New Quantum Algorithm Factors Numbers With One Qubit… The catch: It would require the energy of a few medium-size stars.

> In 1994, the mathematician Peter Shor devised an algorithm that would let quantum computers factor big numbers exponentially faster than classical machines. But Shor’s factoring algorithm also has **limitations:** The bigger the number you want to factor, the bigger and better the quantum computer you need. Cracking an encryption scheme would require a quantum computer running Shor’s algorithm on hundreds of thousands(opens a new tab) of efficient quantum bits, or qubits. Today’s machines are nowhere close.

> In the past, researchers have tried to improve on Shor’s algorithm for factoring by simulating a qubit **using a continuous system**, with its expanded set of possible values. But even if your system computes with continuous qubits, it will still need a lot of them to factor numbers, and it won’t necessarily go any faster. The secret to Shor’s algorithm is that it uses the number it’s factoring to generate what researchers call a periodic function, which has repeating values at regular intervals. Then it uses a mathematical tool called a quantum Fourier transform to identify the value of that period.

> König’s team proved that in a system **using quantum oscillators instead of qubits,** the dynamics of those physical components could indeed perform the mathematical work of factoring — without having to simulate the discrete values of qubits.

> But this method also has a catch: The larger the number to be factored, the more energy the oscillators require to do the math. As a result, factoring a large number uses only one qubit, but it requires a near-unthinkable amount of energy. “If I give you a big number to factor, you have to **harness the energy of multiple stars** just to be able to run the algorithm, let alone control everything that happens,” Chabaud said.

> For Aram Harrow, a physicist at the Massachusetts Institute of Technology, that **renders the new result useless**. But the Munich group is already working on modifying the energy cost by fine-tuning the number of oscillators and how they function. “Maybe **with more oscillators you can get away with less energy**,” König said.