Gapped and gapless phases of frustration-free spin-1/2 chains

We consider a family of translation-invariant quantum spin chains with nearest-neighbor interactions and derive necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit. More precisely, let $\psi$ be an arbitrary two-qubit state. We consider a chain of $n$ qubits with open boundary conditions and Hamiltonian $H_n(\psi)$ which is defined as the sum of rank-1 projectors onto $\psi$ applied to consecutive pairs of qubits. We show that the spectral gap of $H_n(\psi)$ is upper bounded by $1/(n-1)$ if the eigenvalues of a certain two-by-two matrix simply related to $\psi$ have equal non-zero absolute value. Otherwise, the spectral gap is lower bounded by a positive constant independent of $n$ (depending only on $\psi$). A key ingredient in the proof is a new operator inequality for the ground space projector which expresses a monotonicity under the partial trace. This monotonicity property appears to be very general and might be interesting in its own right. As an extension of our main result, we obtain a complete classification of gapped and gapless phases of frustration-free translation-invariant spin-1/2 chains with nearest-neighbor interactions.Comment: v3: published versio

The X-ray light curve of the massive colliding wind Wolf-Rayet + O binary WR21a

Our dedicated XMM-Newton monitoring, as well as archival Chandra and Swift datasets, were used to examine the behaviour of the WN5h+O3V binary WR21a at high energies. For most of the orbit, the X-ray emission exhibits few variations. However, an increase in strength of the emission is seen before periastron, following a 1/D relative trend, where D is the separation between both components. This increase is rapidly followed by a decline due to strong absorption as the Wolf-Rayet (WR) comes in front. The fitted local absorption value appears to be coherent with a mass-loss rate of about 1x10^{-5} M_sol/yr for the WR component. However, absorption is not the only parameter affecting the X-ray emission at periastron as even the hard X-ray emission decreases, suggesting a possible collapse of the colliding wind region near to or onto the photosphere of the companion just before or at periastron. An eclipse may appear as another potential scenario, but it would be in apparent contradiction with several lines of evidence, notably the width of the dip in the X-ray light curve and the absence of variations in the UV light curve. Afterwards, the emission slowly recovers, with a strong hysteresis effect. The observed behaviour is compatible with predictions from general wind-wind collision models although the absorption increase is too shallow.Comment: Accepted for publication in Astronomy & Astrophysic

Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique groundstate by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its $q$-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice

Complexity of the XY antiferromagnet at fixed magnetization

We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model

Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets

We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov and Mosca. Their algorithm takes as input an exactly synthesizable single-qubit unitary--one which can be expressed without error as a product of Clifford and T gates--and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is smallest possible. In this paper, for each positive even integer $n$ we consider the "Clifford-cyclotomic" gate set consisting of the Clifford group plus a z-rotation by $\frac{\pi}{n}$. We present an efficient exact synthesis algorithm which outputs a decomposition using the minimum number of $\frac{\pi}{n}$ z-rotations. For the Clifford+T case $n=4$ the group of exactly synthesizable unitaries was shown to be equal to the group of unitaries with entries over the ring $\mathbb{Z}[e^{i\frac{\pi}{n}},1/2]$. We prove that this characterization holds for a handful of other small values of $n$ but the fraction of positive even integers for which it fails to hold is 100%.Comment: v2: published versio

An exceptional X-ray view of the young open cluster NGC 6231: what XMM-Newton has taught us

Considered as the core of the Sco OB1 association, the young open cluster NGC 6231 harbours a rich O-type star population. In 2001, the XMM-Newton satellite targeted the cluster for a nominal duration of about 180 ks. Thanks to the detector sensitivity, the EPIC cameras provided an unprecedented X-ray view of NGC 6231, revealing about 600 point-like sources. In this contribution, we review the main results that have been obtained thanks to this unprecedented data set. Concerning the O-type stars, we present the latest developments related to the so-called 'canonical' Lx-Lbol relation. The dispersion around this relation might actually be much smaller than previously thought. In our data set, the sole mechanism that yields a significant deviation from this scheme is wind interaction. It is also the sole mechanism that induces a significant variation of the early-type star X-ray flux. In a second part of this contribution, we probe the properties of the optically faint X-ray sources. Most of them are believed to be low mass pre-main sequence stars. Their analysis provides direct insight into the star formation history of the cluster.Comment: 6 pages, 5 figures, to appear in "The X-Ray Universe 2005", ESA Symposium held at El Escorial, Madrid (Spain), 26-30 Sep 200