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FragQC: An Efficient Quantum Error Reduction Technique using Quantum Circuit Fragmentation

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arXiv 2023年

作者： Basu, Saikat Das, Arnav Saha, Amit Chakrabarti, Amlan Sur-Kolay, Susmita A.K.Choudhury School of Information Technology U. of Calcutta Kolkata India LTIMindtree Ltd. Kolkata India Dept. of Computer Science St. Xavier's University Kolkata India Pune India Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata India

Quantum computers must meet extremely stringent qualitative and quantitative requirements on their qubits in order to solve real-life problems. Quantum circuit fragmentation techniques divide a large quantum circuit into a number of sub-circuits that can be executed on the smaller noisy quantum hardware available. However, the process of quantum circuit fragmentation involves finding an ideal cut that has exponential time complexity, and also classical post-processing required to reconstruct the output. In this paper, we represent a quantum circuit using a weighted graph and propose a novel classical graph partitioning algorithm for selecting an efficient fragmentation that reduces the entanglement between the sub-circuits along with balancing the estimated error in each sub-circuit. We also demonstrate a comparative study over different classical and quantum approaches of graph partitioning for finding such a cut. We present FragQC, a software tool that cuts a quantum circuit into sub-circuits when its error probability exceeds a certain threshold. With this proposed approach, we achieve an increase of fidelity by 14.83% compared to direct execution without cutting the circuit, and 8.45% over the state-of-the-art ILP-based method, for the benchmark circuits. © 2023, CC BY.

关键词： Genetic algorithms

Special Session: Quantum Error Correction in Near Term Systems

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Special Session: Quantum Error Correction in Near Term Syste...

IEEE International Conference on Computer Design: VLSI in Computers and Processors, (ICCD)

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

ISBN: (数字)9781728197104

ISBN: (纸本)9781728197111

Large-scale quantum computers mandate error correction and fault tolerance. Due to constraints on the number of qubits, fault tolerance is difficult to achieve in near-term quantum systems. Therefore, error correction should require minimal resources. Gates in the near-term devices are also noisy. Quantum error correction code blocks built with these noisy gates can inject further error in the circuit. The goals for error correction in near-term systems are as follows: (i) using a small number of qubits for encoding, and (ii) keeping cost of circuits for encoding and decoding low. In this paper, we propose two techniques to achieve these mutually orthogonal goals. For a binary quantum system we propose an error estimation method that can aid in reducing the number of error correcting blocks via sparse scheduling. For ternary quantum systems, we propose an approximate code that can correct errors with high probability while significantly reducing the circuit cost. These techniques are expected to be helpful for error mitigation in near-term systems in the absence of fault tolerance.

关键词： Fault tolerance Fault tolerant systems Qubit Logic gates Error correction Error correction codes Noise measurement

Exploiting degeneracy to construct good ternary quantum error correcting code

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arXiv 2020年

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

Quantum error-correcting code for higher dimensional systems can, in general, be directly constructed from the codes for qubit systems. What remains unknown is whether there exist efficient code design techniques for higher dimensional systems. In this paper, we propose a 7-qutrit error-correcting code for the ternary quantum system and show that this design formulation has no equivalence in qubit systems. This code is optimum in the number of qutrits required to correct a single error while maintaining the CSS structure. This degenerate CSS code can (i) correct up to seven simultaneous phase errors and a single bit error, (ii) correct two simultaneous bit errors on pre-defined pairs of qutrits on eighteen out of twenty-one possible pairs, and (iii) in terms of the cost of implementation, the depth of the circuit of this code is only two more than that of the ternary Steane code. Our proposed code shows that it is possible to design better codes explicitly for ternary quantum systems instead of simply carrying over codes from binary quantum systems. Copyright © 2020, The Authors. All rights reserved.

关键词： Quantum optics

Approximate Ternary Quantum Error Correcting Code with Low Circuit Cost

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Approximate Ternary Quantum Error Correcting Code with Low C...

International Symposium on Multiple-Valued Logic

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

ISBN: (数字)9781728154060

ISBN: (纸本)9781728154077

Quantum error correcting code (QECC) with encoding and decoding circuits having low gate count, is an important criterion for realizing quantum computing systems. CSS QECCs are known to have simple circuits. Shaw et al. showed that it is not possible to have a 6-qubit CSS type QECC without sharing entanglement between the encoder and the decoder. In this paper, we propose a 6-qutrit approximate QECC (AQECC) of CSS structure which can simultaneously correct phase errors in upto six qutrits, and one bit error in only four of the six qutrits, without sharing prior entanglement. Our AQECC corrects a single error with probability 0.75 for symmetric error model, and probability 0.9988 for asymmetric error model. It also maintains CSS structure without sharing prior entanglement. Furthermore, the quantum cost of a circuit for this AQECC is 55.72% less than that for the 9-qutrit exact QECC. Overall, low qutrit count, low cost circuit realization with low depth and the ability to correct multiple phase errors make our proposed AQECC a suitable candidate for real life quantum channels.

关键词： Cascading style sheets Qubit Encoding Quantum computing Error correction codes Logic gates Error correction

Voting in Watts-Strogatz Small-World Network

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Voting in Watts-Strogatz Small-World Network

International Conference on Frontiers in computing and Systems, COMSYS 2020

作者： Ray, Soujanya Chatterjee, Kingshuk Majumdar, Ritaji Ganguly, Debayan Department of Computer Science and Engineering Netaji Subhash Engineering College Kolkata India Department of Computer Science Government College of Engineering and Ceramic Technology Kolkata India Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata India Department of Computer Science Government College of Engineering and Leather Technology Kolkata India

ISBN: (纸本)9789811578335

Social network science and social interaction science is an interesting and steadily growing field of research in current time. Social network influences the lives of millions, and therefore the propagation of influence in such a network deserves study. In this paper, we have studied voting in a Watts-Strogatz small-world network for two parties. In our model, each node has an initial bias towards one of the parties (or can be neutral) and are influenced by their neighbours to vote for a particular party. We show via simulation that (i) for linear of logarithmic voting function, the small-scale variation is minimum, but the majority of the nodes tend to align towards one of the parties in the long term, (ii) for periodic voting function, the small-scale variations are sharp and oscillating, but in the long term the number of voters in each party roughly remains the same, (iii) the degree of the graph does not seem to have a strong influence on the result, and (iv) networks with higher small-world probability tend to resist the alignment of voters towards a particular party for a longer time as compared to networks with lower small-world probability. This majority voting model seems to efficiently capture the potential behaviour of voters on small-world network over a campaigning period. © 2021, Springer Nature Singapore Pte Ltd.

关键词： Small-world networks

Multihop D2D Communication to Minimize and Balance SAR in 5G

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Multihop D2D Communication to Minimize and Balance SAR in 5G

International Communication Systems and Networks and Workshops, COMSNETS

作者： Avirup Das Nabanita Das Advanced Computing & Microelectronics Unit Indian Statistical Institute Kolkata India

ISBN: (数字)9781728131870

ISBN: (纸本)9781728131887

To cope with the exponential growth in wireless traffic to be induced by the advancement of 5G and IoT technologies, higher frequency bands will be in use to achieve high performance. But this will enhance the associated electromagnetic field (EMF) around us and may have harmful effects on all living creatures and the environment, unless necesSARy precautionary measures are followed to limit it. In this paper, we propose an elegant method of band selection with appropriate data rate for multi-hop packet routing, to minimize and also to balance the transmission power and hence the associated EMF effect on us in terms of the Specific Absorption Rate (SAR). Theoretical analysis has been presented for linear networks that results an upper bound on the number of hops permitted for a given spectrum band. Simulation results on random networks show that the proposed technique achieves a 30 - 70% improvement in terms of SAR, compared to the conventional direct communication via base station.

关键词： Routing Wireless communication Spread spectrum communication Receivers Transmitters 5G mobile communication Base stations

A Framework for Automated Correctness Checking of Biochemical Protocol Realizations on Digital Microfluidic Biochips

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arXiv 2022年

作者： Bhattacharjee, Sukanta Banerjee, Ansuman Chakrabarty, Krishnendu Bhattacharya, Bhargab B. Department of Computer Science and Engineering Indian Institute of Technology Assam Guwahati781039 India Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata700108 India Department of Electrical and Computer Engineering Duke University United States Department of Computer Science and Engineering National Institute of Technology Rourkela Odisha769008 India

Recent advances in digital microfluidic (DMF) technologies offer a promising platform for a wide variety of biochemical applications, such as DNA analysis, automated drug discovery, and toxicity monitoring. For on-chip implementation of complex bioassays, automated synthesis tools have been developed to meet the design challenges. Currently, the synthesis tools pass through a number of complex design steps to realize a given biochemical protocol on a target DMF architecture. Thus, design errors can arise during the synthesis steps. Before deploying a DMF biochip on a safety critical system, it is necessary to ensure that the desired biochemical protocol has been correctly implemented, i.e., the synthesized output (actuation sequences for the biochip) is free from any design or realization errors. We propose a symbolic constraint-based analysis framework for checking the correctness of a synthesized biochemical protocol with respect to the original design specification. The verification scheme based on this framework can detect several post-synthesis fluidic violations and realization errors in 2D-array based or pin-constrained biochips as well as in cyberphysical systems. It further generates diagnostic feedback for error localization. We present experimental results on the polymerase chain reaction (PCR) and in-vitro multiplexed bioassays to demonstrate the proposed verification approach. © 2022, CC BY.

关键词： Polymerase chain reaction

Gathering over Meeting Nodes in Infinite Grid

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arXiv 2021年

作者： Bhagat, Subhash Chakraborty, Abhinav Das, Bibhuti Mukhopadhyaya, Krishnendu Département d’Informatique Université du Québec en Outaouais Canada Advanced Computing and Microelectronics Unit Indian Statistical Institute Kolkata India

The gathering over meeting nodes problem asks the robots to gather at one of the predefined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid, which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived. Copyright © 2021, The Authors. All rights reserved.

关键词： Robots

Comment on "Quantum key agreement protocol"

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arXiv 2020年

作者： Das, Nayana Majumdar, Ritajit Applied Statistics Unit Indian Statistical Institute India Advanced Computing & Microelectronics Unit Indian Statistical Institute India

The first two party Quantum Key Agreement (QKA) protocol, based on quantum teleportation, was proposed by Zhou et al. (Electronics Letters 40.18 (2004): 1149-1150). In this protocol, to obtain the key bit string, one of the parties use a device to obtain inner product of two quantum states, one being unknown, and the other one performs Bell measurement. However, in this article, we show that it is not possible to obtain a device that would output the inner product of two qubits even when only one of the qubit is unknown. This is so because existence of such device would imply perfectly distinguishing among four different states in a two-dimensional vector space. This is not permissible in quantum mechanics. Furthermore, we argue that existence of such a device would also imply violation of the "No Signalling Theorem" as well. Finally, we also comment that this protocol is not a valid key agreement protocol at all. Copyright © 2020, The Authors. All rights reserved.

关键词： Vector spaces