We present an accreditation protocol for analogue, i.e., continuous-time, quantum simulators. For a given simulation task, it provides an upper bound on the variation distance between the probability distributions at the output of an erroneous and error-free analogue quantum simulator. As its overheads are independent of the size and nature of the simulation, the protocol is ready for immediate usage and practical for the long term. It builds on the recent theoretical advances of strongly universal Hamiltonians and quantum accreditation as well as experimental progress towards the realisation of programmable hybrid analogue-digital quantum simulators.

We present two algorithms, one quantum and one classical, for estimating partition functions of quantum spin Hamiltonians. The former is a DQC1 (Deterministic quantum computation with one clean qubit) algorithm, and the first such for complex temperatures. The latter, for real temperatures, achieves performance comparable to a state-of-the-art DQC1 algorithm [Chowdhury et al. Phys. Rev. A 103, 032422 (2021)]. Both our algorithms take as input the Hamiltonian decomposed as a linear combination Pauli operators. We show this decomposition to be DQC1-hard for a given Hamiltonian, providing new insight into the hardness of estimating partition functions.

A network is said to have the properties of a small world if a suitably defined average distance between any two nodes is proportional to the logarithm of the number of nodes, N. In this paper, we present a novel derivation of the small-world property for Gilbert–Erdös–Renyi random networks. We employ a mean field approximation that permits the analytic derivation of the distribution of shortest paths that exhibits logarithmic scaling away from the phase transition, inferable via a suitably interpreted order parameter. We begin by framing the problem in generality with a formal generating functional for undirected weighted random graphs with arbitrary disorder, recovering the result that the free energy associated with an ensemble of Gilbert graphs corresponds to a system of non-interacting fermions identified with the edge states. We then present a mean field solution for this model and extend it to more general realizations of network randomness. For a two family class of stochastic block models that we refer to as dimorphic networks, which allow for links within the different families to be drawn from two independent discrete probability distributions, we find the mean field approximation maps onto a spin chain combinatorial problem and again yields useful approximate analytic expressions for mean path lengths. Dimorophic networks exhibit a richer phase structure, where distinct small world regimes separate in analogy to the spinodal decomposition of a fluid. We find that is it possible to induce small world behavior in sub-networks that by themselves would not be in the small-world regime.

In this work, we extend our previous blind GW signal estimation method [H. Liu, J. Creswell, S. von Hausegger, A. D. Jackson and P. Naselsky, J. Cosmol. Astropart. Phys. 2 (2018) 013] to the case of multiple detectors and show that, with a full use of redundancy, it gives promising results, e.g. a faster decay of fluctuations than that expected from the central limit theorem. This method, whose design explicitly accounts for redundancy in multiple measurements, considerably improves the efficiency of signal extraction in a multi-detector network.

In 2005, we proposed that the nerve pulse is an electromechanical soliton [1]. This concept represents a challenge to the well-known Hodgkin-Huxley model [2] which is of a purely electrical nature. The soliton theory was criticized by Nimtz and Aichmann in a recent article in Zeitung fr Naturforschung A [3]. Here, we wish to comment on some statements that we regard as misinterpretations of our views. *corresponding author, theimbu@nbi.ku.dk According to the soliton theory, the nerve signal can be described by an exponentially localized adiabatic pulse reminiscent of sound propagating in the membranes of nerve axons. As early as 1852, Helmholtz observed that the propagation velocity of nerves is close to the propagation velocity of sound in a hydrocarbon layer [4]. The pulse-like shape of the soliton results from the non-linear nature of the nerve membrane compressibility close to a phase transition in the membrane [5]. During the pulse, the membrane is partially moved through a phase transition from a liquid disordered membrane state to a solid ordered state. The associated changes in the thickness of the membrane and the length of the axon, and the reversible release of the latent heat have all been found experimentally (reviewed in [6]). As correctly noted by Nimtz and Aichmann, this situation allows for an immediate explanation of anesthesia due to the depression of the freezing point that they produce in membranes. We have discussed this previously in depth [7–9]. Nimtz and Aichmann state in their article: “This process would represent a local transition to the lower entropy of the gel phase and would result in a negative entropy step and also a reconstruction of the hydrogen bonds geometry at this part of the membrane. However, in Heimburgs model the bound water has been never considered.” This statement is incorrect. We base our argument on the experimentally observed changes in heat capacity and the measured relation to the lateral compressibility. Since only the area and the lateral pressure are controlled during the measurement, all free variables of the membrane can change. The compressibility therefore contains changes in the membrane electrostatics and the change in head-group hydration. The fact that area is controlled does not imply that the other free variables are fixed. E.g., charge, polarization, membrane potential, hydration and protonation of the membrane may well change during compression. The same applies to the measurement of the heat capacity. Here the temperature is controlled, but other variables such as area, charge and membrane potential are free to change during the experiment. These changes are included in the measured values of the heat capacity. During the propagation of the soliton, no negentropy is generated. The entropy does not change in any adiabatic processes, which include all propagating processes described by analytical mechanics or hydrodynamics (including both waves and solitons). The compression of the hydrocarbon chains of the membrane obviously changes the configurational entropy. However, in an adiabatic compression of a membrane, this is compensated by a local heating of the membrane because

Abstract In 2005, we proposed that the nerve pulse is an electromechanical soliton (T. Heimburg and A. D. Jackson. “On soliton propagation in biomembranes and nerves,” Proc. Natl. Acad. Sci. U.S.A., vol. 102, pp. 9790–9795, 2005). This concept represents a challenge to the well-known electrochemical Hodgkin–Huxley model. The soliton theory was criticized by Nimtz and Aichmann in a recent article in Zeitung für Naturforschung A (G. Nimtz and H. Aichmann. “On biological signaling,” Z. Naturforsch. A, vol. 75, pp. 507–509, 2020). Here, we wish to comment on some statements that we regard as misinterpretations of our views.

We reexamine the results presented in [1] in which the properties of the noise residuals in the 40 ms chirp domain of GW150914 were investigated. This paper con firmed the presence of strong (i.e., about 0.80) correlations between residual noise in the Hanford and Livingston detectors in the chirp domain as previously seen by [2] when using a numerical relativity template given in [3]. It was also shown in [1] that a so-called maximum likelihood template can reduce these statistically significant cross-correlations. Here, we demonstrate that the reduction of correlation and statistical significance is due to (i) the use of a peculiar template with extreme spin (0.977), which is qualitatively different from the properties of GW150914 originally published by LIGO, (ii) a suspicious MCMC chain, (iii) uncertainties in the matching of the maximum likelihood (ML) template to the data in the Fourier domain, and (iv) a biased estimation of the significance that gives counterintuitive results. We show that rematching the maximum likelihood template to the data in the 0.2 s domain containing the GW150914 signal restores these correlations at the level of 60% of those found previously [1]. With necessary corrections, the probability given in [1] for the residual correlation will decrease by more than one order of magnitude. Since the ML template is itself problematic, results associated with it are illustrative rather than final.

We study the degeneracy of theoretical gravitational waveforms for binary black hole mergers using an aligned-spin effective-one-body model. After appropriate truncation, bandpassing, and matching, we identify regions in the mass–spin parameter space containing waveforms similar to the template proposed for GW150914, with masses m1 = 36+5−4 M⊙ and m2 = 29+4−4 M⊙, using the cross-correlation coefficient as a measure of the similarity between waveforms. Remarkably high cross-correlations are found across broad regions of parameter space. The associated uncertanties exceed these from LIGO's Bayesian analysis considerably. We have shown that waveforms with greatly increased masses, such as m1 = 70 M⊙ and m2 = 35 M⊙, and strong anti-aligned spins (χ1 = 0.95 and χ2 = −0.95) yield almost the same signal-to-noise ratio in the strain data for GW150914.

We propose a blind, template-free method for the extraction of a common signal between the Hanford and Livingston detectors and apply it especially to the GW150914 event. We construct a log-likelihood method that maximizes the cross-correlation between each detector and the common signal and minimizes the cross-correlation between the residuals. The reliability of this method is tested using simulations with an injected common signal. Finally, our method is used to assess the quality of theoretical gravitational wave templates for GW150914.

In the electromechanical theory of nerve stimulation, the nerve impulse consists of a traveling region of solid membrane in a liquid environment. Therefore, the free energy necessary to stimulate a pulse is directly related to the free energy difference necessary to induce a phase transition in the nerve membrane. It is a function of temperature and pressure, and it is sensitively dependent on the presence of anesthetics which lower melting transitions. We investigate the free energy difference of solid and liquid membrane phases under the influence of anesthetics. We calculate stimulus-response curves of electromechanical pulses and compare them to measured stimulus-response profiles in lobster and earthworm axons. We also compare them to stimulus-response experiments on human median nerve and frog sciatic nerve published in the literature.

To date, the LIGO collaboration has detected three gravitational wave (GW) events appearing in both its Hanford and Livingston detectors. In this article we reexamine the LIGO data with regard to correlations between the two detectors. With special focus on GW150914, we report correlations in the detector noise which, at the time of the event, happen to be maximized for the same time lag as that found for the event itself. Specifically, we analyze correlations in the calibration lines in the vicinity of 35 Hz as well as the residual noise in the data after subtraction of the best-fit theoretical templates. The residual noise for the other two events, GW151226 and GW170104, exhibits similar behavior. A clear distinction between signal and noise therefore remains to be established in order to determine the contribution of gravitational waves to the detected signals.

We present a simple method for the identification of weak signals associated with gravitational wave events. Its application reveals a signal with the same time lag as the GW150914 event in the released LIGO strain data with a significance around 3.2 sigma. This signal starts about 10 minutes before GW150914 and lasts for about 45 minutes. Subsequent tests suggest that this signal is likely to be due to external sources.

Investigations of nerve activity have focused predominantly on electrical phenomena. Nerves, however, are thermodynamic systems, and changes in temperature and in the dimensions of the nerve can also be observed during the action potential. Measurements of heat changes during the action potential suggest that the nerve pulse shares many characteristics with an adiabatic pulse. First experiments in the 1980s suggested small changes in nerve thickness and length during the action potential. Such findings have led to the suggestion that the action potential may be related to electromechanical solitons traveling without dissipation. However, there have been no modern attempts to study mechanical phenomena in nerves. Here, we present ultrasensitive AFM recordings of mechanical changes on the order of 2–12 Å in the giant axons of the lobster. We show that the nerve thickness changes in phase with voltage changes. When stimulated at opposite ends of the same axon, colliding action potentials pass through one another and do not annihilate. These observations are consistent with a mechanical interpretation of the nervous impulse.

We present a simplified method for the extraction of meaningful signals from Hanford and Livingston 32 second data for the GW150914 event made publicly available by the LIGO collaboration, and demonstrate its ability to reproduce the LIGO collaboration's own results quantitatively given the assumption that all narrow peaks in the power spectrum are a consequence of physically uninteresting signals and can be removed. After the clipping of these peaks and return to the time domain, the GW150914 event is readily distinguished from broadband background noise. This simple technique allows us to identify the GW150914 event without any assumption regarding its physical origin and with minimal assumptions regarding its shape. We also confirm that the LIGO GW150914 event is uniquely correlated in the Hanford and Livingston detectors for the full 4096 second data at the level of 6 - 7 sigma with a temporal displacement of T = 6.9 +/- 0.4 ms. We have also identified a few events that are morphologically close to GW150914 but less strongly cross correlated with it.

When a Bose-Einstein-condensed cloud of atoms is given some angular momentum, it forms vortices arranged in structures with a discrete rotational symmetry. For these vortex states, the Hilbert space of the exact solution separates into a ``primary'' space related to the mean-field Gross-Pitaevskii solution and a ``complementary'' space including the corrections beyond mean field. Considering a weakly interacting Bose-Einstein condensate of harmonically trapped atoms, we demonstrate how this separation can be used to close the conceptual gap between exact solutions for systems with only a few atoms and the thermodynamic limit for which the mean field is the correct leading-order approximation. Although we illustrate this approach for the case of weak interactions, it is expected to be more generally valid.

We consider a Bose-Einstein-condensed cloud of atoms which rotate in a toroidal or annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number.