4,841 research outputs found
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^{\Omega(n)}. (ii) Quantum branching programs
reading each input variable exactly once are shown to require size
2^{\Omega(n)} for computing the set-disjointness function DISJ_n from
communication complexity theory with two-sided error bounded by a constant
smaller than 1/2-2\sqrt{3}/7. This function is trivially computable even by
deterministic OBDDs of linear size. The technically most involved part is the
proof of the lower bound in (ii). For this, a new model of quantum
multi-partition communication protocols is introduced and a suitable extension
of the information cost technique of Jain, Radhakrishnan, and Sen (2003) to
this model is presented.Comment: 35 pages. Lower bound for disjointness: Error in application of info
theory corrected and regularity of quantum read-once BPs (each variable at
least once) added as additional assumption of the theorem. Some more informal
explanations adde
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
Computation with narrow CTCs
We examine some variants of computation with closed timelike curves (CTCs),
where various restrictions are imposed on the memory of the computer, and the
information carrying capacity and range of the CTC. We give full
characterizations of the classes of languages recognized by polynomial time
probabilistic and quantum computers that can send a single classical bit to
their own past. Such narrow CTCs are demonstrated to add the power of limited
nondeterminism to deterministic computers, and lead to exponential speedup in
constant-space probabilistic and quantum computation. We show that, given a
time machine with constant negative delay, one can implement CTC-based
computations without the need to know about the runtime beforehand.Comment: 16 pages. A few typo was correcte
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