Noisy Logic

Michael Schirber

Focus

Noisy Logic

March 5, 2009• Phys. Rev. Focus 23, 7

Researchers built a digital circuit that relies on noise to perform correctly, offering a possible solution to the problem of electronic background noise in the smallest computer circuits.

Figure caption — **Getting louder.** Engineers need to use increasingly complex schemes to deal with the unsteady voltages in the smallest circuits in computer chips. But a new circuit works *only* when there is enough noise.

As computer chips shrink ever smaller, the background flicker of electronic noise threatens to undermine the vital precision of digital processing. Unlike ordinary circuits, a newly designed digital circuit element only works properly when the noise level is sufficiently high. The circuit, described in the 13 March Physical Review Letters, is not only well-suited for noisy nanoscale operations, but it can also be changed on the fly to perform different logic functions–a property that could lead to reconfigurable computer processors.

The typical logic gate–the core of a digital circuit–is a combination of several transistors that convert two input voltages into a single output that corresponds to a particular logic function. A NAND gate, for example, will output a “one” only if at least one of the two inputs is “zero.” Current logic gates use transistors roughly 90 nanometers across, but chip manufacturers are trying to squeeze the elements down to 65, 45, and even 22.5 nanometers. At these scales, the voltages are no longer steady, due to crosstalk between different wires, thermal fluctuations, and even quantum uncertainty. In the presence of all this noise, logic gates can fail to return the correct output. Engineers are forced to think of new, more complicated designs to work around the noise, but they have limits.

For the last few years, William Ditto of Arizona State University in Tempe and his colleagues have been developing non-linear gates. These have transistors like normal linear gates, but the output does not scale with the inputs because of the way the elements are combined. When Ditto’s team looked at how noise might affect the performance of their gates, they realized that–with a few modifications–their circuits could exhibit so-called stochastic resonance. This phenomenon, which occurs in climate cycles, systems of neurons, and other non-linear systems, enhances a weak signal with the help of a noisy background.

For example, think of the Earth’s climate as having two stable states, normal and ice age. The slight variations in Earth’s orbit around the Sun that occur on a 100,000-year cycle aren’t enough on their own to cool the climate very much. But when added with the annual variability in the weather–say, an occasional extra-cold winter–the orbital variations can push the climate into a stable ice age that lasts many years. Many other systems show this property, where noise that isn’t too strong or too weak can “assist” the system in responding to a weak signal.

To mimic the simplest case of stochastic resonance, the researchers wired up a set of transistors into a non-linear circuit with two stable output voltages, high and low, or “one” and “zero.” They cycled through various combinations of inputs, while injecting different levels of noise into the circuit. They found that at low noise the gate performed unreliably, giving different outputs for the same inputs. However, when the noise was moderately increased, the gate behaved in a repeatable fashion. Apparently, a minimum of noise was needed to push the system into the “correct” state–a classic sign of stochastic resonance.

The optimum noise levels can be comparable to the levels expected for the smallest transisters, Ditto says. These non-linear gates could therefore be used in real microchips to allow further miniaturization. But they have another advantage over current technology: the logic is not fixed. By altering certain applied voltages in the circuit, the researchers could tune the output to match either a NAND or a NOR gate, out of which all other logic functions can be made. Ditto and his colleagues have previously demonstrated morphing gates without stochastic resonance [1]–hardware whose architecture can be rapidly reconfigured for each different task a computer performs. (Other reconfigurable designs can’t be switched quickly, while the chip is operating.)

Kurt Wiesenfeld of the Georgia Institute of Technology in Atlanta believes this is a clever idea for exploiting stochastic resonance. “We now know many examples in physics and biology in which noise improves sensitivity,” he says. Humans and other animals appear to use noise to improve neurological functions. “It makes sense to make devices which ‘cooperate’ with the environment rather than shield it out,” Wiesenfeld says.

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics Magazine based in Lyon, France.