Computing with Noise - Phase Transitions in Boolean Formulas

A short survey is provided about our recent explorations of the young topic of noise-based logic. After outlining the motivation behind noise-based computation schemes, we present a short summary of our ongoing efforts in the introduction, development and design of several noise-based deterministic multivalued logic schemes and elements. In particular, we describe classical, instantaneous, continuum, spike and random-telegraph-signal based schemes with applications such as ci...

In this paper, we show recent results indicating that using electrical noise as information carrier offers outstanding potentials reminding of quantum informatics. One example is noise-based computing and logic that shows certain similarities to quantum logic. However, due to the lack of the collapse of wavefunction and due to the immediate accessibility of superposition components, the use of noise-based and quantum computers will probably be different. Another example is se...

The possibility of a new type of computing, where thermal noise is the information carrier and the clock in a computer, is studied. The information channel capacity and the lower limit of energy requirement/dissipation are studied in a simple digital system with zero threshold voltage, for the case of error probability close to 0.5, when the thermal noise is equal to or greater than the digital signal. In a simple hypothetical realization of a thermal noise driven gate, the l...

Faults are stochastic by nature while most man-made systems, and especially computers, work deterministically. This necessitates the linking of probability theory with mathematical logics, automata, and switching circuit theory. This paper provides such a connecting via quantum information theory which is an intuitive approach as quantum physics obeys probability laws. In this paper we provide a novel approach for computing diagnosis of switching circuits with gate-based quan...

Understanding how errors deteriorate the information encoded in a many-body quantum system is a fundamental problem with practical implications for quantum technologies. Here, we investigate a class of encoding-decoding random circuits subject to local coherent and incoherent errors. We analytically demonstrate the existence of a phase transition from an error-protecting phase to an error-vulnerable phase occurring when the error strength is increased. This transition is acco...

Understanding how much energy is needed and dissipated as heat for a given computational system and for a given program is a physically interesting and practically important problem. However, the thermodynamic costs of computational systems are only partially understood. In this paper, we focus on a specific logic gate, the CMOS NAND gate, operating in the sub-threshold region and analyze the dissipated heat from two aspects. One is the general Landauer bound, which is the ch...

We consider the effect of noise in sparse Boolean Networks with redundant functions. We show that they always exhibit a non-zero error level, and the dynamics undergoes a phase transition from non-ergodicity to ergodicity, as a function of noise, after which the system is no longer capable of preserving a memory if its initial state. We obtain upper-bounds on the critical value of noise for networks of different sparsity.

Modern digital electronics support remarkably reliable computing, especially given the challenge of controlling nanoscale logical components that interact in fluctuating environments. However, we demonstrate that the high-reliability limit is subject to a fundamental error-energy-efficiency tradeoff that arises from time-symmetric control: Requiring a low probability of error causes energy consumption to diverge as logarithm of the inverse error rate for nonreciprocal logical...

We formulate a semi-classical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements. As a starting point we define a random circuit model with nearest neighbor classical gates interrupted by erasure errors. In analogy with the quantum setting, this system undergoes a purification transition at a critical error rate above which the classical information entropy in the output state v...

Modern computing systems based on the von Neumann architecture are built from silicon complementary metal oxide semiconductor (CMOS) transistors that need to operate under practically error free conditions with 1 error in $10^{15}$ switching events. The physical dimensions of CMOS transistors have scaled down over the past five decades leading to exponential increases in functional density and energy consumption. Today, the energy and delay reductions from scaling have stagna...