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Synthesizing efficient circuits for Hamiltonian simulation [article]

Priyanka Mukhopadhyay, Nathan Wiebe, Hong Tao Zhang
2022 arXiv   pre-print
We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to 4. The central idea behind our approach is to collect mutually commuting Hamiltonian terms into groups that satisfy one of several symmetries identified in this work which allow an inexpensive simulation of the entire group of terms. We further show that the
more » ... cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings. We further specifically discuss these optimizations for the case of fermionic dynamics and provide extensive numerical simulations for qDRIFT of our grouping strategy to 6 and 4-qubit Heisenberg models, LiH, H_2 and observe a factor of 1.8-3.2 reduction in the number of non-Clifford gates. This suggests Trotter-based simulation of chemistry in second quantization may be even more practical than previously believed.
arXiv:2209.03478v1 fatcat:lkkp3mzrtvh7hiw77uouf4kpzm

A survey of Hough Transform

Priyanka Mukhopadhyay, Bidyut B. Chaudhuri
2015 Pattern Recognition  
Mukhopadhyay, B.B.  ...  Mukhopadhyay, B.B.  ... 
doi:10.1016/j.patcog.2014.08.027 fatcat:oye56pu2mrastlppxds6cggvue

Error tracing in linear and concatenated quantum circuits [article]

Ritajit Majumdar, Saikat Basu, Priyanka Mukhopadhyay, Susmita Sur-Kolay
2016 arXiv   pre-print
Descriptions of quantum algorithms, communication etc. protocols assume the existence of closed quantum system. However, real life quantum systems are open and are highly sensitive to errors. Hence error correction is of utmost importance if quantum computation is to be carried out in reality. Ideally, an error correction block should be placed after every gate operation in a quantum circuit. This increases the overhead and reduced the speedup of the quantum circuit. Moreover, the error
more » ... on blocks themselves may induce errors as the gates used for error correction may be noisy. In this paper, we have proposed a procedure to trace error probability due to noisy gates and decoherence in quantum circuit and place an error correcting block only when the error probability exceeds a certain threshold. This procedure shows a drastic reduction in the required number of error correcting blocks. Furthermore, we have considered concatenated codes with tile structure layout lattice architecture[25][21],[24] and SWAP gate based qubit transport mechanism. Tracing errors in higher levels of concatenation shows that, in most cases, after 1 or 2 levels of concatenation, the number of QECC blocks required become static. However, since the gate count increases with increasing concatenation, the percentage saving in gate count is considerably high.
arXiv:1612.08044v1 fatcat:xozgyhmlwjdwznn735xit4hzem

Possibilities of Combinatorial Therapy: Insulin Dysregulation and the Growth Hormone Perspective on Neurodegeneration [chapter]

Priyanka Sengupta, Debashis Mukhopadhyay
2021 Tyrosine [Working Title]  
Author details Priyanka Sengupta and Debashis Mukhopadhyay* Biophysics and Structural Genomics Division, Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India *Address all correspondence  ... 
doi:10.5772/intechopen.97002 fatcat:wlmjempi4jaupbski7pngc6x2q

Biophysical Studies on Protein Aggregation and Amyloid Fibril Formation

Mily Bhattacharya, Neha Jain, Priyanka Dogra, Soumyadyuti Samai, Smita Patil, Samrat Mukhopadhyay
2012 Biophysical Journal  
2247-Pos Board B17 Biophysical Studies on Protein Aggregation and Amyloid Fibril Formation Mily Bhattacharya, Neha Jain, Priyanka Dogra, Soumyadyuti Samai, Smita Patil, Samrat Mukhopadhyay.  ...  Mukhopadhyay. ''Chain collapse of an amyloidogenic intrinsically disordered protein'', Biophys. J. 2011 (In press).  ... 
doi:10.1016/j.bpj.2011.11.2425 fatcat:4b6ot2kfirbevefkexh2zmrnw4

T-count and T-depth of any multi-qubit unitary [article]

Vlad Gheorghiu, Michele Mosca, Priyanka Mukhopadhyay
2022 arXiv   pre-print
While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum error-correcting codes the cost of implementing the non-Clifford gate is the highest among all the gates in a universal fault-tolerant gate set. In this paper we design provable algorithm to determine T-count of any n-qubit (n≥ 1) unitary W of size 2^n× 2^n, over the Clifford+T gate set. The space and time complexity of our
more » ... algorithm are poly(2^n) and poly((2^n)^m_ϵ) respectively. m_ϵ (ϵ-T-count) is the T-count of an exactly implementable unitary U i.e. 𝒯(U), such that d(U,W)≤ϵ and 𝒯(U)≤𝒯(U') where U' is any exactly implementable unitary with d(U',W)≤ϵ. d(.,.) is the global phase invariant distance. Our algorithm can also be used to determine T-depth of any multi-qubit unitary and the asymptotic complexity has similar dependence on n and ϵ-T-depth. This is the first algorithm that gives T-count or T-depth of any multi-qubit (n≥ 1) unitary (considering any distance). For small enough ϵ, we can synthesize the T-count and T-depth-optimal circuits. Our results can be used to determine optimal count (or depth) of non-Clifford gates required to implement any multi-qubit unitary with a universal gate set consisting of Clifford and non-Clifford gates like Clifford+CS, Clifford+V, etc. To the best of our knowledge, there were no resource-optimal synthesis algorithm for arbitrary multi-qubit unitaries in any universal gate set.
arXiv:2110.10292v2 fatcat:lyrdimljbrgibenclpnrk6npsu

Adaptive estimation of quantum observables [article]

Ariel Shlosberg, Andrew J. Jena, Priyanka Mukhopadhyay, Jan F. Haase, Felix Leditzky, Luca Dellantonio
2022 arXiv   pre-print
The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive sampling. Here, we introduce a measurement scheme that adaptively modifies the estimator based on previously obtained data. Our algorithm, which we call AEQuO, continuously monitors both the estimated average and the associated error of the considered observable,
more » ... d determines the next measurement step based on this information. We allow both for overlap and non-bitwise commutation relations in the subsets of Pauli operators that are simultaneously probed, thereby maximizing the amount of gathered information. AEQuO comes in two variants: a greedy bucket-filling algorithm with good performance for small problem instances, and a machine learning-based algorithm with more favorable scaling for larger instances. The measurement configuration determined by these subroutines is further post-processed in order to lower the error on the estimator. We test our protocol on chemistry Hamiltonians, for which AEQuO provides error estimates that improve on all state-of-the-art methods based on various grouping techniques or randomized measurements, thus greatly lowering the toll of measurements in current and future quantum applications
arXiv:2110.15339v3 fatcat:ddq3pddl7ncl3e7hviee5tzeru

A Composition Theorem for Randomized Query Complexity [article]

Anurag Anshu, Dmitry Gavinsky, Rahul Jain, Srijita Kundu, Troy Lee, Priyanka Mukhopadhyay, Miklos Santha, Swagato Sanyal
2017 arXiv   pre-print
Let the randomized query complexity of a relation for error probability ϵ be denoted by R_ϵ(·). We prove that for any relation f ⊆{0,1}^n ×R and Boolean function g:{0,1}^m →{0,1}, R_1/3(f∘ g^n) = Ω(R_4/9(f)· R_1/2-1/n^4(g)), where f ∘ g^n is the relation obtained by composing f and g. We also show that R_1/3(f ∘(g^⊕_O( n))^n)=Ω( n · R_4/9(f) · R_1/3(g)), where g^⊕_O( n) is the function obtained by composing the xor function on O( n) bits and g^t.
arXiv:1706.00335v2 fatcat:cfbagbg7ubgghejsptma4ytaeq

Femtosecond Hydration Map of Intrinsically Disordered α -Synuclein

Shruti Arya, Avinash K. Singh, Karishma Bhasne, Priyanka Dogra, Anindya Datta, Payel Das, Samrat Mukhopadhyay
2018 Biophysical Journal  
ACKNOWLEDGMENTS We thank Anita Chacko for initially helping with setting up the simulation systems and the members of the Mukhopadhyay laboratory and Dr.  ... 
doi:10.1016/j.bpj.2018.04.028 pmid:29874605 pmcid:PMC6129475 fatcat:g4cqvnjejzhp3osqkbxjfztytm

A Dynamic Web Page Prediction Model Based on Access Patterns to Offer Better User Latency [article]

Debajyoti Mukhopadhyay, Priyanka Mishra, Dwaipayan Saha, Young-Chon Kim
2011 arXiv   pre-print
The growth of the World Wide Web has emphasized the need for improvement in user latency. One of the techniques that are used for improving user latency is Caching and another is Web Prefetching. Approaches that bank solely on caching offer limited performance improvement because it is difficult for caching to handle the large number of increasingly diverse files. Studies have been conducted on prefetching models based on decision trees, Markov chains, and path analysis. However, the increased
more » ... ses of dynamic pages, frequent changes in site structure and user access patterns have limited the efficacy of these static techniques. In this paper, we have proposed a methodology to cluster related pages into different categories based on the access patterns. Additionally we use page ranking to build up our prediction model at the initial stages when users haven't already started sending requests. This way we have tried to overcome the problems of maintaining huge databases which is needed in case of log based techniques.
arXiv:1102.0684v1 fatcat:ym27kuuxlveshiyn2zujched4m

Sensitivity to Polymyxin B in El TorVibrio choleraeO1 Strain, Kolkata, India

Prosenjit Samanta, Priyanka Ghosh, Goutam Chowdhury, Thandavarayan Ramamurthy, Asish K. Mukhopadhyay
2015 Emerging Infectious Diseases  
doi:10.3201/eid2111.150762 pmid:26488385 pmcid:PMC4622255 fatcat:app3xxeacrdsroyir33ompxola

Liquid-Liquid Phase Separation is Driven by Large-Scale Conformational Unwinding and Fluctuations of Intrinsically Disordered Protein Molecules [article]

Anupa Majumdar, Priyanka Dogra, Shiny Maity, Samrat Mukhopadhyay
2019 bioRxiv   pre-print
Liquid-liquid phase separation occurs via a multitude of transient, non-covalent, intermolecular interactions resulting in phase transition of intrinsically disordered proteins/regions (IDPs/IDRs) and other biopolymers into mesoscopic, dynamic, non-stoichiometric, supramolecular condensates. IDPs resemble associative polymers possessing stereospecific "stickers" and flexible "spacers" that govern the transient chain-chain interactions and fluidity in phase-separated liquid droplets. However,
more » ... fundamental molecular origin of phase separation remains elusive. Here we present a unique case to demonstrate that unusual conformational expansion events coupled with solvation and fluctuations drive phase separation of tau, an IDP associated with Alzheimer's disease. Using intramolecular excimer emission as a powerful proximity readout, we show the unraveling of polypeptide chains within the protein-rich interior environment that can promote critical interchain contacts. Using highly-sensitive picosecond time-resolved fluorescence depolarization measurements, we directly capture rapid large-amplitude torsional fluctuations in the extended chains that can control the relay of making-and-breaking of noncovalent intermolecular contacts maintaining the internal fluidity. Our observations, together with the existing polymer theories, suggest that such an orchestra of concerted molecular shapeshifting events involving chain expansion, solvation, and fluctuations can provide additional favorable free energies to overcome the entropy of mixing term during phase separation. The interplay of these key molecular parameters can also be of prime importance in modulating the mesoscale material property of liquid-like condensates and their maturation of into pathological gel-like and solid-like aggregates.
doi:10.1101/621714 fatcat:bpw6sjapf5bw5ezej5hrxmqm7i

Faster Provable Sieving Algorithms for the Shortest Vector Problem and the Closest Vector Problem on Lattices in ℓp Norm

Priyanka Mukhopadhyay
2021 Algorithms  
Aggarwal and Mukhopadhyay [49] gave an algorithm for SVP and approximate CVP in the ∞ norm using a linear sieving technique that significantly improves the overall running time.  ... 
doi:10.3390/a14120362 fatcat:2brqjjy76jabjkg4th4rfsebse

Nanoscale Assembly of Proteins into Amyloid Oligomers, Pores and Fibrils

Mily Bhattacharya, Neha Jain, Priyanka Dogra, Vijit Dalal, Dominic Narang, Pushpender K. Sharma, Soumyadyuti Samai, Samrat Mukhopadhyay
2014 Biophysical Journal  
Sharma, Soumyadyuti Samai, Samrat Mukhopadhyay. Indian Institute of Science Education and Research (IISER), Mohali, Mohali, India.  ...  both in the cytosolic space and inside the neuritic processes. 3460-Pos 3461-Pos Board B189 Nanoscale Assembly of Proteins into Amyloid Oligomers, Pores and Fibrils Mily Bhattacharya, Neha Jain, Priyanka  ... 
doi:10.1016/j.bpj.2013.11.3781 fatcat:lcp6kggijfcsxpteh7fijilmbu

Liquid-Liquid Phase Separation of Tau: From Molecular Biophysics to Physiology and Disease

Sandeep K Rai, Adriana Savastano, Priyanka Singh, Samrat Mukhopadhyay, Markus Zweckstetter
2021 Protein Science  
Biomolecular condensation via liquid-liquid phase separation (LLPS) of intrinsically disordered proteins/regions (IDPs/IDRs), with and without nucleic acids, has drawn widespread interest due to the rapidly unfolding role of phase-separated condensates in a diverse range of cellular functions and human diseases. Biomolecular condensates form via transient and multivalent intermolecular forces that sequester proteins and nucleic acids into liquid-like membrane-less compartments. However,
more » ... phase transitions into gel-like or solid-like aggregates might play an important role in neurodegenerative and other diseases. Tau, a microtubule-associated neuronal IDP, is involved in microtubule stabilization, regulates axonal outgrowth and transport in neurons. A growing body of evidence indicates that tau can accomplish some of its cellular activities via LLPS. However, liquid-to-solid transition resulting in the abnormal aggregation of tau is associated with neurodegenerative diseases. The physical chemistry of tau is crucial for governing its propensity for biomolecular condensation which is governed by various intermolecular and intramolecular interactions leading to simple one-component and complex multi-component condensates. In this review, we aim at capturing the current scientific state in unveiling the intriguing molecular mechanism of phase separation of tau. We particularly focus on the amalgamation of existing and emerging biophysical tools that offer unique spatiotemporal resolutions on a wide range of length- and time-scales. We also discuss the link between quantitative biophysical measurements and novel biological insights into biomolecular condensation of tau. We believe that this account will provide a broad and multidisciplinary view of phase separation of tau and its association with physiology and disease. This article is protected by copyright. All rights reserved.
doi:10.1002/pro.4093 pmid:33930220 pmcid:PMC8197432 fatcat:tq3rygjzdba6rksmvyqozspona
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