A Quantum Lovasz Local Lemma

The Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of "weakly dependent" criteria. We show that the LLL extends to a much more general geometric setting, where events are replaced with subspaces and probability is replaced with relative dimension, which allows to lower bound the dimension of the intersection of vector spaces under certain independence conditions. Our result immediately applies to the k-QSAT problem: For instance we show that any collection of rank 1 projectors with the property that each qubit appears in at most $2^k/(e \cdot k)$ of them, has a joint satisfiable state. We then apply our results to the recently studied model of random k-QSAT. Recent works have shown that the satisfiable region extends up to a density of 1 in the large k limit, where the density is the ratio of projectors to qubits. Using a hybrid approach building on work by Laumann et al. we greatly extend the known satisfiable region for random k-QSAT to a density of $\Omega(2^k/k^2)$. Since our tool allows us to show the existence of joint satisfying states without the need to construct them, we are able to penetrate into regions where the satisfying states are conjectured to be entangled, avoiding the need to construct them, which has limited previous approaches to product states.Comment: 19 page

General and selective deoxygenation by hydrogen using a reusable earth-abundant metal catalyst

Chemoselective deoxygenation by hydrogen is particularly challenging but crucial for an efficient late-stage modification of functionality-laden fine chemicals, natural products, or pharmaceuticals and the economic upgrading of biomass-derived molecules into fuels and chemicals. We report here on a reusable earth-abundant metal catalyst that permits highly chemoselective deoxygenation using inexpensive hydrogen gas. Primary, secondary, and tertiary alcohols as well as alkyl and aryl ketones and aldehydes can be selectively deoxygenated, even when part of complex natural products, pharmaceuticals, or biomass-derived platform molecules. The catalyst tolerates many functional groups including hydrogenation-sensitive examples. It is efficient, easy to handle, and conveniently synthesized from a specific bimetallic coordination compound and commercially available charcoal. Selective, sustainable, and cost-efficient deoxygenation under industrially viable conditions seems feasible. © 2019 The Authors

Quantum walks with infinite hitting times

Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition, which for discrete time quantum walks is that the degeneracy of the evolution operator be greater than the degree of the graph. The set of initial states which give an infinite hitting time form a subspace. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. In the case of the discrete walk, if this condition is satisfied the walk will have infinite hitting times for any choice of a coin operator, and we give a class of graphs with infinite hitting times for any choice of coin. Hitting times are not very well-defined for continuous time quantum walks, but we show that the idea of infinite hitting-time walks naturally extends to the continuous time case as well.Comment: 28 pages, 3 figures in EPS forma

Solving the liar detection problem using the four-qubit singlet state

A method for solving the Byzantine agreement problem [M. Fitzi, N. Gisin, and U. Maurer, Phys. Rev. Lett. 87, 217901 (2001)] and the liar detection problem [A. Cabello, Phys. Rev. Lett. 89, 100402 (2002)] is introduced. The main advantages of this protocol are that it is simpler and is based on a four-qubit singlet state already prepared in the laboratory.Comment: REVTeX4, 4 page

The effect of large-decoherence on mixing-time in Continuous-time quantum walks on long-range interacting cycles

In this paper, we consider decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are the extensions of the cycle graphs. For this purpose, we use Gurvitz's model and assume that every node is monitored by the corresponding point contact induced the decoherence process. Then, we focus on large rates of decoherence and calculate the probability distribution analytically and obtain the lower and upper bounds of the mixing time. Our results prove that the mixing time is proportional to the rate of decoherence and the inverse of the distance parameter (\emph{m}) squared. This shows that the mixing time decreases with increasing the range of interaction. Also, what we obtain for \emph{m}=0 is in agreement with Fedichkin, Solenov and Tamon's results \cite{FST} for cycle, and see that the mixing time of CTQWs on cycle improves with adding interacting edges.Comment: 16 Pages, 2 Figure

Acting together: ensemble as a democratic process in art and life

Traditionally drama in schools has been seen either as a learning medium with a wide range of curricular uses or as a subject in its own right. This paper argues that the importance of drama in schools is in the processes of social and artistic engagement and experiencing of drama rather than in its outcomes. The paper contrasts the pro-social emphasis in the ensemble model of drama with the pro-technical and limited range of learning in subject-based approaches which foreground technical knowledge of periods, plays, styles and genres. The ensemble-based approach is positioned in the context of professional theatre understandings of ensemble artistry and in the context of revolutionary shifts from the pro-technical to the pro-social in educational and cultural policy making in England. Using ideas drawn from McGrath and Castoriadis, the paper claims that the ensemble approach provides young people with a model of democratic living

Almost uniform sampling via quantum walks

Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic Markov chain $P$ on $S$ for long enough to obtain a random state from within $\epsilon$ total variation distance of the uniform distribution over $S$. The running time of this algorithm, the so-called {\em mixing time} of $P$, is $O(\delta^{-1} (\log N + \log \epsilon^{-1}))$, where $\delta$ is the spectral gap of $P$. We present a natural quantum version of this algorithm based on repeated measurements of the {\em quantum walk} $U_t = e^{-iPt}$. We show that it samples almost uniformly from $S$ with logarithmic dependence on $\epsilon^{-1}$ just as the classical walk $P$ does; previously, no such quantum walk algorithm was known. We then outline a framework for analyzing its running time and formulate two plausible conjectures which together would imply that it runs in time $O(\delta^{-1/2} \log N \log \epsilon^{-1})$ when $P$ is the standard transition matrix of a constant-degree graph. We prove each conjecture for a subclass of Cayley graphs.Comment: 13 pages; v2 added NSF grant info; v3 incorporated feedbac

Decoherence vs entanglement in coined quantum walks

Quantum versions of random walks on the line and cycle show a quadratic improvement in their spreading rate and mixing times respectively. The addition of decoherence to the quantum walk produces a more uniform distribution on the line, and even faster mixing on the cycle by removing the need for time-averaging to obtain a uniform distribution. We calculate numerically the entanglement between the coin and the position of the quantum walker and show that the optimal decoherence rates are such that all the entanglement is just removed by the time the final measurement is made.Comment: 11 pages, 6 embedded eps figures; v2 improved layout and discussio

Response of Multi-strip Multi-gap Resistive Plate Chamber

A prototype of Multi-strip Multi-gap Resistive Plate chamber (MMRPC) with active area 40 cm $\times$ 20 cm has been developed at SINP, Kolkata. Detailed response of the developed detector was studied with the pulsed electron beam from ELBE at Helmholtz-Zentrum Dresden-Rossendorf. In this report the response of SINP developed MMRPC with different controlling parameters is described in details. The obtained time resolution ($\sigma_t$) of the detector after slew correction was 91.5$\pm$3 ps. Position resolution measured along ($\sigma_x$) and across ($\sigma_y$) the strip was 2.8$\pm$0.6 cm and 0.58 cm, respectively. The measured absolute efficiency of the detector for minimum ionizing particle like electron was 95.8$\pm$1.3 $\%$. Better timing resolution of the detector can be achieved by restricting the events to a single strip. The response of the detector was mainly in avalanche mode but a few percentage of streamer mode response was also observed. A comparison of the response of these two modes with trigger rate was studiedComment: 19 pages, 26 figure

Entanglement vs. gap for one-dimensional spin systems

We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap Delta is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small Delta. To help resolve this asymptotic behavior, we construct a family of one-dimensional local systems for which some intervals have entanglement entropy which is polynomial in 1/Delta, whereas previously studied systems, such as free fermion systems or systems described by conformal field theory, had the entropy of all intervals bounded by a constant times log(1/Delta).Comment: 16 pages. v2 is final published version with slight clarification