Non-producibility of arbitrary non-Gaussian states using zero-mean Gaussian states and partial photon number resolving detection

Gaussian states and measurements collectively are not powerful-enough resources for quantum computing, as any Gaussian dynamics can be simulated efficiently, classically. However, it is known that any one non-Gaussian resource -- either a state, a unitary operation, or a measurement -- together with Gaussian unitaries, makes for universal quantum resources. Photon number resolving (PNR) detection, a readily-realizable non-Gaussian measurement, has been a popular tool to try and engineer non-Gaussian states for universal quantum processing. In this paper, we consider PNR detection of a subset of the modes of a zero-mean pure multi-mode Gaussian state as a means to herald a target non-Gaussian state on the undetected modes. This is motivated from the ease of scalable preparation of Gaussian states that have zero mean, using squeezed vacuum and passive linear optics. We calculate upper bounds on the fidelity between the actual heralded state and the target state. We find that this fidelity upper bound is $1/2$ when the target state is a multi-mode coherent cat-basis cluster state, a resource sufficient for universal quantum computing. This proves that there exist non-Gaussian states that are not producible by this method. Our fidelity upper bound is a simple expression that depends only on the target state represented in the photon-number basis, which could be applied to other non-Gaussian states of interest.Comment: Revised version which now considers state engineering based on partial PNR detection, which subsumes subtraction and addition of photons. Said generalization allowed for cleaner and easier mathematical derivations. Appendix was taken from arXiv:2108.08290, co-authored by present authors and collaborators. Comments welcome and appreciate

Near-Optimal Distributed Approximation of Minimum-Weight Connected Dominating Set

This paper presents a near-optimal distributed approximation algorithm for the minimum-weight connected dominating set (MCDS) problem. The presented algorithm finds an $O(\log n)$ approximation in $\tilde{O}(D+\sqrt{n})$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. MCDS is a classical NP-hard problem and the achieved approximation factor $O(\log n)$ is known to be optimal up to a constant factor, unless P=NP. Furthermore, the $\tilde{O}(D+\sqrt{n})$ round complexity is known to be optimal modulo logarithmic factors (for any approximation), following [Das Sarma et al.---STOC'11].Comment: An extended abstract version of this result appears in the proceedings of 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014

Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene

The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical lattice) to simulate properties of rippled graphene. We suggest that the Dirac Hamiltonian in a curved background space can also be effectively simulated by a suitable driving scheme in optical lattice. The time dependent system yields, in the approximate limit of high frequency pulsing, an effective time independent Hamiltonian that governs the time evolution, except for an initial and a final kick. We use a specific form of 4-phase pulsed forcing with suitably tuned choice of modulating operators to mimic the effects of curvature. The extent of curvature is found to be directly related to $\omega^{-1}$ the time period of the driving field at the leading order. We apply the method to engineer the effects of curved background space. We find that the imprint of curvilinear geometry modifies the electronic properties, such as LDOS, significantly. We suggest that this method shall be useful in studying the response of various properties of such systems to non-trivial geometry without requiring any actual physical deformations.Comment: 16 pages, 1 figure. Suggestions and comments are welcom

Magnetic Field resulting from non-linear electrical transport in single crystals of charge-ordered Pr0.63_{0.63} Ca0.37_{0.37} MnO3_{3}}

In this letter we report that the current induced destabilization of the charge ordered (CO) state in a rare-earth manganite gives rise to regions with ferromagnetic correlation. We did this experiment by measurement of the I-V curves in single crystal of the CO system Pr$_{0.63}$Ca$_{0.37}$MnO$_{3}$ and simultanously measuring the magnetization of the current carrying conductor using a high T$_c$ SQUID working at T = 77K. We have found that the current induced destabilization of the CO state leads to a regime of negative differential resistance which leads to a small enhancement of the magnetization of the sample, indicating ferromagnetically aligned moments.Comment: 4 pages LateX, 4 eps figure