On Computational Power of Quantum Branching Programs

Quantum Branching Programs and Space-Bounded Nonuniform Quantum Complexity

In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the paper, simulations between quantum branching programs and nonuniform quantum Turing machines are presented which allow to transfer lower and upper bound results between the two models. In the second part of the paper, different variants of quantum OBDDs are compared with their deterministic and randomized counterparts. In the third part, quantum branching p…

Quantum and Stochastic Branching Programs of Bounded Width

In this paper we show that one qubit polynomial time computations are at least as powerful as $\NC^1$ circuits. More precisely, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and lower bounds on their power. We show any $\NC^1$ language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless $\NC^1=\ACC$. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of mu…

Quantum vs. Classical Read-once Branching Programs

The paper presents the first nontrivial upper and lower bounds for (non-oblivious) quantum read-once branching programs. It is shown that the computational power of quantum and classical read-once branching programs is incomparable in the following sense: (i) A simple, explicit boolean function on 2n input bits is presented that is computable by error-free quantum read-once branching programs of size O(n^3), while each classical randomized read-once branching program and each quantum OBDD for this function with bounded two-sided error requires size 2^{Ω(n)}. (ii) Quantum branching programs rea…

ONDA：一种支持顺序执行和条件分支的高级量子编程语言

ONDA: A High-Level Quantum Programming Language with Sequential Execution and Conditional Branching

本文提出高级量子编程语言 ONDA，利用自主量子微架构支持顺序执行、条件分支与循环等控制结构，从而降低量子编程复杂度。

一种广义量子分支程序

A Generalized Quantum Branching Program

针对现有两种量子分支程序模型无法实现单步叠加查询变量的不足，提出具备该能力的GQBP模型，给出多类问题的最优长度示例，证明其与既有模型及查询复杂度的等价性，可用于量子解法的时空下界证明。

Quantum Ordered Binary Decision Diagrams with Repeated Tests

Quantum branching programs (quantum binary decision diagrams, respectively) are a convenient tool for examining quantum computations using only a logarithmic amount of space. Recently several types of restricted quantum branching programs have been considered, e. g. read--once quantum branching programs. This paper considers quantum ordered binary decision diagrams (QOBDDs) and answers the question: How does the computational power of QOBDDs increase, if we allow repeated tests. Additionally it is described how to synthesize QOBDDs according to Boolean operations.