Nondeterministic Unitary OBDDs

Gainutdinova, Aida; Yakaryılmaz, Abuzer

doi:10.1007/978-3-319-58747-9_13

Cited by 11 publications

(5 citation statements)

References 20 publications

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“…In this paper, we focus on online streaming algorithms (one-way automata for online minimization problems) that read an input only once. The question of comparing quantum and classical models was explored for streaming computation models (OBDDs and automata), but not for the online streaming algorithms [22,16,3,4,24,19,2,12,7,8,21,14,15,13].…”

Section: Introductionmentioning

confidence: 99%

Quantum Online Streaming Algorithms with Logarithmic Memory

Khadiev

Khadieva

2019

Int J Theor Phys

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Section: Introductionmentioning

confidence: 99%

Quantum Online Streaming Algorithms with Logarithmic Memory

Khadiev

Khadieva

2019

Int J Theor Phys

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“…A relation between deterministic OBDD and probabilistic, quantum OBDDs was presented in [4]. Furthermore, different relations between models were discussed, for example, in [7,5,13,1,19,14,18]. Additionally, we apply this lower bound to Matrix XOR Pointer Jumping function and present k-QOBDD for this function.…”

Section: Introductionmentioning

confidence: 99%

Lower Bounds and Hierarchies for Quantum Memoryless Communication Protocols and Quantum Ordered Binary Decision Diagrams with Repeated Test

Ablayev

Ambainis

Khadiev

et al. 2017

SOFSEM 2018: Theory and Practice of Computer Science

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Abstract. We explore multi-round quantum memoryless communication protocols. These are restricted version of multi-round quantum communication protocols. The "memoryless" term means that players forget history from previous rounds, and their behavior is obtained only by input and message from the opposite player. The model is interesting because this allows us to get lower bounds for models like automata, Ordered Binary Decision Diagrams and streaming algorithms. At the same time, we can prove stronger results with this restriction. We present a lower bound for quantum memoryless protocols. Additionally, we show a lower bound for Disjointness function for this model. As an application of communication complexity results, we consider Quantum Ordered Readk-times Branching Programs (k-QOBDD). Our communication complexity result allows us to get lower bound for k-QOBDD and to prove hierarchies for sublinear width bounded error k-QOBDDs, where k = o( √ n). Furthermore, we prove a hierarchy for polynomial size bounded error kQOBDDs for constant k. This result differs from the situation with an unbounded error where it is known that an increase of k does not give any advantage.

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“…Quantum OBDDs (QOBDD) using superoperators are non-trivial generalizations of POBDDs [2]. In this paper, we use the most restricted version of quantum OBDDs called unitary OBDDs (UOBDDs) [13]. Note that UOBDDs and POBDDs are incomparable [23].…”

Section: Preliminariesmentioning

confidence: 99%