5,581 research outputs found
Asymptotically Optimal Quantum Circuits for d-level Systems
As a qubit is a two-level quantum system whose state space is spanned by |0>,
|1>, so a qudit is a d-level quantum system whose state space is spanned by
|0>,...,|d-1>. Quantum computation has stimulated much recent interest in
algorithms factoring unitary evolutions of an n-qubit state space into
component two-particle unitary evolutions. In the absence of symmetry, Shende,
Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit
unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa
(VMS) use the QR matrix factorization and Gray codes in an optimal order
construction involving two-particle evolutions. In this work, we note that
Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a
generic (symmetry-less) n-qudit evolution. However, the VMS result applied to
virtual-qubits only recovers optimal order in the case that d is a power of
two. We further construct a QR decomposition for d-multi-level quantum logics,
proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing
the complexity question for all d-level systems (d finite.) Gray codes are not
required, and the optimal Theta(d^{2n}) asymptotic also applies to gate
libraries where two-qudit interactions are restricted by a choice of certain
architectures.Comment: 18 pages, 5 figures (very detailed.) MatLab files for factoring qudit
unitary into gates in MATLAB directory of source arxiv format. v2: minor
change
Synthesis of Quantum Logic Circuits
We discuss efficient quantum logic circuits which perform two tasks: (i)
implementing generic quantum computations and (ii) initializing quantum
registers. In contrast to conventional computing, the latter task is nontrivial
because the state-space of an n-qubit register is not finite and contains
exponential superpositions of classical bit strings. Our proposed circuits are
asymptotically optimal for respective tasks and improve published results by at
least a factor of two.
The circuits for generic quantum computation constructed by our algorithms
are the most efficient known today in terms of the number of expensive gates
(quantum controlled-NOTs). They are based on an analogue of the Shannon
decomposition of Boolean functions and a new circuit block, quantum
multiplexor, that generalizes several known constructions. A theoretical lower
bound implies that our circuits cannot be improved by more than a factor of
two. We additionally show how to accommodate the severe architectural
limitation of using only nearest-neighbor gates that is representative of
current implementation technologies. This increases the number of gates by
almost an order of magnitude, but preserves the asymptotic optimality of gate
counts.Comment: 18 pages; v5 fixes minor bugs; v4 is a complete rewrite of v3, with
6x more content, a theory of quantum multiplexors and Quantum Shannon
Decomposition. A key result on generic circuit synthesis has been improved to
~23/48*4^n CNOTs for n qubit
The Implications of Galaxy Formation Models for the TeV Observations of Current Detectors
This paper represents a step toward constraining galaxy formation models via
TeV gamm a ray observations. We use semi-analytic models of galaxy formation to
predict a spectral distribution for the intergalactic infrared photon field,
which in turn yields information about the absorption of TeV gamma rays from
extra-galactic sources. By making predictions for integral flux observations at
>200 GeV for several known EGRE T sources, we directly compare our models with
current observational upper limits obtained by Whipple. In addition, our
predictions may offer a guide to the observing programs for the current
population of TeV gamma ray observatories.Comment: 6 pages, 11 figures, to appear in the proceedings of the 6th TeV
Workshop at Snowbird, U
Angular Momentum Profiles of Warm Dark Matter Halos
We compare the specific angular momentum profiles of virialized dark halos in
cold dark matter (CDM) and warm dark matter (WDM) models using high-resolution
dissipationless simulations. The simulations were initialized using the same
set of modes, except on small scales, where the power was suppressed in WDM
below the filtering length. Remarkably, WDM as well as CDM halos are
well-described by the two-parameter angular momentum profile of Bullock et al.
(2001), even though the halo masses are below the filtering scale of the WDM.
Although the best-fit shape parameters change quantitatively for individual
halos in the two simulations, we find no systematic variation in profile shapes
as a function of the dark matter type. The scatter in shape parameters is
significantly smaller for the WDM halos, suggesting that substructure and/or
merging history plays a role producing scatter about the mean angular momentum
distribution, but that the average angular momentum profiles of halos originate
from larger-scale phenomena or a mechanism associated with the virialization
process. The known mismatch between the angular momentum distributions of dark
halos and disk galaxies is therefore present in WDM as well as CDM models. Our
WDM halos tend to have a less coherent (more misaligned) angular momentum
structure and smaller spin parameters than do their CDM counterparts, although
we caution that this result is based on a small number of halos.Comment: 5 pages, 1 figure, Submitted to ApJ
Minimal Universal Two-qubit Quantum Circuits
We give quantum circuits that simulate an arbitrary two-qubit unitary
operator up to global phase. For several quantum gate libraries we prove that
gate counts are optimal in worst and average cases. Our lower and upper bounds
compare favorably to previously published results. Temporary storage is not
used because it tends to be expensive in physical implementations.
For each gate library, best gate counts can be achieved by a single universal
circuit. To compute gate parameters in universal circuits, we only use
closed-form algebraic expressions, and in particular do not rely on matrix
exponentials. Our algorithm has been coded in C++.Comment: 8 pages, 2 tables and 4 figures. v3 adds a discussion of asymetry
between Rx, Ry and Rz gates and describes a subtle circuit design problem
arising when Ry gates are not available. v2 sharpens one of the loose bounds
in v1. Proof techniques in v2 are noticeably revamped: they now rely less on
circuit identities and more on directly-computed invariants of two-qubit
operators. This makes proofs more constructive and easier to interpret as
algorithm
System analysis approach to deriving design criteria (loads) for Space Shuttle and its payloads. Volume 1: General statement of approach
Space shuttle, the most complex transportation system designed to date, illustrates the requirement for an analysis approach that considers all major disciplines simultaneously. Its unique cross coupling and high sensitivity to aerodynamic uncertainties and high performance requirements dictated a less conservative approach than those taken in programs. Analyses performed for the space shuttle and certain payloads, Space Telescope and Spacelab, are used a examples. These illustrate the requirements for system analysis approaches and criteria, including dynamic modeling requirements, test requirements control requirements and the resulting design verification approaches. A survey of the problem, potential approaches available as solutions, implications for future systems, and projected technology development areas are addressed
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