’s Law describes an observed trend in the number of transistors on a chip over time; over several decades, this number has doubled roughly every two years. The influence of this phenomenon has had a profound effect on virtually all aspects of modern life: everything from your phone to your microwave exhibits the results.

The problem facing scientists and engineers is this: Moore’s Law is not a law. Nothing guarantees that this doubling trend will continue; computers as you and I know them are approaching a dead end. The basis of modern computer is the doped silicon semiconductor, but in order to increase the number of silicon transistors on a chip, the size of the transistors needs to be decreased. The approach of making smaller transistors has worked for decades, but will eventually run up against the limits of solid state physics. Fundamentally, a different material is needed to fulfill the projections of Moore’s Law.

Over the coming decades, a host of new technologies will supplement and (perhaps) replace the ubiquitous silicon chip. New materials like graphene seem like they may offer at least incremental improvements over silicon, but is there hope for really continuing this exponential growth in the face of the very limits of physics?

Many scientists believe that the next leap stems from a technology called “quantum computation.” If we can’t surmount the challenge of “more computation in a smaller space” by making transistors smaller, a quantum computer offers a different approach. A property of quantum-mechanical particles called “superposition” means that they can be in multiple states simultaneously; they only converge to a single state when measured. While silicon transistors are limited to being in state 0 or 1 (i.e. on or off), a so-called qubit can be in both at the same time. Though this doesn’t allow a quantum computer to do more than one completely different calculation simultaneously, it does provide an enormous speed increase for solving certain classes of problems.

The initial excitement for quantum computers stems from a particular class of problems that it solves exceptionally well: searching large trees. Put another way, quantum computers are exceptionally good at factoring very large numbers. This is the chief approach behind many of the modern cryptographic systems that underlay the Internet, as well as military communications. As such, the field receives significant funding from sources like the DOD and NSA.

Does this mean that everyone will be cracking RSA encryption from the comfort of her own home in a decade? Not exactly. The challenge of quantum computation stems from more than just the manufacturing techniques. Heat and vibrations can knock the qubits out of their superposition, adding noise and time to a calculation. Because of this, quantum computation must be performed at temperatures associated with liquid helium (around 4 K, or -452 degrees Fahrenheit.) Just as the earliest computers in the last century took up whole rooms, any quantum computer needs to be fairly enormous (closet-sized, at minimum) for the cooling equipment associated with it.

So, are quantum computers among us? At the most basic level, the answer is, “yes.” Though several companies are working on producing commercial quantum computers, the closest is a company called D-Wave. Since 2007, they’ve produced a series of what are called adiabatic quantum computers. These computers don’t show all of the truly mind-boggling properties expected of the quantum computers of the future, but they do appear to have the capacity to solve problems (like the Ising model) with a quantum speed-up. There has been significant skepticism in the field, with prominent theorist aligned on both sides of the debate. Whichever side you take, the possibilities are too exciting to ignore.