13,568 research outputs found
Quantum Computing and Nuclear Magnetic Resonance
Quantum information processing is the use of inherently quantum mechanical
phenomena to perform information processing tasks that cannot be achieved using
conventional classical information technologies. One famous example is quantum
computing, which would permit calculations to be performed that are beyond the
reach of any conceivable conventional computer. Initially it appeared that
actually building a quantum computer would be extremely difficult, but in the
last few years there has been an explosion of interest in the use of techniques
adapted from conventional liquid state nuclear magnetic resonance (NMR)
experiments to build small quantum computers. After a brief introduction to
quantum computing I will review the current state of the art, describe some of
the topics of current interest, and assess the long term contribution of NMR
studies to the eventual implementation of practical quantum computers capable
of solving real computational problems.Comment: 8 pages pdf including 6 figures. Perspectives article commissioned by
PhysChemCom
An Introduction to Quantum Computing for Non-Physicists
Richard Feynman's observation that quantum mechanical effects could not be
simulated efficiently on a computer led to speculation that computation in
general could be done more efficiently if it used quantum effects. This
speculation appeared justified when Peter Shor described a polynomial time
quantum algorithm for factoring integers.
In quantum systems, the computational space increases exponentially with the
size of the system which enables exponential parallelism. This parallelism
could lead to exponentially faster quantum algorithms than possible
classically. The catch is that accessing the results, which requires
measurement, proves tricky and requires new non-traditional programming
techniques.
The aim of this paper is to guide computer scientists and other
non-physicists through the conceptual and notational barriers that separate
quantum computing from conventional computing. We introduce basic principles of
quantum mechanics to explain where the power of quantum computers comes from
and why it is difficult to harness. We describe quantum cryptography,
teleportation, and dense coding. Various approaches to harnessing the power of
quantum parallelism are explained, including Shor's algorithm, Grover's
algorithm, and Hogg's algorithms. We conclude with a discussion of quantum
error correction.Comment: 45 pages. To appear in ACM Computing Surveys. LATEX file. Exposition
improved throughout thanks to reviewers' comment
Logical operations with Localized Structures
We show how to exploit excitable regimes mediated by localized structures
(LS) to perform AND, OR, and NOT logical operations providing full logical
functionality. Our scheme is general and can be implemented in any physical
system displaying LS. In particular, LS in nonlinear photonic devices can be
used for all-optical computing applications where several reconfigurable logic
gates can be implemented in the transverse plane of a single device, allowing
for parallel computing.Comment: 11 pages, 6 figure
Renyi entropies as a measure of the complexity of counting problems
Counting problems such as determining how many bit strings satisfy a given
Boolean logic formula are notoriously hard. In many cases, even getting an
approximate count is difficult. Here we propose that entanglement, a common
concept in quantum information theory, may serve as a telltale of the
difficulty of counting exactly or approximately. We quantify entanglement by
using Renyi entropies S(q), which we define by bipartitioning the logic
variables of a generic satisfiability problem. We conjecture that
S(q\rightarrow 0) provides information about the difficulty of counting
solutions exactly, while S(q>0) indicates the possibility of doing an efficient
approximate counting. We test this conjecture by employing a matrix computing
scheme to numerically solve #2SAT problems for a large number of uniformly
distributed instances. We find that all Renyi entropies scale linearly with the
number of variables in the case of the #2SAT problem; this is consistent with
the fact that neither exact nor approximate efficient algorithms are known for
this problem. However, for the negated (disjunctive) form of the problem,
S(q\rightarrow 0) scales linearly while S(q>0) tends to zero when the number of
variables is large. These results are consistent with the existence of fully
polynomial-time randomized approximate algorithms for counting solutions of
disjunctive normal forms and suggests that efficient algorithms for the
conjunctive normal form may not exist.Comment: 13 pages, 4 figure
Experimental Heat-Bath Cooling of Spins
Algorithmic cooling (AC) is a method to purify quantum systems, such as
ensembles of nuclear spins, or cold atoms in an optical lattice. When applied
to spins, AC produces ensembles of highly polarized spins, which enhance the
signal strength in nuclear magnetic resonance (NMR). According to this cooling
approach, spin-half nuclei in a constant magnetic field are considered as bits,
or more precisely, quantum bits, in a known probability distribution.
Algorithmic steps on these bits are then translated into specially designed NMR
pulse sequences using common NMR quantum computation tools. The
cooling of spins is achieved by alternately combining reversible,
entropy-preserving manipulations (borrowed from data compression algorithms)
with , the transfer of entropy from selected spins to the
environment. In theory, applying algorithmic cooling to sufficiently large spin
systems may produce polarizations far beyond the limits due to conservation of
Shannon entropy.
Here, only selective reset steps are performed, hence we prefer to call this
process "heat-bath" cooling, rather than algorithmic cooling. We experimentally
implement here two consecutive steps of selective reset that transfer entropy
from two selected spins to the environment. We performed such cooling
experiments with commercially-available labeled molecules, on standard
liquid-state NMR spectrometers. Our experiments yielded polarizations that
- , so that the entire
spin-system was cooled. This paper was initially submitted in 2005, first to
Science and then to PNAS, and includes additional results from subsequent years
(e.g. for resubmission in 2007). The Postscriptum includes more details.Comment: 20 pages, 8 figures, replaces quant-ph/051115
Layered architecture for quantum computing
We develop a layered quantum computer architecture, which is a systematic
framework for tackling the individual challenges of developing a quantum
computer while constructing a cohesive device design. We discuss many of the
prominent techniques for implementing circuit-model quantum computing and
introduce several new methods, with an emphasis on employing surface code
quantum error correction. In doing so, we propose a new quantum computer
architecture based on optical control of quantum dots. The timescales of
physical hardware operations and logical, error-corrected quantum gates differ
by several orders of magnitude. By dividing functionality into layers, we can
design and analyze subsystems independently, demonstrating the value of our
layered architectural approach. Using this concrete hardware platform, we
provide resource analysis for executing fault-tolerant quantum algorithms for
integer factoring and quantum simulation, finding that the quantum dot
architecture we study could solve such problems on the timescale of days.Comment: 27 pages, 20 figure
Hybrid quantum computing with ancillas
In the quest to build a practical quantum computer, it is important to use
efficient schemes for enacting the elementary quantum operations from which
quantum computer programs are constructed. The opposing requirements of
well-protected quantum data and fast quantum operations must be balanced to
maintain the integrity of the quantum information throughout the computation.
One important approach to quantum operations is to use an extra quantum system
- an ancilla - to interact with the quantum data register. Ancillas can mediate
interactions between separated quantum registers, and by using fresh ancillas
for each quantum operation, data integrity can be preserved for longer. This
review provides an overview of the basic concepts of the gate model quantum
computer architecture, including the different possible forms of information
encodings - from base two up to continuous variables - and a more detailed
description of how the main types of ancilla-mediated quantum operations
provide efficient quantum gates.Comment: Review paper. An introduction to quantum computation with qudits and
continuous variables, and a review of ancilla-based gate method
Sequential Circuit Design for Embedded Cryptographic Applications Resilient to Adversarial Faults
In the relatively young field of fault-tolerant cryptography, the main research effort has focused exclusively on the protection of the data path of cryptographic circuits. To date, however, we have not found any work that aims at protecting the control logic of these circuits against fault attacks, which thus remains the proverbial Achilles’ heel. Motivated by a hypothetical yet realistic fault analysis attack that, in principle, could be mounted against any modular exponentiation engine, even one with appropriate data path protection, we set out to close this remaining gap. In this paper, we present guidelines for the design of multifault-resilient sequential control logic based on standard Error-Detecting Codes (EDCs) with large minimum distance. We introduce a metric that measures the effectiveness of the error detection technique in terms of the effort the attacker has to make in relation to the area overhead spent in
implementing the EDC. Our comparison shows that the proposed EDC-based technique provides superior performance when compared against regular N-modular redundancy techniques. Furthermore, our technique scales well and does not affect the critical path delay
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