Can biological quantum networks solve NP-hard problems?

There is a widespread view that the human brain is so complex that it cannot be efficiently simulated by universal Turing machines. During the last decades the question has therefore been raised whether we need to consider quantum effects to explain the imagined cognitive power of a conscious mind. This paper presents a personal view of several fields of philosophy and computational neurobiology in an attempt to suggest a realistic picture of how the brain might work as a basis for perception, consciousness and cognition. The purpose is to be able to identify and evaluate instances where quantum effects might play a significant role in cognitive processes. Not surprisingly, the conclusion is that quantum-enhanced cognition and intelligence are very unlikely to be found in biological brains. Quantum effects may certainly influence the functionality of various components and signalling pathways at the molecular level in the brain network, like ion ports, synapses, sensors, and enzymes. This might evidently influence the functionality of some nodes and perhaps even the overall intelligence of the brain network, but hardly give it any dramatically enhanced functionality. So, the conclusion is that biological quantum networks can only approximately solve small instances of NP-hard problems. On the other hand, artificial intelligence and machine learning implemented in complex dynamical systems based on genuine quantum networks can certainly be expected to show enhanced performance and quantum advantage compared with classical networks. Nevertheless, even quantum networks can only be expected to efficiently solve NP-hard problems approximately. In the end it is a question of precision - Nature is approximate.Comment: 38 page

Distributing the Kalman Filter for Large-Scale Systems

This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional, where $n_l\ll n$) sub-systems that are obtained after spatially decomposing the large-scale system. The resulting sub-systems overlap, which along with an assimilation procedure on the local Kalman filters, preserve an $L$th order Gauss-Markovian structure of the centralized error processes. The information loss due to the $L$th order Gauss-Markovian approximation is controllable as it can be characterized by a divergence that decreases as $L\uparrow$. The order of the approximation, $L$, leads to a lower bound on the dimension of the sub-systems, hence, providing a criterion for sub-system selection. The assimilation procedure is carried out on the local error covariances with a distributed iterate collapse inversion (DICI) algorithm that we introduce. The DICI algorithm computes the (approximated) centralized Riccati and Lyapunov equations iteratively with only local communication and low-order computation. We fuse the observations that are common among the local Kalman filters using bipartite fusion graphs and consensus averaging algorithms. The proposed algorithm achieves full distribution of the Kalman filter that is coherent with the centralized Kalman filter with an $L$th order Gaussian-Markovian structure on the centralized error processes. Nowhere storage, communication, or computation of $n-$dimensional vectors and matrices is needed; only $n_l \ll n$ dimensional vectors and matrices are communicated or used in the computation at the sensors

Quantum Sampling Problems, BosonSampling and Quantum Supremacy

There is a large body of evidence for the potential of greater computational power using information carriers that are quantum mechanical over those governed by the laws of classical mechanics. But the question of the exact nature of the power contributed by quantum mechanics remains only partially answered. Furthermore, there exists doubt over the practicality of achieving a large enough quantum computation that definitively demonstrates quantum supremacy. Recently the study of computational problems that produce samples from probability distributions has added to both our understanding of the power of quantum algorithms and lowered the requirements for demonstration of fast quantum algorithms. The proposed quantum sampling problems do not require a quantum computer capable of universal operations and also permit physically realistic errors in their operation. This is an encouraging step towards an experimental demonstration of quantum algorithmic supremacy. In this paper, we will review sampling problems and the arguments that have been used to deduce when sampling problems are hard for classical computers to simulate. Two classes of quantum sampling problems that demonstrate the supremacy of quantum algorithms are BosonSampling and IQP Sampling. We will present the details of these classes and recent experimental progress towards demonstrating quantum supremacy in BosonSampling.Comment: Survey paper first submitted for publication in October 2016. 10 pages, 4 figures, 1 tabl

Toward bio-inspired information processing with networks of nano-scale switching elements

Unconventional computing explores multi-scale platforms connecting molecular-scale devices into networks for the development of scalable neuromorphic architectures, often based on new materials and components with new functionalities. We review some work investigating the functionalities of locally connected networks of different types of switching elements as computational substrates. In particular, we discuss reservoir computing with networks of nonlinear nanoscale components. In usual neuromorphic paradigms, the network synaptic weights are adjusted as a result of a training/learning process. In reservoir computing, the non-linear network acts as a dynamical system mixing and spreading the input signals over a large state space, and only a readout layer is trained. We illustrate the most important concepts with a few examples, featuring memristor networks with time-dependent and history dependent resistances

Design Automation and Design Space Exploration for Quantum Computers

A major hurdle to the deployment of quantum linear systems algorithms and recent quantum simulation algorithms lies in the difficulty to find inexpensive reversible circuits for arithmetic using existing hand coded methods. Motivated by recent advances in reversible logic synthesis, we synthesize arithmetic circuits using classical design automation flows and tools. The combination of classical and reversible logic synthesis enables the automatic design of large components in reversible logic starting from well-known hardware description languages such as Verilog. As a prototype example for our approach we automatically generate high quality networks for the reciprocal $1/x$, which is necessary for quantum linear systems algorithms.Comment: 6 pages, 1 figure, in 2017 Design, Automation & Test in Europe Conference & Exhibition, DATE 2017, Lausanne, Switzerland, March 27-31, 201

Impact Assessment of Hypothesized Cyberattacks on Interconnected Bulk Power Systems

The first-ever Ukraine cyberattack on power grid has proven its devastation by hacking into their critical cyber assets. With administrative privileges accessing substation networks/local control centers, one intelligent way of coordinated cyberattacks is to execute a series of disruptive switching executions on multiple substations using compromised supervisory control and data acquisition (SCADA) systems. These actions can cause significant impacts to an interconnected power grid. Unlike the previous power blackouts, such high-impact initiating events can aggravate operating conditions, initiating instability that may lead to system-wide cascading failure. A systemic evaluation of "nightmare" scenarios is highly desirable for asset owners to manage and prioritize the maintenance and investment in protecting their cyberinfrastructure. This survey paper is a conceptual expansion of real-time monitoring, anomaly detection, impact analyses, and mitigation (RAIM) framework that emphasizes on the resulting impacts, both on steady-state and dynamic aspects of power system stability. Hypothetically, we associate the combinatorial analyses of steady state on substations/components outages and dynamics of the sequential switching orders as part of the permutation. The expanded framework includes (1) critical/noncritical combination verification, (2) cascade confirmation, and (3) combination re-evaluation. This paper ends with a discussion of the open issues for metrics and future design pertaining the impact quantification of cyber-related contingencies