Quantum Computing in Arrays Coupled by 'Always On' Interactions

It has recently been shown that one can perform quantum computation in a Heisenberg chain in which the interactions are 'always on', provided that one can abruptly tune the Zeeman energies of the individual (pseudo-)spins. Here we provide a more complete analysis of this scheme, including several generalizations. We generalize the interaction to an anisotropic form (incorporating the XY, or Forster, interaction as a limit), providing a proof that a chain coupled in this fashion tends to an effective Ising chain in the limit of far off-resonant spins. We derive the primitive two-qubit gate that results from exploiting abrupt Zeeman tuning with such an interaction. We also demonstrate, via numerical simulation, that the same basic scheme functions in the case of smoothly shifted Zeeman energies. We conclude with some remarks regarding generalisations to two- and three-dimensional arrays.Comment: 16 pages (preprint format) inc. 3 figure

Assessing non-linear models for galaxy clustering III: Theoretical accuracy for Stage IV surveys

We provide in depth MCMC comparisons of two different models for the halo redshift space power spectrum, namely a variant of the commonly applied Taruya-Nishimichi-Saito (TNS) model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using many simulation realisations and Stage IV survey-like specifications for the covariance matrix, we check each model's range of validity by testing for bias in the recovery of the fiducial growth rate of structure formation. The robustness of the determined range of validity is then tested by performing additional MCMC analyses using higher order multipoles, a larger survey volume and a more highly biased tracer catalogue. We find that under all tests, the TNS model's range of validity remains robust and is found to be much higher than previous estimates. The EFTofLSS model fails to capture the spectra for highly biased tracers as well as becoming biased at higher wavenumbers when considering a very large survey volume. Further, we find that the marginalised constraints on $f$ for all analyses are stronger when using the TNS model.Comment: 25 pages, 19 figures. Accepted version for publication in JCA

Multi-Qubit Gates in Arrays Coupled by 'Always On' Interactions

Recently there has been interest in the idea of quantum computing without control of the physical interactions between component qubits. This is highly appealing since the 'switching' of such interactions is a principal difficulty in creating real devices. It has been established that one can employ 'always on' interactions in a one-dimensional Heisenberg chain, provided that one can tune the Zeeman energies of the individual (pseudo-)spins. It is important to generalize this scheme to higher dimensional networks, since a real device would probably be of that kind. Such generalisations have been proposed, but only at the severe cost that the efficiency of qubit storage must *fall*. Here we propose the use of multi-qubit gates within such higher-dimensional arrays, finding a novel three-qubit gate that can in fact increase the efficiency beyond the linear model. Thus we are able to propose higher dimensional networks that can constitute a better embodiment of the 'always on' concept - a substantial step toward bringing this novel concept to full fruition.Comment: 20 pages in preprint format, inc. 3 figures. This version has fixed typos and printer-friendly figures, and is to appear in NJ

Revealing modified gravity signal in matter and halo hierarchical clustering

We use a set of N-body simulations employing a modified gravity (MG) model with Vainshtein screening to study matter and halo hierarchical clustering. As test-case scenarios we consider two normal branch Dvali-Gabadadze-Porrati (nDGP) gravity models with mild and strong growth rate enhancement. We study higher-order correlation functions $\xi_n(R)$ up to $n=9$ and associated hierarchical amplitudes $S_n(R)\equiv\xi_n(R)/\sigma(R)^{2n-2}$. We find that the matter PDFs are strongly affected by the fifth-force on scales up to $50h^{-1}$Mpc, and the deviations from GR are maximised at $z=0$. For reduced cumulants $S_n$, we find that at small scales $R\leq10h^{-1}$Mpc the MG is characterised by lower values, with the deviation growing from $7\%$ in the reduced skewness up to even $40\%$ in $S_5$. To study the halo clustering we use a simple abundance matching and divide haloes into thee fixed number density samples. The halo two-point functions are weakly affected, with a relative boost of the order of a few percent appearing only at the smallest pair separations ($r\leq 5h^{-1}$Mpc). In contrast, we find a strong MG signal in $S_n(R)$'s, which are enhanced compared to GR. The strong model exhibits a $>3\sigma$ level signal at various scales for all halo samples and in all cumulants. In this context, we find that the reduced kurtosis to be an especially promising cosmological probe of MG. Even the mild nDGP model leaves a $3\sigma$ imprint at small scales $R\leq3h^{-1}$Mpc, while the stronger model deviates from a GR-signature at nearly all scales with a significance of $>5\sigma$. Since the signal is persistent in all halo samples and over a range of scales, we advocate that the reduced kurtosis estimated from galaxy catalogues can potentially constitute a strong MG-model discriminatory as well as GR self-consistency test.Comment: 19 pages, 11 figures, comments are welcom

Quantum Computing with an 'Always On' Heisenberg Interaction

Many promising ideas for quantum computing demand the experimental ability to directly switch 'on' and 'off' a physical coupling between the component qubits. This is typically the key difficulty in implementation, and precludes quantum computation in generic solid state systems, where interactions between the constituents are 'always on'. Here we show that quantum computation is possible in strongly coupled (Heisenberg) systems even when the interaction cannot be controlled. The modest ability of 'tuning' the transition energies of individual qubits proves to be sufficient, with a suitable encoding of the logical qubits, to generate universal quantum gates. Furthermore, by tuning the qubits collectively we provide a scheme with exceptional experimental simplicity: computations are controlled via a single 'switch' of only six settings. Our schemes are applicable to a wide range of physical implementations, from excitons and spins in quantum dots through to bulk magnets.Comment: 4 pages, 3 figs, 2 column format. To appear in PR