The connectivity degree controls the difficulty in reservoir design of random boolean networks.

Reservoir Computing (RC) is a paradigm in artificial intelligence where a recurrent neural network (RNN) is used to process temporal data, leveraging the inherent dynamical properties of the reservoir to perform complex computations. In the realm of RC, the excitatory-inhibitory balance b has been shown to be pivotal for driving the dynamics and performance of Echo State Networks (ESN) and, more recently, Random Boolean Network (RBN). However, the relationship between b and other parameters of the network is still poorly understood. This article explores how the interplay of the balance b, the connectivity degree K (i.e., the number of synapses per neuron) and the size of the network (i.e., the number of neurons N) influences the dynamics and performance (memory and prediction) of an RBN reservoir. Our findings reveal that K and b are strongly tied in optimal reservoirs. Reservoirs with high K have two optimal balances, one for globally inhibitory networks (b < 0), and the other one for excitatory networks (b > 0). Both show asymmetric performances about a zero balance. In contrast, for moderate K, the optimal value being K = 4, best reservoirs are obtained when excitation and inhibition almost, but not exactly, balance each other. For almost all K, the influence of the size is such that increasing N leads to better performance, even with very large values of N. Our investigation provides clear directions to generate optimal reservoirs or reservoirs with constraints on size or connectivity.

Excitatory/inhibitory balance emerges as a key factor for RBN performance, overriding attractor dynamics.

Reservoir computing provides a time and cost-efficient alternative to traditional learning methods. Critical regimes, known as the "edge of chaos," have been found to optimize computational performance in binary neural networks. However, little attention has been devoted to studying reservoir-to-reservoir variability when investigating the link between connectivity, dynamics, and performance. As physical reservoir computers become more prevalent, developing a systematic approach to network design is crucial. In this article, we examine Random Boolean Networks (RBNs) and demonstrate that specific distribution parameters can lead to diverse dynamics near critical points. We identify distinct dynamical attractors and quantify their statistics, revealing that most reservoirs possess a dominant attractor. We then evaluate performance in two challenging tasks, memorization and prediction, and find that a positive excitatory balance produces a critical point with higher memory performance. In comparison, a negative inhibitory balance delivers another critical point with better prediction performance. Interestingly, we show that the intrinsic attractor dynamics have little influence on performance in either case.

Graphene field effect transistor scaling for ultra-low-noise sensors.

The discovery of the field effect in graphene initiated the development of graphene field effect transistor (FET) sensors, wherein high mobility surface conduction is readily modulated by surface adsorption. For all graphene transistor sensors, low-frequency 1/f noise determines sensor resolution, and the absolute measure of 1/f noise is thus a crucial performance metric for sensor applications. Here we report a simple method for reducing 1/f noise by scaling the active area of graphene FET sensors. We measured 1/f noise in graphene FETs with size 5 µm × 5 µm to 5.12 mm × 5.12 mm, observing more than five orders of magnitude reduction in 1/f noise. We report the lowest normalized graphene 1/f noise parameter observed to date, 5 × 10-13, and we demonstrate a sulfate ion sensor with a record resolution of 1.2 × 10-3 log molar concentration units. Our work highlights the importance of area scaling in graphene FET sensor design, wherein increased channel area improves sensor resolution.

Shot Noise of a Temperature-Biased Tunnel Junction.

We report the measurement of the current noise of a tunnel junction driven out of equilibrium by a temperature and/or voltage difference, i.e., the charge noise of heat and/or electrical current. This is achieved by a careful control of electron temperature below 1 K at the nanoscale, and a sensitive measurement of noise with wide bandwidth, from 0.1 to 1 GHz. An excellent agreement between experiment and theory with no fitting parameter is obtained. In particular, we find that the current noise of the junction of resistance R when one electrode is at temperature T and the other one at zero temperature is given by S=2 ln2k_{B}T/R.

Non-Gaussian Current Fluctuations in a Short Diffusive Conductor.

We report the measurement of the third moment of current fluctuations in a short metallic wire at low temperature. The data are deduced from the statistics of voltage fluctuations across the conductor using a careful determination of environmental contributions. Our results at low bias agree very well with theoretical predictions for coherent transport with no fitting parameter. By increasing the bias voltage we explore the crossover from elastic to inelastic transport.

Direct Measurement of the Electron Energy Relaxation Dynamics in Metallic Wires.

We present measurements of the dynamical response of thermal noise to an ac excitation in conductors at low temperature. From the frequency dependence of this response function-the (noise) thermal impedance-in the range 1 kHz-1 GHz we obtain direct determinations of the inelastic relaxation times relevant in metallic wires at low temperature: the electron-phonon scattering time and the diffusion time of electrons along the wires. Combining these results with that of resistivity provides a measurement of heat capacity of samples made of thin film. The simplicity and reliability of this technique makes it very promising for future applications in other systems.

Quantum Optics Theory of Electronic Noise in Coherent Conductors.

We consider the electromagnetic field generated by a coherent conductor in which electron transport is described quantum mechanically. We obtain an input-output relation linking the quantum current in the conductor to the measured electromagnetic field. This allows us to compute the outcome of measurements on the field in terms of the statistical properties of the current. We moreover show how under ac bias the conductor acts as a tunable medium for the field, allowing for the generation of single- and two-mode squeezing through fermionic reservoir engineering. These results explain the recently observed squeezing using normal tunnel junctions [G. Gasse et al., Phys. Rev. Lett. 111, 136601 (2013); J.-C. Forgues et al., Phys. Rev. Lett. 114, 130403 (2015)].

Pauli-Heisenberg Oscillations in Electron Quantum Transport.

We measure the current fluctuations emitted by a normal-metal-insulator-normal-metal tunnel junction with a very wide bandwidth, from 0.3 to 13 GHz, down to very low temperature T=35 mK. This allows us to perform the spectroscopy (i.e., measure the frequency dependence) of thermal noise (no dc bias, variable temperature) and shot noise (low temperature, variable dc voltage bias). Because of the very wide bandwidth of our measurement, we deduce the current-current correlator in the time domain. We observe the thermal decay of this correlator as well as its oscillations with a period h/eV, a direct consequence of the effect of the Pauli and Heisenberg principles in quantum electron transport.

Experimental violation of bell-like inequalities by electronic shot noise.

We report measurements of the correlations between electromagnetic field quadratures at two frequencies f1=7 GHz and f1=7.5 GHz of the radiation emitted by a tunnel junction placed at very low temperature and excited at frequency f1+f2. We demonstrate the existence of two-mode squeezing and violation of a Bell-like inequality, thereby proving the existence of entanglement in the quantum shot noise radiated by the tunnel junction.

Emission of microwave photon pairs by a tunnel junction.

We report the observation of photon pairs in the photoassisted shot noise of a tunnel junction in the quantum regime at very high frequency and very low temperature. We have measured the fluctuations of the noise power generated by the junction at two different frequencies, f(1) = 4.4 and f(2) = 7.2 GHz, while driving the junction with a microwave excitation of frequency f(0) = f(1) + f(2). We observe clear correlations between the fluctuations of the two noise powers even when the mean photon number per measurement is much smaller than one. This is strong evidence for photons being emitted in pairs. We also demonstrate that the electromagnetic field generated by the junction exhibits two-mode amplitude squeezing, a proof of its nonclassicality. The data agree very well with predictions based on the fourth cumulant of the current fluctuations generated by the junction.

Noise intensity-intensity correlations and the fourth cumulant of photo-assisted shot noise.

We report the measurement of the fourth cumulant of current fluctuations in a tunnel junction under both dc and ac (microwave) excitation. This probes the non-Gaussian character of photo-assisted shot noise. Our measurement reveals the existence of correlations between noise power measured at two different frequencies, which corresponds to two-mode intensity correlations in optics. We observe positive correlations, i.e. photon bunching, which exist only for certain relations between the excitation frequency and the two detection frequencies, depending on the dc bias of the sample.

Observation of squeezing in the electron quantum shot noise of a tunnel junction.

We report the measurement of the fluctuations of the two quadratures of the electromagnetic field generated by a quantum conductor, a dc- and ac-biased tunnel junction placed at very low temperature. We observe that the variance of the fluctuations on one quadrature can go below that of vacuum, i.e., that the radiated field is squeezed. This demonstrates the quantum nature of the radiated electromagnetic field.

Nonsymmetrized correlations in quantum noninvasive measurements.

A long-standing problem in quantum mesoscopic physics is which operator order corresponds to noise expressions like , where I(ω) is the measured current at frequency ω. Symmetrized order describes a classical measurement while nonsymmetrized order corresponds to a quantum detector, e.g., one sensitive to either emission or absorption of photons. We show that both order schemes can be embedded in quantum weak-measurement theory taking into account measurements with memory, characterized by a memory function which is independent of a particular experimental detection scheme. We discuss the resulting quasiprobabilities for different detector temperatures and how their negativity can be tested on the level of second-order correlation functions already. Experimentally, this negativity can be related to the squeezing of the many-body state of the transported electrons in an ac-driven tunnel junction.