Quantum Ordered Binary Decision Diagrams with Repeated Tests

Width Hierarchies for Quantum and Classical Ordered Binary Decision Diagrams with Repeated Test

We consider quantum, nondterministic and probabilistic versions of known computational model Ordered Read-$k$-times Branching Programs or Ordered Binary Decision Diagrams with repeated test ($k$-QOBDD, $k$-NOBDD and $k$-POBDD). We show width hierarchy for complexity classes of Boolean function computed by these models and discuss relation between different variants of $k$-OBDD.

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

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…

加权上下文无关语言有序二元决策图

Weighted Context-Free-Language Ordered Binary Decision Diagrams

本文提出加权上下文无关语言有序二元决策图（WCFLOBDDs），通过层次化结构和过程调用机制实现比WBDDs更简洁的函数表示，在量子电路仿真中可处理的量子比特数量是WBDDs的1-64倍，实现了性能上的两全其美。

Scaling maps of $s$-ordered quasiprobabilities are either nonpositive or completely positive

Continuous-variable systems in quantum theory can be fully described through any one of the ${\rm s}$-ordered family of quasiprobabilities $Λ_{\rm s}(α)$, ${\rm s} \in [-1,1]$. We ask for what values of $({\rm s}, a)$ is the scaling map $Λ_{\rm s}(α) \rightarrow a^{-2} Λ_{\rm s}(a^{-1}α)$ a positive map? Our analysis based on a duality we establish settles this issue (i) the scaling map generically fails to be positive, showing that there is no useful entanglement witness of the scaling type beyond the transpose map, and (ii) in the two particular cases $({\rm s}=1, |a| \leq 1)$ and $({\rm s}=…

Exponential Separation between Quantum and Classical Ordered Binary Decision Diagrams, Reordering Method and Hierarchies

In this paper, we study quantum Ordered Binary Decision Diagrams($OBDD$) model; it is a restricted version of read-once quantum branching programs, with respect to "width" complexity. It is known that the maximal gap between deterministic and quantum complexities is exponential. But there are few examples of functions with such a gap. We present a new technique ("reordering") for proving lower bounds and upper bounds for OBDD with an arbitrary order of input variables if we have similar bounds for the natural order. Using this transformation, we construct a total function $REQ$ such that the d…

Effects of long-range hopping and interactions on quantum walk in ordered and disordered lattices

We study the effects of long-range hopping and long-range inter-particle interactions on quantum walk of hard-core bosons in ideal and disordered one-dimensional lattices. We find that the range of hopping has a much more significant effect on the particle correlation dynamics than the range of interactions. We illustrate that long-range hopping makes the correlation diagrams asymmetric with respect to the sign of the interaction and examine the relative role of repulsive and attractive interactions on the dynamics of scattering by isolated impurities and Anderson localization in dis- ordered …