125 research outputs found
Notaries of color in colonial Panama: Limpieza de Sangre, legislation, and imperial practices in the administration of the Spanish empire
This is the final version of the article. Available from Cambridge University Press via the DOI in this record.Funding from the Federation of Women Graduates Charitable Foundation, the AHRC Doctoral
Award, and the Society for Latin American Studies Post-doctoral Travel Grant (UK) made possible the
archival research
Makers and Keepers of Networks: Amerindian Spaces, Migrations, and Exchanges in the Brazilian Amazon and French Guiana, 1600–1730.
This is the author accepted manuscript. The final version is available from Duke University Press via the DOI in this record.This article focuses on the geographical space between the Amazon delta and the Maroni River (nowadays Brazilian Amapá and French Guiana) in 1600–1730. An imperial frontier between France and Portugal South American possessions, it has been conceptualized as a refuge zone for Amerindians fleeing European colonization. On the contrary, this article argues that the migrations and movements of people toward and within this Amerindian space have to be understood as a continuation of a pre-European set of indigenous networks. Through the reconstruction of multilingual and multiethnic networks, this article brings to light connections and exchanges that make of this space an Amerindian center as well as a European frontier. It analyzes conflicts, gatherings, celebrations, migrations, and alliances between European and Amerindian groups, including the Aruã, Maraon, Arikaré, Palikur, and Galibi. Rather than a refuge zone, this space remained central to Amerindian life and to the upholding of indigenous autonomy due to the maintenance of inter- and intra-ethnic connections and the regular use of routes across this space
Universal topological phase of 2D stabilizer codes
Two topological phases are equivalent if they are connected by a local
unitary transformation. In this sense, classifying topological phases amounts
to classifying long-range entanglement patterns. We show that all 2D
topological stabilizer codes are equivalent to several copies of one universal
phase: Kitaev's topological code. Error correction benefits from the
corresponding local mappings.Comment: 4 pages, 3 figure
Clifford Gates by Code Deformation
Topological subsystem color codes add to the advantages of topological codes
an important feature: error tracking only involves measuring 2-local operators
in a two dimensional setting. Unfortunately, known methods to compute with them
were highly unpractical. We give a mechanism to implement all Clifford gates by
code deformation in a planar setting. In particular, we use twist braiding and
express its effects in terms of certain colored Majorana operators.Comment: Extended version with more detail
Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group
We study the error threshold of topological color codes on Union Jack
lattices that allow for the full implementation of the whole Clifford group of
quantum gates. After mapping the error-correction process onto a statistical
mechanical random 3-body Ising model on a Union Jack lattice, we compute its
phase diagram in the temperature-disorder plane using Monte Carlo simulations.
Surprisingly, topological color codes on Union Jack lattices have similar error
stability than color codes on triangular lattices, as well as the Kitaev toric
code. The enhanced computational capabilities of the topological color codes on
Union Jack lattices with respect to triangular lattices and the toric code
demonstrate the inherent robustness of this implementation.Comment: 8 pages, 4 figures, 1 tabl
Structure of 2D Topological Stabilizer Codes
We provide a detailed study of the general structure of two-dimensional
topological stabilizer quantum error correcting codes, including subsystem
codes. Under the sole assumption of translational invariance, we show that all
such codes can be understood in terms of the homology of string operators that
carry a certain topological charge. In the case of subspace codes, we prove
that two codes are equivalent under a suitable set of local transformations if
and only they have equivalent topological charges. Our approach emphasizes
local properties of the codes over global ones.Comment: 54 pages, 11 figures, version accepted in journal, improved
presentation and result
Finite temperature quantum simulation of stabilizer Hamiltonians
We present a scheme for robust finite temperature quantum simulation of
stabilizer Hamiltonians. The scheme is designed for realization in a physical
system consisting of a finite set of neutral atoms trapped in an addressable
optical lattice that are controllable via 1- and 2-body operations together
with dissipative 1-body operations such as optical pumping. We show that these
minimal physical constraints suffice for design of a quantum simulation scheme
for any stabilizer Hamiltonian at either finite or zero temperature. We
demonstrate the approach with application to the abelian and non-abelian toric
codes.Comment: 13 pages, 2 figure
Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes
We compute the error threshold of color codes, a class of topological quantum
codes that allow a direct implementation of quantum Clifford gates, when both
qubit and measurement errors are present. By mapping the problem onto a
statistical-mechanical three-dimensional disordered Ising lattice gauge theory,
we estimate via large-scale Monte Carlo simulations that color codes are stable
against 4.5(2)% errors. Furthermore, by evaluating the skewness of the Wilson
loop distributions, we introduce a very sensitive probe to locate first-order
phase transitions in lattice gauge theories.Comment: 12 pages, 5 figures, 1 tabl
On the robustness of bucket brigade quantum RAM
We study the robustness of the bucket brigade quantum random access memory
model introduced by Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett. 100,
160501 (2008)]. Due to a result of Regev and Schiff [ICALP '08 pp. 773], we
show that for a class of error models the error rate per gate in the bucket
brigade quantum memory has to be of order (where is the
size of the memory) whenever the memory is used as an oracle for the quantum
searching problem. We conjecture that this is the case for any realistic error
model that will be encountered in practice, and that for algorithms with
super-polynomially many oracle queries the error rate must be
super-polynomially small, which further motivates the need for quantum error
correction. By contrast, for algorithms such as matrix inversion [Phys. Rev.
Lett. 103, 150502 (2009)] or quantum machine learning [Phys. Rev. Lett. 113,
130503 (2014)] that only require a polynomial number of queries, the error rate
only needs to be polynomially small and quantum error correction may not be
required. We introduce a circuit model for the quantum bucket brigade
architecture and argue that quantum error correction for the circuit causes the
quantum bucket brigade architecture to lose its primary advantage of a small
number of "active" gates, since all components have to be actively error
corrected.Comment: Replaced with the published version. 13 pages, 9 figure
Qudit surface codes and gauge theory with finite cyclic groups
Surface codes describe quantum memory stored as a global property of
interacting spins on a surface. The state space is fixed by a complete set of
quasi-local stabilizer operators and the code dimension depends on the first
homology group of the surface complex. These code states can be actively
stabilized by measurements or, alternatively, can be prepared by cooling to the
ground subspace of a quasi-local spin Hamiltonian. In the case of spin-1/2
(qubit) lattices, such ground states have been proposed as topologically
protected memory for qubits. We extend these constructions to lattices or more
generally cell complexes with qudits, either of prime level or of level
for prime and , and therefore under tensor
decomposition, to arbitrary finite levels. The Hamiltonian describes an exact
gauge theory whose excitations
correspond to abelian anyons. We provide protocols for qudit storage and
retrieval and propose an interferometric verification of topological order by
measuring quasi-particle statistics.Comment: 26 pages, 5 figure
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