# Top arXiv papers

• The problem 2-quantum-satisfiability (2-QSAT) is the generalisation of the 2-CNF-SAT problem to quantum bits, and is equivalent to determining whether or not a spin-1/2 Hamiltonian with two-body terms is frustration-free. Similarly to the classical problem #2-SAT, the counting problem #2-QSAT of determining the size (i.e. the dimension) of the set of satisfying states is #P-complete. However, if we consider random instances of 2-QSAT in which constraints are sampled from the Haar measure, intractible instances have measure zero. An apparent reason for this is that almost all two-qubit constraints are entangled, which more readily give rise to long-range constraints. We investigate under what conditions product constraints also give rise to families of #2-QSAT instances which are efficiently solvable, by considering #2-QSAT involving only discrete distributions over tensor product operators. This special case of #2-QSAT interpolates between classical #2-SAT, and #2-QSAT involving arbitrary product constraints. We find that such instances of #2-QSAT, defined on Erdos--Renyi graphs or bond-percolated lattices, are almost surely efficiently solvable except to the extent that they are biased to resemble monotone instances #2-SAT.
• We show that a highly-mixed state in terms of a large min-entropy is useless as a resource state for measurement-based quantum computation in the sense that if a classically efficiently verifiable problem is efficiently solved with such a highly-mixed measurement-based quantum computation then such a problem can also be classically efficiently solved. We derive a similar result also for the DQC1$_k$ model, which is a generalized version of the DQC1 model where $k$ output qubits are measured. We also show that the measurement-based quantum computing on a highly-mixed resource state in terms of the von Neumann entropy, and DQC1$_k$ model are useless in another sense that the mutual information between the computation results and inputs is very small.
• Mar 10 2014 quant-ph
Protective measurements illustrate how Yakir Aharonov's fundamental insights into quantum theory yield new experimental paradigms that allow us to test quantum mechanics in ways that were not possible before. As for quantum theory itself, protective measurements demonstrate that a quantum state describes a single system, not only an ensemble of systems, and reveal a rich ontology in the quantum state of a single system. We discuss in what sense protective measurements anticipate the theorem of Pusey, Barrett, and Rudolph (PBR), stating that, if quantum predictions are correct, then two distinct quantum states cannot represent the same physical reality.
• Mar 10 2014 cond-mat.str-el
We suggest a construction of a large class of topological states using an array of quantum wires. First, we show how to construct a Chern insulator using an array of alternating wires that contain electrons and holes, correlated with an alternating magnetic field. This is supported by semi-classical arguments and a full quantum mechanical treatment of an analogous tight-binding model. We then show how electron-electron interactions can stabilize fractional Chern insulators (Abelian and non-Abelian). In particular, we construct a relatively stable non-Abelian $\mathbb{Z}_{3}$ parafermion state. Our construction is generalized to alternating wires with spin-orbit couplings, which then gives rise to integer and fractional (Abelian and non-Abelian) topological insulators. The states we construct are effectively two-dimensional, and are therefore less sensitive to disorder than one-dimensional systems. The possibility of experimental realization of our construction is addressed.
• Mar 10 2014 quant-ph hep-th
Enhanced quantization offers a different classical/quantum connection than that of canonical quantization in which $\hbar >0$ throughout. This result arises when the only allowed Hilbert space vectors allowed in the quantum action functional are coherent states, which leads to the classical action functional augmented by additional terms of order $\hbar$. Canonical coherent states are defined by unitary transformations of a fixed, fiducial vector. While Gaussian vectors are commonly used as fiducial vectors, they cannot be used for all systems. We focus on choosing fiducial vectors for several systems including bosons, fermions, and anyons.
• Entanglement entropy in even dimensional conformal field theories (CFTs) contains well-known universal terms arising from the conformal anomaly. Renyi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Renyi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four-dimensional Renyi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four-dimensional free massless Renyi entropies across cylindrical entangling surfaces to corresponding three-dimensional massive Renyi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of three-dimensional Renyi entropy, including the massless renormalized Renyi entropy and calculable contributions to the perimeter law.
• Mar 10 2014 math.CO cs.DM
Addressing a question of Gowers, we determine the order of the tower height for the partition size in a version of Szemerédi's regularity lemma.
• Mar 10 2014 cond-mat.mes-hall
Graphene, with its quantum Hall topological (Chern) number reflecting the massless Dirac particle, is shown to harbor yet another topological quantum number. This is obtained by combining Streda's general formula for the polarization associated with a second topological number in the Diophantine equation for the Hofstadter problem, and the adiabatic continuity, earlier shown to exist between the square and honeycomb lattices by Hatsugai et al. Specifically, we can regard, from the adiabatic continuity, graphene as a simulator" of square lattice with half flux quantum per unit cell, which implies that the polarization topological numbers in graphene in weak magnetic fields is 1/2 per Dirac cone for the energy region between the van Hove singularities, signifying a new quantum number characterizing graphene.
• Mar 10 2014 math.AG
Let $\mathbf{G}$ be a connected reductive complex algebraic group with split real form $G$. In this paper, we introduce a distribution character for the regular representation of $G$ on the real locus $X$ of a strict wonderful $\mathbf{G}$-variety $\bf{X}$, showing that on a certain open subset of $G$ of transversal elements it is locally integrable, and given by a sum over fixed points.
• We present a full analytical solution of the multiconfigurational strongly-correlated mixed-valence problem corresponding to the $N$-Hubbard ring filled with $N-1$ electrons, and infinite on-site repulsion. While the eigenvalues and the eigenstates of the model are known already, analytical determination of their degeneracy is presented here for the first time. The full solution, including degeneracy count, is achieved for each spin configuration by mapping the Hubbard model into a set of Huckel-annulene problems for rings of variable size. The number and size of these effective Huckel annulenes, both crucial to obtain Hubbard states and their degeneracy, are determined by solving a well-known combinatorial enumeration problem, the necklace problem for $N-1$ beads and two colors, within each subgroup of the $C_{N-1}$ permutation group. Symmetry-adapted solution of the necklace enumeration problem is finally achieved by means of the subduction of coset representation technique [S. Fujita, Theor. Chim. Acta 76, 247 (1989)], which provides a general and elegant strategy to solve the one-hole infinite-$U$ Hubbard problem, including degeneracy count, for any ring size. The proposed group theoretical strategy to solve the infinite-$U$ Hubbard problem for $N-1$ electrons, is easily generalized to the case of arbitrary electron count $L$, by analyzing the permutation group $C_L$ and all its subgroups.
• Mar 10 2014 math.OC
• Mar 10 2014 physics.med-ph
• Mar 10 2014 cs.CR
• Mar 10 2014 gr-qc
• Mar 10 2014 math.AG math.DG
• Mar 10 2014 cs.LG cs.SY
• Mar 10 2014 hep-ph
• Mar 10 2014 cs.SY
• Mar 10 2014 quant-ph
• Mar 10 2014 hep-th
• Mar 10 2014 math.GT
• Mar 10 2014 hep-th
• Mar 10 2014 astro-ph.SR
• Mar 10 2014 math.KT
• Mar 10 2014 nucl-th hep-ph
• Mar 10 2014 math.AP
• Mar 10 2014 hep-ph
• Mar 10 2014 math.CO
• Mar 10 2014 cs.NI
• Mar 10 2014 math.CO
• Mar 10 2014 math.CO
• Mar 10 2014 gr-qc astro-ph.HE
• Mar 10 2014 math.GR
• Mar 10 2014 math.QA math.GT
• Mar 10 2014 cs.CV
• Mar 10 2014 astro-ph.SR
• Mar 10 2014 cond-mat.mtrl-sci
• Mar 10 2014 math.AP
• Mar 10 2014 cond-mat.dis-nn
• Mar 10 2014 hep-ex hep-ph
• Mar 10 2014 nlin.SI
• Mar 10 2014 stat.ME
• Mar 10 2014 nlin.SI math-ph math.MP
• Mar 10 2014 hep-th
• Mar 10 2014 hep-th
• Mar 10 2014 cs.IT cs.DC math.IT
• Mar 10 2014 physics.soc-ph q-fin.GN
• Mar 10 2014 math.AP
• Mar 10 2014 astro-ph.HE astro-ph.IM
• Mar 10 2014 astro-ph.HE
• Mar 10 2014 math.CO cs.DM cs.IT math.IT
• Mar 10 2014 astro-ph.CO astro-ph.GA
• Mar 10 2014 gr-qc math-ph math.MP
• Mar 10 2014 math.AG
• Mar 10 2014 astro-ph.EP
• Mar 10 2014 cond-mat.mes-hall
• Mar 10 2014 nucl-th
• Mar 10 2014 cond-mat.mes-hall
• Mar 10 2014 stat.ME
• Mar 10 2014 math.LO
• Mar 10 2014 q-fin.CP

Man-Hong Yung about 11 hours ago
I enjoyed reading this paper, which makes an interesting connection between quantum state preparation and Bayesian network; the latter is something I am not familiar with. Although this paper is well written, there is some overlap with the existing literature not covered, in particular the problem o ...(continued)
Man-Hong Yung about 11 hours ago
This is a very serious study of the performance of quantum computation for quantum chemistry. I personally believe that quantum chemistry is the "killer application" for quantum simulation; it involves much smaller scale quantum systems, compared with condensed matter systems. I have one suggest ...(continued)
Man-Hong Yung about 12 hours ago
I have no more excuse for not learning IPython for scientific-graph plotting. Thanks Noon!
Noon Silk 3 days ago
For fun, I created the following IPython notebook replicating the graphs in this paper: http://nbviewer.ipython.org/github/silky/paper_workings/blob/master/arxiv_1403.0069.ipynb. (Actually, it's on the sagemath cloud, where if you have an account you can probably edit it - https://cloud.sagemath. ...(continued)
Marco 3 days ago
The author writes "My ideas towards the proof of these results in this paper originates from the observations made by Carlen in [13]". Actually, the first main result is a direct corollary of theorem 2.3 of [13], in the sense of directly applying theorem 2.3 of [13], which regards monotonicity of re ...(continued)
Frédéric Grosshans 5 days ago
I read this paper as an appendix of an unwritten Fantasy novel, where a 21st century cosmologist is trapped in an alternate Aristotelian 13th century universe ! Thanks for the nice read !
Anthony 25 days ago
"Of course, ghosts do not exist..." seems like a rather strange assumption in order to define "ghost world".
Juan Miguel Arrazola 26 days ago
This is a very useful exposition and classification of entanglement witnesses, which I expect will prove very useful for those of us working in the field. I must note that for future work, you may be interested in considering nonlinear witnesses as well, as they provide a generalization of linea ...(continued)
Martin Aulbach 28 days ago
Very impressive. I wonder if this method can be extended to electrons, to develop an entanglement-enhanced electron microscope?
Yuichiro Fujiwara about 2 months ago
This is just amazing. Since combinatorics isn't the most popular section on SciRate, here's a blog post about this by Gil Kalai: http://gilkalai.wordpress.com/2014/01/16/amazing-peter-keevash-constructed-general-steiner-systems-and-designs/ Wilson said at today's seminar at Caltech that Kee ...(continued)