5,092 research outputs found
On Computational Power of Quantum Read-Once Branching Programs
In this paper we review our current results concerning the computational
power of quantum read-once branching programs. First of all, based on the
circuit presentation of quantum branching programs and our variant of quantum
fingerprinting technique, we show that any Boolean function with linear
polynomial presentation can be computed by a quantum read-once branching
program using a relatively small (usually logarithmic in the size of input)
number of qubits. Then we show that the described class of Boolean functions is
closed under the polynomial projections.Comment: In Proceedings HPC 2010, arXiv:1103.226
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
Algorithms for Quantum Branching Programs Based on Fingerprinting
In the paper we develop a method for constructing quantum algorithms for
computing Boolean functions by quantum ordered read-once branching programs
(quantum OBDDs). Our method is based on fingerprinting technique and
representation of Boolean functions by their characteristic polynomials. We use
circuit notation for branching programs for desired algorithms presentation.
For several known functions our approach provides optimal QOBDDs. Namely we
consider such functions as Equality, Palindrome, and Permutation Matrix Test.
We also propose a generalization of our method and apply it to the Boolean
variant of the Hidden Subgroup Problem
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
SurveyMan: Programming and Automatically Debugging Surveys
Surveys can be viewed as programs, complete with logic, control flow, and
bugs. Word choice or the order in which questions are asked can unintentionally
bias responses. Vague, confusing, or intrusive questions can cause respondents
to abandon a survey. Surveys can also have runtime errors: inattentive
respondents can taint results. This effect is especially problematic when
deploying surveys in uncontrolled settings, such as on the web or via
crowdsourcing platforms. Because the results of surveys drive business
decisions and inform scientific conclusions, it is crucial to make sure they
are correct.
We present SurveyMan, a system for designing, deploying, and automatically
debugging surveys. Survey authors write their surveys in a lightweight
domain-specific language aimed at end users. SurveyMan statically analyzes the
survey to provide feedback to survey authors before deployment. It then
compiles the survey into JavaScript and deploys it either to the web or a
crowdsourcing platform. SurveyMan's dynamic analyses automatically find survey
bugs, and control for the quality of responses. We evaluate SurveyMan's
algorithms analytically and empirically, demonstrating its effectiveness with
case studies of social science surveys conducted via Amazon's Mechanical Turk.Comment: Submitted version; accepted to OOPSLA 201
- …