arXiv subjects

Debajyoti Bera

Publications and source records attributed to Debajyoti Bera.

26 records · Page 2Linked to original sources

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.

quant-ph↗

arXiv2019

Error reduction of quantum algorithms

We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of multiple independent executions of an algorithm. Denoting by $ρ$ an upper bound of this probability (wlog., assume $ρ\le \frac{1}{2}$), classical techniques require $O(\fracρ{[(1-ρ) - ρ]^2})$ executions to reduce the error to a negligible constant. We investigated when and how quantum algorithmic techniques like amplitude amplification and estimation may reduce the number of executions. On one hand, the former idea does not directly benefit algorithms that can err on both yes and no answers and the number of executions in the latter approach is $O(\frac{1}{(1-ρ) - ρ})$. We propose a novel approach named as {\em Amplitude Separation} that combines both these approaches and achieves $O(\frac{1}{\sqrt{1-ρ} - \sqrtρ})$ executions that betters existing approaches when the errors are high. In the Multiple-Weight Decision Problem, the input is an $n$-bit Boolean function $f()$ given as a black-box and the objective is to determine the number of $x$ for which $f(x)=1$, denoted as $wt(f)$, given some possible values $\{w_1, \ldots, w_k\}$ for $wt(f)$. When our technique is applied to this problem, we obtain the correct answer, maybe with a negligible error, using $O(\log_2 k \sqrt{2^n})$ calls to $f()$ that shows a quadratic speedup over classical approaches and currently known quantum algorithms.

cs.CC↗

arXiv2017

STREAK: An Efficient Engine for Processing Top-k SPARQL Queries with Spatial Filters

The importance of geo-spatial data in critical applications such as emergency response, transportation, agriculture etc., has prompted the adoption of recent GeoSPARQL standard in many RDF processing engines. In addition to large repositories of geo-spatial data -- e.g., LinkedGeoData, OpenStreetMap, etc. -- spatial data is also routinely found in automatically constructed knowledgebases such as Yago and WikiData. While there have been research efforts for efficient processing of spatial data in RDF/SPARQL, very little effort has gone into building end-to-end systems that can holistically handle complex SPARQL queries along with spatial filters. In this paper, we present Streak, a RDF data management system that is designed to support a wide-range of queries with spatial filters including complex joins, top-k, higher-order relationships over spatially enriched databases. Streak introduces various novel features such as a careful identifier encoding strategy for spatial and non-spatial entities, the use of a semantics-aware Quad-tree index that allows for early-termination and a clever use of adaptive query processing with zero plan-switch cost. We show that Streak can scale to some of the largest publicly available semantic data resources such as Yago3 and LinkedGeoData which contain spatial entities and quantifiable predicates useful for result ranking. For experimental evaluations, we focus on top-k distance join queries and demonstrate that Streak outperforms popular spatial join algorithms as well as state of the art end-to-end systems like Virtuoso and PostgreSQL.

cs.DB↗

arXiv2016

Two-sided Quantum Amplitude Amplification and Exact-Error Algorithms

Amplitude amplification is a central tool used in Grover's quantum search algorithm and has been used in various forms in numerous quantum algorithms since then. It has been shown to completely eliminate one-sided error of quantum search algorithms where input is accessed in the form of black-box queries. We generalize amplitude amplification for two-sided error quantum algorithm for decision problems in the familiar form where input is accessed in the form of initial states of quantum circuits and where arbitrary projective measurements may be used to ascertain success or failure. This generalization allows us to derive interesting applications of amplitude amplification for distinguishing between two given distributions based on their samples, detection of faults in quantum circuits and eliminating error of one and two-sided quantum algorithms with exact errors.

cs.CC↗

arXiv2016

Frequent-Itemset Mining using Locality-Sensitive Hashing

The Apriori algorithm is a classical algorithm for the frequent itemset mining problem. A significant bottleneck in Apriori is the number of I/O operation involved, and the number of candidates it generates. We investigate the role of LSH techniques to overcome these problems, without adding much computational overhead. We propose randomized variations of Apriori that are based on asymmetric LSH defined over Hamming distance and Jaccard similarity.

cs.DB↗

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.

quant-ph↗

arXiv2015

Efficient Reverse k Nearest Neighbor evaluation for hierarchical index

"Reverse Nearest Neighbor" query finds applications in decision support systems, profile-based marketing, emergency services etc. In this paper, we point out a few flaws in the branch and bound algorithms proposed earlier for computing monochromatic RkNN queries over data points stored in hierarchical index. We give suitable counter examples to validate our claims and propose a correct algorithm for the corresponding problem. We show that our algorithm is correct by identifying necessary conditions behind correctness of algorithms for this problem.

cs.DS↗

arXiv2008

Universal Quantum Circuits

We define and construct efficient depth-universal and almost-size-universal quantum circuits. Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational power of the circuit class being simulated. For depth we construct universal circuits whose depth is the same order as the circuits being simulated. For size, there is a log factor blow-up in the universal circuits constructed here. We prove that this construction is nearly optimal.

cs.CC↗