arXiv subjects

Subhamoy Maitra

Publications and source records attributed to Subhamoy Maitra.

27 records · Page 2Linked to original sources

arXiv2020

Classical-Quantum Separations in Certain Classes of Boolean Functions-- Analysis using the Parity Decision Trees

In this paper we study the separation between the deterministic (classical) query complexity ($D$) and the exact quantum query complexity ($Q_E$) of several Boolean function classes using the parity decision tree method. We first define the Query Friendly (QF) functions on $n$ variables as the ones with minimum deterministic query complexity $(D(f))$. We observe that for each $n$, there exists a non-separable class of QF functions such that $D(f)=Q_E(f)$. Further, we show that for some values of $n$, all the QF functions are non-separable. Then we present QF functions for certain other values of $n$ where separation can be demonstrated, in particular, $Q_E(f)=D(f)-1$. In a related effort, we also study the Maiorana McFarland (M-M) type Bent functions. We show that while for any M-M Bent function $f$ on $n$ variables $D(f) = n$, separation can be achieved as $\frac{n}{2} \leq Q_E(f) \leq \lceil \frac{3n}{4} \rceil$. Our results highlight how different classes of Boolean functions can be analyzed for classical-quantum separation exploiting the parity decision tree method.

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arXiv2020

On Actual Preparation of Dicke State on a Quantum Computer

The exact number of CNOT and single qubit gates needed to implement a Quantum Algorithm in a given architecture is one of the central problems of Quantum Computation. In this work we study the importance of concise realizations of Partially defined Unitary Transformations for better circuit construction using the case study of Dicke State Preparation. The Dicke States $(\left|D^n_k \right>)$ are an important class of entangled states with uses in many branches of Quantum Information. In this regard we provide the most efficient Deterministic Dicke State Preparation Circuit in terms of CNOT and single qubit gate counts in comparison to existing literature. We further observe that our improvements also reduce architectural constraints of the circuits. We implement the circuit for preparing $\left| D^4_2 \right>$ on the "ibmqx2" machine of the IBM QX service and observe that the error induced due to noise in the system is lesser in comparison to the existing circuit descriptions. We conclude by describing the CNOT map of the generic $\left| D^n_k \right>$ preparation circuit and analyze different ways of distributing the CNOT gates in the circuit and its affect on the induced error.

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arXiv2019

Efficient Quantum Algorithms related to Autocorrelation Spectrum

In this paper, we propose efficient probabilistic algorithms for several problems regarding the autocorrelation spectrum. First, we present a quantum algorithm that samples from the Walsh spectrum of any derivative of $f()$. Informally, the autocorrelation coefficient of a Boolean function $f()$ at some point $a$ measures the average correlation among the values $f(x)$ and $f(x \oplus a)$. The derivative of a Boolean function is an extension of autocorrelation to correlation among multiple values of $f()$. The Walsh spectrum is well-studied primarily due to its connection to the quantum circuit for the Deutsch-Jozsa problem. We extend the idea to "Higher-order Deutsch-Jozsa" quantum algorithm to obtain points corresponding to large absolute values in the Walsh spectrum of a certain derivative of $f()$. Further, we design an algorithm to sample the input points according to squares of the autocorrelation coefficients. Finally we provide a different set of algorithms for estimating the square of a particular coefficient or cumulative sum of their squares.

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arXiv2015

Diagnosis of single faults in quantum circuits

Detecting and isolating faults is crucial for synthesis of quantum circuits. Under the single fault assumption that is now routinely accepted in circuit fault analysis, we show that the behaviour of faulty quantum circuits can be fully characterized by the single faulty gate and the corresponding fault model. This allows us to efficiently determine test input states as well as measurement strategy that can be used to detect every single-gate fault using very few test cases and with minimal probability of error; in fact we demonstrate that most commonly used quantum gates can be isolated without any error under the single missing gate fault (SMGF) model. We crucially exploit the quantum nature of circuits to show vast improvement upon the existing works of automatic test pattern generation (ATPG) for quantum circuits.

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arXiv2013

Improved quantum test for linearity of a Boolean function

Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $ε$-far from having that property. The efficiency of the algorithm is judged by the number of calls to the oracle so that one can decide, with high probability, between these two alternatives. The best known quantum algorithm for testing whether a function is linear or $ε$-far $(0 < ε< \frac{1}{2})$ from linear functions requires $O(ε^{-\frac{2}{3}})$ many calls [Hillery and Andersson, Physical Review A 84, 062329 (2011)]. We show that this can be improved to $O(ε^{-\frac{1}{2}})$ by using the Deutsch-Jozsa and the Grover Algorithms.

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arXiv2013

Efficient quantum algorithm to construct arbitrary Dicke states

In this paper, we study efficient algorithms towards the construction of any arbitrary Dicke state. Our contribution is to use proper symmetric Boolean functions that involve manipulations with Krawtchouk polynomials. Deutsch-Jozsa algorithm, Grover algorithm and the parity measurement technique are stitched together to devise the complete algorithm. Further, motivated by the work of Childs et al (2002), we explore how one can plug the biased Hadamard transformation in our strategy. Our work compares fairly with the results of Childs et al (2002).

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arXiv2012

An Attack on Privacy Preserving Data Aggregation Protocol for Wireless Sensor Networks

In-network data aggregation in Wireless Sensor Networks (WSNs) provides efficient bandwidth utilization and energy-efficient computing.Supporting efficient in-network data aggregation while preserving the privacy of the data of individual sensor nodes has emerged as an important requirement in numerous WSN applications. For privacy-preserving data aggregation in WSNs, He et al. (INFOCOM 2007) have proposed a Cluster-based Private Data Aggregation (CPDA) that uses a clustering protocol and a well-known key distribution scheme for computing an additive aggregation function in a privacy-preserving manner. In spite of the wide popularity of CPDA, it has been observed that the protocol is not secure and it is also possible to enhance its efficiency. In this paper, we first identify a security vulnerability in the existing CPDA scheme, wherein we show how a malicious participant node can launch an attack on the privacy protocol so as to get access to the private data of its neighboring sensor nodes. Next it is shown how the existing CPDA scheme can be made more efficient by suitable modification of the protocol. Further, suitable modifications in the existing protocol have been proposed so as to plug the vulnerability of the protocol.

cs.CR↗

arXiv2005

Quantum algorithm to distinguish Boolean functions of different weights

We exploit Grover operator of database search algorithm for weight decision algorithm. In this research, weight decision problem is to find an exact weight w from given two weights as w1 and w2 where w1+w2=1 and 0 2. Hence the quantum algorithm achieves at least quadratic speedup.

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arXiv2004

Deutsch-Jozsa Algorithm Revisited in the Domain of Cryptographically Significant Boolean Functions

Boolean functions are important building blocks in cryptography for their wide application in both stream and block cipher systems. For cryptanalysis of such systems one tries to find out linear functions that are correlated to the Boolean functions used in the crypto system. Let $f$ be an $n$-variable Boolean function and its Walsh spectra is denoted by $W_f(ω)$ at the point $ω\in \{0, 1\}^n$. The Boolean function is available in the form of an oracle. We like to find an $ω$ such that $W_f(ω) \neq 0$ as this will provide one of the linear functions which are correlated to $f$. We show that the quantum algorithm proposed by Deutsch and Jozsa (1992) solves the above mentioned problem in constant time. However, the best known classical algorithm to solve this problem requires exponential time in $n$. We also analyse certain classes of cryptographically significant Boolean functions and highlight how the basic Deutsch-Jozsa algorithm performs on them.

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