170 research outputs found
On the Necessity of Entanglement for the Explanation of Quantum Speedup
In this paper I argue that entanglement is a necessary component for any
explanation of quantum speedup and I address some purported counter-examples
that some claim show that the contrary is true. In particular, I address Biham
et al.'s mixed-state version of the Deutsch-Jozsa algorithm, and Knill &
Laflamme's deterministic quantum computation with one qubit (DQC1) model of
quantum computation. I argue that these examples do not demonstrate that
entanglement is unnecessary for the explanation of quantum speedup, but that
they rather illuminate and clarify the role that entanglement does play.Comment: Many clarificatory changes, and improved argumentation. Comments and
criticisms are still welcom
Information-Theoretic Meaning of Quantum Information Flow and Its Applications to Amplitude Amplification Algorithms
The advantages of quantum information processing are in many cases obtained
as consequences of quantum interactions, especially for computational tasks
where two-qubit interactions are essential. In this work, we establish the
framework of analyzing and quantifying loss or gain of information on a quantum
system when the system interacts with its environment. We show that the
information flow, the theoretical method of characterizing (non-)Markovianity
of quantum dynamics, corresponds to the rate of the minimum uncertainty about
the system given quantum side information. Thereafter, we analyze the
information exchange among subsystems that are under the performance of quantum
algorithms, in particular, the amplitude amplification algorithms where the
computational process relies fully on quantum evolution. Different realizations
of the algorithm are considered, such as i)quantum circuits, ii) analog
computation, and iii) adiabatic computation. It is shown that, in all the
cases, our formalism provides insights about the process of amplifying the
amplitude from the information flow or leakage on the subsystems.Comment: 7 pages, 5 figures, close to the published versio
Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches
We compare pseudopure state ensemble implementations, quantified by their
initial polarization and ensemble size, of Grover's search algorithm to
probabilistic classical sequential search algorithms in terms of their success
and failure probabilities. We propose a criterion for quantifying the resources
used by the ensemble implementation via the aggregate number of oracle
invocations across the entire ensemble and use this as a basis for comparison
with classical search algorithms. We determine bounds for a critical
polarization such that the ensemble algorithm succeeds with a greater
probability than the probabilistic classical sequential search. Our results
indicate that the critical polarization scales as N^(-1/4) where N is the
database size and that for typical room temperature solution state NMR, the
polarization is such that the ensemble implementation of Grover's algorithm
would be advantageous for N > 10^2
Hands-on Quantum Programming Labs for EECS Students
This report presents a practical approach to teaching quantum computing to
Electrical Engineering & Computer Science (EECS) students through dedicated
hands-on programming labs. The labs cover a diverse range of topics,
encompassing fundamental elements, such as entanglement, quantum gates and
circuits, as well as advanced algorithms including Quantum Key Distribution,
Deutsch and Deutsch-Jozsa Algorithms, Simon's algorithm, and Grover's
algorithm. As educators, we aim to share our teaching insights and resources
with fellow instructors in the field. The full lab handouts and program
templates are provided for interested instructors. Furthermore, the report
elucidates the rationale behind the design of each experiment, enabling a
deeper understanding of quantum computing.Comment: 68 pages, 29 figures; several typos correcte
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