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Quantum error correcting code for ternary logic

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arXiv 2018年

作者： Majumdar, Ritajit Basu, Saikat Ghosh, Shibashis Sur-Kolay, Susmita Advanced Computing & Microelectronics Unit Indian Statistical Institute India A. K. Choudhury School of Information Technology University of Calcutta India

Ternary quantum systems are being studied because these provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2 × 2)-dimensional as well as (3 × 3)-dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2 × 2)-dimensional as well as (3 × 3)-dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a new type of error called quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization. Copyright © 2018, The Authors. All rights reserved.

关键词： Errors

Dilution with digital microfluidic biochips: How unbalanced splits corrupt target-concentration

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arXiv 2019年

作者： Poddar, Sudip Wille, Robert Rahaman, Hafizur Bhattacharya, Bhargab B. Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata700108 India Department of Computer Science & Engineering Indian Institute of Technology Kharagpur721 302 India Indian Statistical Institute Kolkata700108 India School of VLSI Technology Indian Institute of Engineering Science and Technology Shibpur711103 India Institute for Integrated Circuits Johannes Kepler University Linz Austria

Sample preparation is an indispensable component of almost all biochemical protocols, and it involves, among others, making dilutions and mixtures of fluids in certain ratios. Recent microfluidic technologies offer suitable platforms for automating dilutions on-chip, and typically on a digital microfluidic biochip (DMFB), a sequence of (1: 1) mix-split operations is performed on fluid droplets to achieve the target concentration factor (CF) of a sample. An (1: 1) mixing model ideally comprises mixing of two unit-volume droplets followed by a (balanced) splitting into two unit-volume daughter-droplets. However, a major source of error in fluidic operations is due to unbalanced splitting, where two unequal-volume droplets are produced following a split. Such volumetric split-errors occurring in different mix-split steps of the reaction path often cause a significant drift in the target-CF of the sample, the precision of which cannot be compromised in life-critical assays. In order to circumvent this problem, several error-recovery or error-tolerant techniques have been proposed recently for DMFBs. Unfortunately, the impact of such fluidic errors on a target-CF and the dynamics of their behavior have not yet been rigorously analyzed. In this work, we investigate the effect of multiple volumetric split-errors on various target-CFs during sample preparation. We also perform a detailed analysis of the worst-case scenario, i.e., the condition when the error in a target-CF is maximized. This analysis may lead to the development of new techniques for error-tolerant sample preparation with DMFBs without using any sensing operation. Copyright © 2019, The Authors. All rights reserved.

关键词： Digital microfluidics

Load Balanced Coverage with Graded Node Deployment in Wireless Sensor Networks

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Load Balanced Coverage with Graded Node Deployment in Wirele...

作者： Chatterjee, Punyasha Ghosh, Sasthi C. Das, Nabanita School of Mobile Computing and Communication Jadavpur University Kolkata West Bengal700032 India Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata West Bengal700108 India

In this paper, to gather streams of data in static wireless sensor networks, a novel graded node deployment strategy is proposed that generates minimum traffic, just sufficient for coverage. Based on this node distribution, a distributed, nearly load-balanced data gathering algorithm is developed to deliver packets to the sink node via minimum-hop paths that also in turn helps to limit the network traffic. An average case probabilistic analysis is done based on perfect matching of random bipartite graphs to establish a theoretical lower bound on the number of nodes to be deployed. Analysis and simulation studies show that the proposed model results huge enhancement in network lifetime that significantly overrides the cost due to over deployment. Hence, this technique offers an excellent cost-effective and energy-efficient solution for node deployment and routing in large wireless sensor networks to operate with prolonged lifetime. © 2015 IEEE.

关键词： Cost effectiveness

Quantum error correction for non-maximally entangled states

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arXiv 2017年

作者： Majumdar, Ritajit Sur-Kolay, Susmita Advanced Computing and Microelectronics Unit Indian Statistical Institute India

Quantum states have high affinity for errors and hence error correction is of utmost importance to realise a quantum computer. Laflamme showed that 5 qubits are necessary to correct a single error on a qubit. In a Pauli error model, four different types of errors can occur on a qubit. Maximally entangled states are orthogonal to each other and hence can be uniquely distinguished by a measurement in the Bell basis. Thus a measurement in Bell basis and a unitary transformation is sufficient to correct error in Bell states. However, such a measurement is not possible for non-maximally entangled states. In this work we show that the 16 possible errors for a non-maximally entangled two qubit system map to only 8 distinct error states. Hence, it is possible to correct the error without perfect knowledge of the type of error. Furthermore, we show that the possible errors can be grouped in such a way that all 4 errors can occur on one qubit, whereas only bit flip error can occur on the second qubit. As a consequence, instead of 10, only 8 qubits are sufficient to correct a single error. We propose an 8-qubit error correcting code to correct a single error in a non-maximally entangled state. We further argue that for an n-qubit non-maximally entangled state of the form a |0)0n+ ß |1)0n, it is always possible to correct a single error with fewer than 5n qubits, in fact only 3n + 2 qubits suffice. Copyright © 2017, The Authors. All rights reserved.

关键词： Quantum entanglement

Demand-driven single- and multitarget mixture preparation using digital microfluidic biochips

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Demand-driven single- and multitarget mixture preparation us...

作者： Shalu Kumar, Srijan Singla, Ananya Roy, Sudip Chakrabarty, Krishnendu Chakrabarti, Partha P. Bhattacharya, Bhargab B. CoDA Laboratory Department of Computer Science and Engineering Indian Institute of Technology Roorkee Roorkee247667 India Department of Computer Science Stanford University StanfordCA94305 United States Department of Electrical and Computer Engineering Duke University Durham27708 United States Department of Computer Science and Engineering Indian Institute of Technology Kharagpur Kharagpur721302 India Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata Kolkata700108 India

Recent studies in algorithmic microfluidics have led to the development of several techniques for automated solution preparation using droplet-based digital microfluidic (DMF) biochips. A major challenge in this direction is to produce a mixture of several reactants with a desired ratio while optimizing reactant cost and preparation time. The sequence of mix-split operations that are to be performed on the droplets is usually represented as a mixing tree (or graph). In this article, we present an efficient mixing algorithm, namely, Mixing Tree with Common Subtrees (MTCS), for preparing single-target mixtures. MTCS attempts to best utilize intermediate droplets, which were otherwise wasted, and uses morphing based on permutation of leaf nodes to further reduce the graph size. The technique can be generalized to produce multitarget ratios, and we present another algorithm, namely, Multiple Target Ratios (MTR). Additionally, in order to enhance the output load, we also propose an algorithm for droplet streaming called Multitarget Multidemand (MTMD). Simulation results on a large set of target ratios show that MTCS can reduce the mean values of the total number of mix-split steps (Tms) and waste droplets (W) by 16% and 29% over Min-Mix (Thies et al. 2008) and by 22% and 34% over RMA (Roy et al. 2015), respectively. Experimental results also suggest that MTR can reduce the average values of Tms andW by 23% and 44% over the repeated version of Min-Mix, by 30% and 49% over the repeated version of RMA, and by 9% and 22% over the repeated-version of MTCS, respectively. It is observed that MTMD can reduce the mean values ofTms andW by 64% and 85%, respectively, over MTR. Thus, the proposed multitarget techniques MTR and MTMD provide efficient solutions to multidemand, multitarget mixture preparation on a DMF platform. © 2018 ACM.

关键词： Digital microfluidics

A predictive handoff mechanism for 5G ultra dense networks

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A predictive handoff mechanism for 5G ultra dense networks

IEEE International Symposium on Network computing and Applications

作者： Shankar K. Ghosh Sasthi C. Ghosh Advanced Computing & Microelectronics Unit Indian Statistical Institute Kolkata India

The fifth generation (5G) ultra dense network (UDN) is envisioned as a very dense deployment of low power base stations where heterogeneous radio access technologies are used to satisfy the data rate demand of users employing both licensed and unlicensed spectrum. In UDN scenario, conditions of the channels operating in licensed band may exhibit intermittent characteristics due to the varying level of interference received from large number of nearby access networks. On the other hand, channel conditions in unlicensed band may fluctuate drastically due to the interference caused by the co-existence of long term evolution (LTE-U) and wireless local area network (WLAN) in unlicensed band. The traditional handover mechanisms rely on the instantaneous assessments of link qualities such as RSS and SINR. The target network selected based on such instantaneous values may not be the appropriate one when the actual handover is executed. In this work, we have proposed a predictive handover mechanism which can estimate achievable throughput values from different candidate access networks after handoff execution. Simulation results confirm that our proposed predictive handover mechanism significantly outperforms an existing reference base station efficiency based approach.

关键词： Interference Handover Wireless LAN Throughput Long Term Evolution Logic gates

Mutual visibility by robots with persistent memory

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arXiv 2017年

作者： Bhagat, Subhash Mukhopadhyaya, Krishnendu Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata India

This paper addresses the mutual visibility problem for a set of semi-synchronous, opaque robots occupying distinct positions in the Euclidean plane. Since robots are opaque, if three robots lie on a line, the middle robot obstructs the visions of the two other robots. The mutual visibility problem asks the robots to coordinate their movements to form a configuration, within finite time and without collision, in which no three robots are collinear. Robots are endowed with a constant bits of persistent memory. In this work, we consider the FSTATE computational model in which the persistent memory is used by the robots only to remember their previous internal states. Except from this persistent memory, robots are oblivious i.e., they do not carry forward any other information from their previous computational cycles. The paper presents a distributed algorithm to solve the mutual visibility problem for a set of semi-synchronous robots using only 1 bit of persistent memory. The proposed algorithm does not impose any other restriction on the capability of the robots and guarantees collision-free movements for the robots. Copyright © 2017, The Authors. All rights reserved.

关键词： Visibility

A distributed algorithm for D2D communication in 5G using stochastic model

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A distributed algorithm for D2D communication in 5G using st...

IEEE International Symposium on Network computing and Applications

作者： Durgesh Singh Sasthi C. Ghosh Advanced Computing & Microelectronics Unit Indian Statistical Institute Kolkata India

Device to device (D2D) communication in 5G is on the spurge to compensate for the exponential increase in mobile users and their data requirements. In D2D communication, proximity users can communicate and control the links among themselves without the need of base station. This brings a real challenge to model the network to incorporate uncertainty which arises due to the mobility of users. We have developed a stochastic integer programming (SIP) based model to optimize the average network delay while keeping the packet loss below a threshold. This SIP model involves a probabilistic constraint which deals with conditional probability of link breakage in the next time instance given it was active at current time instance. By exploiting the SIP model, we have developed a greedy metric termed as connectivity factor (CF) which captures the nodes' mobility and hence takes care of link reliability which in turn controls packet loss and delay per hop. Based on CF we give a pure distributed greedy algorithm for forwarding the packets to an appropriate next hop node. Advantage of our algorithm to find an appropriate next hop node is that it requires only to compute the expectation and variance of path loss, which in turn can be computed from the distributions of mobility related parameters. Here we have used random walk mobility model for simplicity, but it can be extended to other mobility model with known relevant distributions. Through simulation we have shown that our proposed algorithm gives a significant improvement in packet loss due to mobility of nodes over the traditional received signal strength (RSS) based approach and an existing contention based forwarding (CBF) approach.

关键词： Packet loss Device-to-device communication Delays Mobile nodes

Micro-Bump Assignment for Efficient Routing on Re-Distribution Layer (RDL) in 3D-ICs 14

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Micro-Bump Assignment for Efficient Routing on Re-Distributi...

14th IEEE India Council International Conference, INDICON 2017

作者： Banerjee, Sabyasachee Majumder, Subhashis Basu, Saikat Bhattacharya, Bhargab B. Department of Computer Science and Engineering Heritage Institute of Technology Kolkata West Bengal700107 India Advanced Computing and Microelectronics Unit Nanotechnology Research Triangle Indian Statistical Institute Kolkata West Bengal700108 India

ISBN: (纸本)9781538643181

RDL (Re-Distribution Layers) routing from the IO pads to micro-bumps plays an important role for transmitting signal between two adjacent layers in 3D IC. The quality of RDL-routing strongly depends on the positions of micro-bumps between two adjacent dies. Initially, I/O pads are assigned to micro-bumps and then single-layer routing is performed over the two RDLs that are adjacent to two respective layers. We propose an improved method for RDL-routing in 3D IC. Experimental results show that 100% routability can be achieved with reduced wire-length for all five test-cases that we have studied. © 2017 IEEE.

关键词： Timing circuits