speedups and enable more complex data representations and analysis. We then point the keen reader towards three practical applications and provide some evidence for their quantum advantages – Scientific Discovery, Creativity and Breakthrough Thinking, Complex Systems, and Future of Sports – that we regard as largely unexplored in popular accounts of quantum theory; as such, we suggest these are low hanging fruit for the more-immediately feasible applications of quantum technologies. [ABSTRACT FROM AUTHOR]

Clustering algorithms are used to classify the unlabeled data into a number of categories with polynomial time complexity. Quantum clustering algorithms are developed to improve the performance and to achieve higher gain. In this work, we implement the quantum k-means clustering algorithm on field-programmable gate array (FPGA) by exploiting the implicit parallelism of the FPGA technology to achieve high speed among the software-implemented recent proposals. To do that, we establish a new method to measure the inner product between two qubits which is based on the correlation between the Euclidean distance and the inner product. We also optimize the quantum gates in terms of speed and removing the discretization error. Experimental results show a reduction in the running time by 500× as compared to the classical k-means algorithm for the A1 standard dataset. [ABSTRACT FROM AUTHOR]

Anomalous behavior identification is the process of detecting behavior that differs from its normal. These incidents will vary from violence to war, road crashes to kidnapping, and so on in a surveillance model. Video anomaly detection from video surveillance is a difficult research activity due to the frequency of anomalous cases. Since certain devices need manual evaluation for the detection of violent or criminal situations at the same time video monitoring of security cameras is also a challenging task and is unreliable. When the data or model dimension is sufficiently large, convolutional neural networks have the limitation of learning inefficiently. Quantum Convolutional Neural Network (QCNN) is the name given to a technology that combines CNN and quantum computing. Quantum computation and CNN are combined to create a more efficient and outperforming solution for solving complicated machine-learning problems. To analyze the anomalies in a sequence of video frames, two models are proposed in this research. In this research 07 layers of Javeria deep convolutional neural network (DCNN) are proposed on the selected hyperparameters named J. DCNN which is also different from the existing models to analyze the abnormal behavior in a video segment. Furthermore, for a comprehensive analysis of the abnormal video frames a model is proposed which is the combination of Javeria quantum and convolutional neural networks (J. QCNN). In this model 04-qubit quantum neural network is used with five layers and an optimal loss rate named J. QCNN. The proposed J. QCNN model is different from the existing deep learning architectures. The proposed models are trained from the scratch for the detection of anomalous from top challenging publicly available video surveillance datasets such as UNI-Crime and UCF Crime. The proposed J. QCNN model classifies the number of violent robberies such as armed thefts containing handguns or knives, and robberies displaying varying levels of viciousness with 0.99 accuracy while J. DCNN model gives 0.97 accuracy. The obtained results are superior in comparison with recent existing cutting-edge published work for real-time anomaly detection in video CCTV. • Quantum computation and CNN are combined to solve complicated machine-learning problems. • To analyze the anomalies in a sequence of video frames, two models are proposed. • Seven layers of deep convolutional neural network (DCNN) is proposed. • Four-qubit quantum neural network is used with five layers and an optimal loss rate is proposed. • The two proopsed mopdels prvide 0.99 and 0.97 accuracy. [ABSTRACT FROM AUTHOR]

The power of quantum computing may allow for solving the problems which are not practically feasible on classical computers and suggest a considerable speed up to the best known classical approaches. In this paper, we present the contemporary quantum behaved approach which is based on Schrödinger equation and Monte Carlo method. The three basic steps of proposed technique are also mathematically modeled and discussed for effective movement of particles. The performance of the proposed approach is tested for solving the dynamic nonlinear problem. Experimental results reveal the supremacy of proposed approach for solving the nonlinear problem as compared to other approaches. [ABSTRACT FROM AUTHOR]

The Winter Colloquium on the Physics of Quantum Electronics (PQE) has been a seminal force in quantum optics and related areas since 1971. It is rather mind-boggling to recognize how the concepts presented at these conferences have transformed scientific understanding and human society. In January 2017, the participants of PQE were asked to consider the equally important prospects for the future, and to formulate a set of questions representing some of the greatest aspirations in this broad field. The result is this multi-authored paper, in which many of the world’s leading experts address the following fundamental questions: (1) What is the future of gravitational wave astronomy? (2) Are there new quantum phases of matter away from equilibrium that can be found and exploited - such as the time crystal? (3) Quantum theory in uncharted territory: What can we learn? (4) What are the ultimate limits for laser photon energies? (5) What are the ultimate limits to temporal, spatial and optical resolution? (6) What novel roles will atoms play in technology? (7) What applications lie ahead for nitrogen-vacancy centres in diamond? (8) What is the future of quantum coherence, squeezing and entanglement for enhanced super-resolution and sensing? (9) How can we solve (some of) humanity’s biggest problems through new quantum technologies? (10) What new understanding of materials and biological molecules will result from their dynamical characterization with free-electron lasers? (11) What new technologies and fundamental discoveries might quantum optics achieve by the end of this century? (12) What novel topological structures can be created and employed in quantum optics? [ABSTRACT FROM AUTHOR]

By combining the advantages of quantum computing and soft computing, the paper shows that rough sets can be used with quantum logic for classification and recognition systems. We suggest the new definition of rough set theory as quantum logic theory. Rough approximations are essential elements in rough set theory, the quantum rough set model for set-valued data directly construct set approximation based on a kind of quantum similarity relation which is presented here. Theoretical analyses demonstrate that the new model for quantum rough sets has new type of decision rule with less redundancy which can be used to give accurate classification using principles of quantum superposition and non-linear quantum relations. To our knowledge, this is the first attempt aiming to define rough sets in representation of a quantum rather than logic or sets. The experiments on data-sets have demonstrated that the proposed model is more accuracy than the traditional rough sets in terms of finding optimal classifications. [ABSTRACT FROM PUBLISHER]

Reversible logic is getting more and more attention in quantum computing, optical computing, nanotechnology and low-power complementary metal oxide semiconductor designs since reversible circuits do not loose information during computation and have only small energy dissipation. In this paper, a novel carry-selected reversible adder is proposed primarily optimised for low latency. A 4-bit reversible full adder with two kinds of outputs, minimum delay and optimal quantum cost is presented as the building block for-bit reversible adder. Three new reversible gates NPG (new Peres gate), TEPG (triple extension of Peres gate) and RMUX21 (reversible 2-to-1 multiplexer) are proposed and utilised to design efficient adder units. The secondary carry propagation chain is carefully designed to reduce the time consumption. The novelty of the proposed design is the consideration of low latency. The comparative study shows that the proposed adder achieves the improvement from 61.46% to 95.29% in delay over the existing designs. [ABSTRACT FROM PUBLISHER]

We obtain a general connection between a large quantum advantage in communication complexity and Bell nonlocality. We show that given any protocol offering a sufficiently large quantum advantage in communication complexity, there exists a way of obtaining measurement statistics that violate some Bell inequality. Our main tool is port-based teleportation. If the gap between quantum and classical communication complexity can grow arbitrarily large, the ratio of the quantum value to the classical value of the Bell quantity becomes unbounded with the increase in the number of inputs and outputs. [ABSTRACT FROM AUTHOR]

Recently quantum computation and cryptography principles are exploited in the design of security systems for wireless sensor networks (WSNs), which are consequently named as quantum WSN. Quantum cryptography is presumably secure against any eavesdropper and thus labeled as providing unconditional security. This paper tries to analyze the aspect of the applicative use of quantum principles in WSN. The outcome of the analysis elaborates a summary about the inadequacy of applicative use of quantum cryptography in WSN and presents an overview of all possible applicative challenges and problems while designing quantum-based security systems for WSN. Since WSNs are highly complex frameworks, with many restrictions and constraints, every security system has to be fully compatible and worthwhile. The aim of the paper was to contribute a verdict about this topic, backed up by equitable facts. [ABSTRACT FROM AUTHOR]

Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations. [ABSTRACT FROM AUTHOR]

We introduce a new variant of quantum multiprover interactive proofs (QMIP) where the provers and the verifier are quantum. The verifier can exchange quantum messages with the provers. The provers cannot communicate quantumly between themselves and do not share entanglement, but are unlimited in the classical communication between them, even after receiving messages from the verifier. We show that any language in nondeterministic exponential time (NEXP) can be recognized in this model efficiently, with just two provers and two rounds of communication, and with a constant completeness/soundness gap. This is in contrast to the result of [R. Jain et al., Comm. ACM, 53 (2010), pp. 102-109], which shows that QIP = PSPACE, or equivalently that the set of languages that can be recognized by a quantum verifier communicating with a single quantum prover is equal to PSPACE. To analyze the cheating power of the provers, we give them more power and allow them to perform any separable operation. We then show a unique two-phase protocol in which the provers first commit to a superposition of correct answers to all possible questions, and then in the second phase the verifier opens up the committed answer and checks for correctness and consistency. [ABSTRACT FROM AUTHOR]

We propose a new scheme to implement gate operations in a one dimensional linear nearest neighbor array, by using dynamic learning algorithm. This is accomplished by training quantum system using a back propagation technique, to find the system parameters that implement gate operations directly. The key feature of our scheme is that, we can reduce the computational overhead of a quantum circuit by finding the parameters to implement the desired gate operation directly, without decomposing them into a sequence of elementary gate operations. We show how the training algorithm can be used as a tool for finding the parameters for implementing controlled-NOT (CNOT) and Toffoli gates between next-to-nearest neighbor qubits in an Ising-coupled linear nearest neighbor system. We then show how the scheme can be used to find parameters for realizing swap gates first, between two adjacent qubits and then, between two next-to-nearest-neighbor qubits, in each case without decomposing it into 3 CNOT gates. Finally, we show how the scheme can be extended to systems with non-diagonal interactions. To demonstrate, we train a quantum system with Heisenberg interactions to find the parameters to realize a swap operation. [ABSTRACT FROM AUTHOR]

• Systematic quantum circuit design to represent a generic discrete Bayesian network. • Controlled rotation gates are used to represent conditional probability tables. • Ancilla qubits are used to represent higher-order controlled rotation gates. • Illustration using three Bayesian networks from financial industry. Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become computationally expensive in large-scale systems. While demonstrations of true quantum supremacy remain rare, quantum computing applications managing to exploit the advantages of amplitude amplification have shown significant computational benefits when compared against their classical counterparts. We develop a systematic method for designing a quantum circuit to represent a generic discrete Bayesian network with nodes that may have two or more states, where nodes with more than two states are mapped to multiple qubits. The marginal probabilities associated with root nodes (nodes without any parent nodes) are represented using rotation gates, and the conditional probability tables associated with non-root nodes are represented using controlled rotation gates. The controlled rotation gates with more than one control qubit are represented using ancilla qubits. The proposed approach is demonstrated for three examples: a 4-node oil company stock prediction, a 10-node network for liquidity risk assessment, and a 9-node naive Bayes classifier for bankruptcy prediction. The circuits were designed and simulated using Qiskit, a quantum computing platform that enables simulations and also has the capability to run on real quantum hardware. The results were validated against those obtained from classical Bayesian network implementations. [ABSTRACT FROM AUTHOR]

• Quantum computing is today more mature and many of their application are today real. • Classical information systems will not be throw away in a short-term period. • Reengineering of classical-quantum system is needed to preserve business knowledge. • Quantum knowledge can be represented with extensions of KDM and UML. • KDM and UML makes reengineering systematic and technologically-agnostic. Quantum Computing is becoming an increasingly mature area, with a simultaneous escalation of investment in many sectors. Quantum technology will revolutionize all the engineering fields. For example, companies will need to add quantum computing progressively to some or all of their daily operations. It is clear that all existing classical information systems cannot be done away with. Rather than that occurring, it is expected that some quantum algorithms will be added, so that they can work alongside classical information systems. There has been no systematic solution offered to deal with this challenge so far. This research proposes a software modernization approach (model-driven reengineering) designed to restructure classical systems to work in conjunction with quantum systems, thereby providing target environments that combine both of these computational paradigms. The approach proposed is systematic, and based on existing software engineering standards like the Knowledge Discovery Metamodel and the Unified Modelling Language. It could therefore be applied in industry in a way that complies with the existing software evolution processes. The independence of this proposal with respect to quantum programming environments is also guaranteed, making its application feasible in the changing environment in today's quantum industry. The main implication of this approach is technical, but also economic, since it enables the reuse of the knowledge embedded in legacy systems, while at the same time the new quantum-based projects are speeded up. [ABSTRACT FROM AUTHOR]