Stochastic magnetic circuits rival quantum computing

Circuits based on the stochastic evolution of nanoscale magnets have been used to split large numbers into prime-number factors — a problem that only quantum computers were previously expected to solve efficiently.

Data encryption typically relies on the practical difficulty of a process called prime factorization. In this process, a huge number (represented by 1,024 or more bits) is decomposed into a product of prime numbers. Such a task is notoriously time-consuming for conventional computers and is estimated1 to be much more efficient for a future quantum computer — assuming that such a machine is built and uses a method called Shor’s algorithm2. Writing in Nature, Borders et al.3 demonstrate that an integrated circuit (a computer chip) containing nanoscale magnets can split numbers up to 945 into prime factors efficiently. Such a nanomagnet chip is much easier to make than a quantum computer and, if improved, could threaten data encryption.

If you are reading this article on a computer, you are probably using electronic bits in the machine’s processor and magnetic bits in its hard drive. Electronic bits are based on semiconducting devices called transistors. Such a bit has a definite state (0 or 1) that depends on whether a net negative or net positive charge of thousands of electrons is stored in the gate (a terminal of the transistor) (Fig. 1a). By contrast, a magnetic bit is based on hundreds of thousands of electron spins (magnetic moments) in a magnet. The state of this bit can also be either 0 or 1, depending on whether the net spin of the electrons points down or up (Fig. 1b).

Figure 1 | Four types of computing bit. a, Electronic bits are based on tiny switches called transistors. The state of such a bit can be 0 or 1, depending on whether the gate — a terminal of the transistor — is negatively or positively charged. b, A typical magnetic bit also has a state of 0 or 1, depending on whether the net spin (magnetic moment) of electrons in a magnet points down or up. c, Borders et al.3 report experiments on stochastic magnetic bits, which randomly fluctuate between the 0 and 1 states with a certain probability (represented by arrow size) of being in each state. d, Quantum bits are based on spins of single electrons and are simultaneously in the 0 and 1 states. Two such bits can be entangled, which means that the first bit is in the 1 state and the second is in the 0 state, and vice versa, simultaneously.

For these two types of computing bit, a large energy barrier needs to be overcome to switch between the 0 and 1 states. As a result, the states persist despite random ‘relaxation’ forces caused by thermal fluctuations in the environment. Borders and colleagues’ chip uses nanomagnets in which the barrier between the 0 and 1 states is small. Consequently, random relaxation forces cause the nanomagnets to randomly fluctuate between the two states, with a certain probability that the net spin points up or down (Fig. 1c). Such bits are therefore called probabilistic bits (p-bits). Borders et al. used their chip to perform prime factorization on numbers as large as 945.

A further type of bit, which is used in quantum computers, is known as a quantum bit (qubit) and is based on the spin of a single electron (Fig. 1d). To understand how qubits work, a good start is to consider Schrödinger’s cat. In this famous thought experiment, a cat in a closed box can be considered to be both dead and alive, until the box is opened and the cat’s status is revealed. Note that, when the box is closed, the cat does not simply have a certain probability of being dead and a certain probability of being alive, as in usual (classical) probabilities. Instead, it exists in a quantum-correlated state, in which it is simultaneously dead and alive.

For Shor’s algorithm, an even more intricate state of two qubits, called an entangled state, is required (Fig. 1d). The analogue would be a quantum-correlated state in which one cat is alive and a second cat is dead, and vice versa, simultaneously. Random relaxation forces are the main headache for quantum computers, because they destroy entanglement. There is a type of quantum computing, termed adiabatic, that does not need entanglement. But no theoretical work has claimed that this approach is more efficient than conventional computing.

By contrast, for p-bits, random relaxation forces are turned into a mechanism of operation, in the spirit of the theory of inventive problem solving4 (commonly referred to by its Russian acronym TRIZ). These differences between p-bits and qubits hopefully convince you that, even conceptually, p-bits are much simpler to operate than are qubits.

There are two other advantages of the authors’ approach over quantum computing. First, the nanomagnet chip is fabricated using a process that has already been developed for magnetic memories, whereas a suitable quantum computer would call for a new and highly sophisticated manufacturing process. Second, the nanomagnet chip works at room temperature, whereas the quantum computer would need refrigeration to keep it well under 1 kelvin. In addition to being a nuisance, such refrigeration would require about a kilowatt of power for every watt consumed by the computer5, and would increase the difficulty in developing and operating this technology.

I should mention another example of an experimental proof of prime factorization that did not require quantum computing. In 2016, a Russian–US collaboration6 carried out such factorization using spin waves, which are propagating precessions of spins in nanomagnets. Unfortunately, that work did not receive as much attention as perhaps it should have.

The nanomagnet methods of prime factorization are still in their infancy. Many developments are needed to turn these nanomagnet chips into practical computing engines: the ability to connect thousands of p-bits to each other; a demonstration of combining p-bits and transistors in an integrated circuit; and a calculation of the time and energy needed to achieve prime factorization of huge numbers using these methods.

However, owing to the aforementioned advantages, there is a high chance that these requirements will be fulfilled more quickly and more easily than for quantum computing. Given Borders and colleagues’ results, the attention of research groups and the funding from many agencies might be diverted from quantum computing to nanomagnet chips.

Nature 573, 351-352 (2019)


  1. 1.

    Van Meter III, R. D. Preprint at (2006).

  2. 2.

    Shor, P. SIAM J. Comput. 26, 1484–1509 (1997).

  3. 3.

    Borders, W. A. et al. Nature 573, 390–393 (2019).

  4. 4.

    Altshuller, G. S. The Innovation Algorithm: TRIZ, Systematic Innovation and Technical Creativity (Technical Innovation Center, 1999).

  5. 5.

    Holmes, D. S., Ripple, A. L. & Manheimer, M. A. IEEE Trans. Appl. Supercond, 23, 1701610 (2013).

  6. 6.

    Khivintsev, Y. et al. J. Appl. Phys. 120, 123901 (2016).

Download references

Nature Briefing

An essential round-up of science news, opinion and analysis, delivered to your inbox every weekday.


Sign up to Nature Briefing

An essential round-up of science news, opinion and analysis, delivered to your inbox every weekday.

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing