237 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
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 Communications Based on Quantum Hashing
In this paper we consider an application of the recently proposed quantum
hashing technique for computing Boolean functions in the quantum communication
model. The combination of binary functions on non-binary quantum hash function
is done via polynomial presentation, which we have called a characteristic of a
Boolean function. Based on the characteristic polynomial presentation of
Boolean functions and quantum hashing technique we present a method for
computing Boolean functions in the quantum one-way communication model, where
one of the parties performs his computations and sends a message to the other
party, who must output the result after his part of computations. Some of the
results are also true in a more restricted Simultaneous Message Passing model
with no shared resources, in which communicating parties can interact only via
the referee. We give several examples of Boolean functions whose polynomial
presentations have specific properties allowing for construction of quantum
communication protocols that are provably exponentially better than classical
ones in the simultaneous message passing setting
On Quantum Fingerprinting and Quantum Cryptographic Hashing
Fingerprinting and cryptographic hashing have quite different usages in computer science, but have similar properties. Interpretation of their properties is determined by the area of their usage: fingerprinting methods are methods for constructing efficient randomized and quantum algorithms for computational problems, whereas hashing methods are one of the central cryptographical primitives. Fingerprinting and hashing methods are being developed from the mid of the previous century, whereas quantum fingerprinting and quantum hashing have a short history. In this chapter, we investigate quantum fingerprinting and quantum hashing. We present computational aspects of quantum fingerprinting and quantum hashing and discuss cryptographical properties of quantum hashing
New Bounds for the Garden-Hose Model
We show new results about the garden-hose model. Our main results include
improved lower bounds based on non-deterministic communication complexity
(leading to the previously unknown bounds for Inner Product mod 2
and Disjointness), as well as an upper bound for the
Distributed Majority function (previously conjectured to have quadratic
complexity). We show an efficient simulation of formulae made of AND, OR, XOR
gates in the garden-hose model, which implies that lower bounds on the
garden-hose complexity of the order will be
hard to obtain for explicit functions. Furthermore we study a time-bounded
variant of the model, in which even modest savings in time can lead to
exponential lower bounds on the size of garden-hose protocols.Comment: In FSTTCS 201
From Graphs to Keyed Quantum Hash Functions
We present two new constructions of quantum hash functions: the first based
on expander graphs and the second based on extractor functions and estimate the
amount of randomness that is needed to construct them. We also propose a keyed
quantum hash function based on extractor function that can be used in quantum
message authentication codes and assess its security in a limited attacker
model
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