Quantum and stochastic branching programs of bounded width

We prove upper and lower bounds on the power of quantum and stochastic branching programs of bounded width. We show any NC1 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 NC1 = ACC. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC 1.© 2002 Springer-Verlag Berlin Heidelberg

On the computational power of probabilistic and quantum branching program

In this paper, we show that one-qubit polynomial time computations are as powerful as NC1 circuits. More generally, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and lower bounds on their power. We show that any NC1 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 multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC1. For read-once quantum branching programs (QBPs), we give a symmetric Boolean function which is computable by a read-once QBP with O (log n) width, but not by a deterministic read-once BP with o (n) width, or by a classical randomized read-once BP with o (n) width which is "stable" in the sense that its transitions depend on the value of the queried variable but do not vary from step to step. Finally, we present a general lower bound on the width of read-once QBPs, showing that our O (log n) upper bound for this symmetric function is almost tight. © 2005 Elsevier Inc. All rights reserved

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 programs are considered where the performed unitary operation may depend on the result of a previous measurement. For this model a simulation of randomized OBDDs and exponential lower bounds are presented.Comment: 45 pages, 3 Postscript figures. Proofs rearranged, typos correcte

Классические и квантовые ветвящиеся программы

Классические и квантовые ветвящиеся программыбакалавриа

Quantum and stochastic branching programs of bounded width

We prove upper and lower bounds on the power of quantum and stochastic branching programs of bounded width. We show any NC1 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 NC1 = ACC. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC 1.© 2002 Springer-Verlag Berlin Heidelberg

Quantum and stochastic branching programs of bounded width

We prove upper and lower bounds on the power of quantum and stochastic branching programs of bounded width. We show any NC1 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 NC1 = ACC. This separates width-2 quantum programs from width-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC 1.© 2002 Springer-Verlag Berlin Heidelberg