3,599 research outputs found
Hard limits on the postselectability of optical graph states
Coherent control of large entangled graph states enables a wide variety of
quantum information processing tasks, including error-corrected quantum
computation. The linear optical approach offers excellent control and
coherence, but today most photon sources and entangling gates---required for
the construction of large graph states---are probabilistic and rely on
postselection. In this work, we provide proofs and heuristics to aid
experimental design using postselection. We derive a fundamental limitation on
the generation of photonic qubit states using postselected entangling gates:
experiments which contain a cycle of postselected gates cannot be postselected.
Further, we analyse experiments that use photons from postselected photon pair
sources, and lower bound the number of classes of graph state entanglement that
are accessible in the non-degenerate case---graph state entanglement classes
that contain a tree are are always accessible. Numerical investigation up to
9-qubits shows that the proportion of graph states that are accessible using
postselection diminishes rapidly. We provide tables showing which classes are
accessible for a variety of up to nine qubit resource states and sources. We
also use our methods to evaluate near-term multi-photon experiments, and
provide our algorithms for doing so.Comment: Our manuscript comprises 4843 words, 6 figures, 1 table, 47
references, and a supplementary material of 1741 words, 2 figures, 1 table,
and a Mathematica code listin
Exactly Solvable Lattice Models with Crossing Symmetry
We show how to compute the exact partition function for lattice
statistical-mechanical models whose Boltzmann weights obey a special "crossing"
symmetry. The crossing symmetry equates partition functions on different
trivalent graphs, allowing a transformation to a graph where the partition
function is easily computed. The simplest example is counting the number of
nets without ends on the honeycomb lattice, including a weight per branching.
Other examples include an Ising model on the Kagome' lattice with three-spin
interactions, dimers on any graph of corner-sharing triangles, and non-crossing
loops on the honeycomb lattice, where multiple loops on each edge are allowed.
We give several methods for obtaining models with this crossing symmetry, one
utilizing discrete groups and another anyon fusion rules. We also present
results indicating that for models which deviate slightly from having crossing
symmetry, a real-space decimation (renormalization-group-like) procedure
restores the crossing symmetry
Computation by measurements: a unifying picture
The ability to perform a universal set of quantum operations based solely on
static resources and measurements presents us with a strikingly novel viewpoint
for thinking about quantum computation and its powers. We consider the two
major models for doing quantum computation by measurements that have hitherto
appeared in the literature and show that they are conceptually closely related
by demonstrating a systematic local mapping between them. This way we
effectively unify the two models, showing that they make use of interchangeable
primitives. With the tools developed for this mapping, we then construct more
resource-effective methods for performing computation within both models and
propose schemes for the construction of arbitrary graph states employing
two-qubit measurements alone.Comment: 13 pages, 18 figures, REVTeX
Sparse Graph Codes for Quantum Error-Correction
We present sparse graph codes appropriate for use in quantum
error-correction. Quantum error-correcting codes based on sparse graphs are of
interest for three reasons. First, the best codes currently known for classical
channels are based on sparse graphs. Second, sparse graph codes keep the number
of quantum interactions associated with the quantum error correction process
small: a constant number per quantum bit, independent of the blocklength.
Third, sparse graph codes often offer great flexibility with respect to
blocklength and rate. We believe some of the codes we present are unsurpassed
by previously published quantum error-correcting codes.Comment: Version 7.3e: 42 pages. Extended version, Feb 2004. A shortened
version was resubmitted to IEEE Transactions on Information Theory Jan 20,
200
Dimers and cluster integrable systems
We show that the dimer model on a bipartite graph on a torus gives rise to a
quantum integrable system of special type - a cluster integrable system. The
phase space of the classical system contains, as an open dense subset, the
moduli space of line bundles with connections on the graph. The sum of
Hamiltonians is essentially the partition function of the dimer model. Any
graph on a torus gives rise to a bipartite graph on the torus. We show that the
phase space of the latter has a Lagrangian subvariety. We identify it with the
space parametrizing resistor networks on the original graph.We construct
several discrete quantum integrable systems.Comment: This is an updated version, 75 pages, which will appear in Ann. Sci.
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