35 research outputs found
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
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
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
Classical Simulation Complexity of Quantum Branching Programs
We present classical simulation techniques for measure once quantum
branching programs.
For bounded error syntactic quantum branching program of width
that computes a function with error we present a classical
deterministic branching program of the same length and width at most
that computes the same function.
Second technique is a classical stochastic simulation technique for
bounded error and unbounded error quantum branching programs. Our
result is that it is possible stochastically-classically simulate
quantum branching programs with the same length and almost the same
width, but we lost bounded error acceptance property
Hybrid classical-quantum text search based on hashing
The paper considers the problem of finding a given substring in a text. It is
known that the complexity of a classical search query in an unordered database
is linear in the length of the text and a given substring. At the same time,
Grover's quantum search provides a quadratic speedup in the complexity of the
query and gives the correct result with a high probability.
We propose a hybrid classical-quantum algorithm (hybrid random-quantum
algorithm to be more precise), that implements Grover's search to find a given
substring in a text. As expected, the algorithm works a) with a high
probability of obtaining the correct result and b) with a quadratic query
acceleration compared to the classical one.
What's new is that our algorithm uses the uniform hash family functions
technique. As a result, our algorithm is much more memory efficient (in terms
of the number of qubits used) compared to previously known quantum algorithms