Ground State Spin Logic

Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground state subspace encoding the truth tables of Boolean formulas. The ground state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground state embeddings found in both classical optimization as well as adiabatic quantum optimization.Comment: 6 pages + 3 pages appendix, 7 figures, 1 tabl

The Computational Power of Minkowski Spacetime

The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.Comment: 6 pages, LaTeX, feedback welcom

Fault Models for Quantum Mechanical Switching Networks

The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered fault. Classical faults are modelled at the logical level by fault models that act on classical states. The stuck fault model, thought of as a lead connected to a power rail or to a ground, is most typically considered. A classical test set complete for the stuck fault model propagates both binary basis states, 0 and 1, through all nodes in a network and is known to detect many physical faults. A classical test set complete for the stuck fault model allows all circuit nodes to be completely tested and verifies the function of many gates. It is natural to ask if one may adapt any of the known classical methods to test quantum circuits. Of course, classical fault models do not capture all the logical failures found in quantum circuits. The first obstacle faced when using methods from classical test is developing a set of realistic quantum-logical fault models. Developing fault models to abstract the test problem away from the device level motivated our study. Several results are established. First, we describe typical modes of failure present in the physical design of quantum circuits. From this we develop fault models for quantum binary circuits that enable testing at the logical level. The application of these fault models is shown by adapting the classical test set generation technique known as constructing a fault table to generate quantum test sets. A test set developed using this method is shown to detect each of the considered faults.Comment: (almost) Forgotten rewrite from 200

PO-032 The knock-down of ferritin heavy subunit induces xenobiotic-resistance in k562 cells through the activation of nf-kb pathway

Introduction The transcriptional factor NF-κB, composed by five subunits (RelA/p65, c-Rel, RelB, p50, p52), is largely involved in many facets of cellular physiology such as innate and adaptive immunity as well as inflammation. In addition, NF-kB play a central role in cancer cell survival and chemoresistance partly by its implication in cross-talks with redox-regulating proteins. Ferritin is the major iron storage protein; it is composed by a variable assembly of Heavy (FHC) and Light (FLC) subunits. FHC, in particular, has been widely demonstrated to be devoted in iron uptake and release thus controlling the redox homeostasis. Material and methods K562 erythroleukemia cells were stably silenced for FHC by using the shRNA method. Then FHC reconstitution was achieved by transient transfection of a FHC specific expression vector. ROS were determined by incubating cells with the redox-sensitive probe 2'−7'-DCF. NAC was used to inhibit ROS production. MTT assay was performed to analyse cell viability. Increasing concentrations of Doxorubicin, ranging from 0 to 5 µM, were used to treat K562 cells. Results and discussions The results of this study highlighted that FHC amounts negatively affect NF-kB activation in K562 cells. FHC silencing was accompanied by an increased expression of the nuclear NF-kB subunit p65, FHC rescue determined nuclear p65 decrease. FHC silencing is responsible for intracellular ROS production and ROS are implicated in NF-kB pathway. To elucidate the relationship between ROS amount and nuclear p65 content, we determined ROS amounts in our in vitro model and evaluated p65 nuclear expression after treatment with the ROS scavenger NAC. First, we observed that, as expected, ROS levels increased upon FHC silencing and return to basal levels upon NAC treatment. Interestingly, NAC was also able to decrease nuclear p65 amount in FHC-silenced K562 cells. Considering the effect of NF-kB activated pathway on cell survival, we analysed the effect of FHC silencing-mediated p65 increase in K562 cells upon treatment with increasing doses of Doxorubicin. Cell viability assay highlighted that FHC-silencing was accompanied by an increased resistance to the drug with an IC 50 about doubled compared to that of the K562 control cells at each the time points. This resistance of FHC-silenced cells was reverted upon NF-kB inhibitor transfection. Conclusion FHC silencing induced NF-kB activation in K562 cells through the modulation of intracellular ROS content. This regulatory axis can be used to modulate K562 chemoresistance

Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory

One of the central problems in quantum mechanics is to determine the ground state properties of a system of electrons interacting via the Coulomb potential. Since its introduction by Hohenberg, Kohn, and Sham, Density Functional Theory (DFT) has become the most widely used and successful method for simulating systems of interacting electrons, making their original work one of the most cited in physics. In this letter, we show that the field of computational complexity imposes fundamental limitations on DFT, as an efficient description of the associated universal functional would allow to solve any problem in the class QMA (the quantum version of NP) and thus particularly any problem in NP in polynomial time. This follows from the fact that finding the ground state energy of the Hubbard model in an external magnetic field is a hard problem even for a quantum computer, while given the universal functional it can be computed efficiently using DFT. This provides a clear illustration how the field of quantum computing is useful even if quantum computers would never be built.Comment: 8 pages, 3 figures. v2: Version accepted at Nature Physics; differs significantly from v1 (including new title). Includes an extra appendix (not contained in the journal version) on the NP-completeness of Hartree-Fock, which is taken from v