In the past, researchers have tried to improve on Shor\u2019s 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\u2019t necessarily go any faster. \u201cWe were wondering whether there\u2019s a better way of using continuous variable systems,\u201d K\u00f6nig said.<\/p>\n
They decided to go back to basics. The secret to Shor\u2019s algorithm is that it uses the number it\u2019s 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 \u2014 how long it takes for the function to repeat. From there, some straightforward algebra can reveal the original number\u2019s factors.<\/p>\n
When K\u00f6nig and Brenner tried to think of another continuous approach to factoring, they quickly thought of quantum oscillators, which produce a repeating pattern that can take on any continuous value after being measured (unlike qubits). Those patterns act like a built-in quantum Fourier transform, said K\u00f6nig.<\/p>\n
\u201cLukas and I started talking about this hybrid qubit-oscillator system,\u201d K\u00f6nig said. But they had only vague ideas, so the pair brought in their colleagues Libor Caha and Xavier Coiteux-Roy to design a quantum algorithm based on this system.<\/p>\n
After a few months, K\u00f6nig\u2019s 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 \u2014 without having to simulate the discrete values of qubits. The single qubit in their system reads and organizes information in the oscillators but doesn\u2019t perform the actual computation, as qubits do in other quantum computers. Like Shor\u2019s algorithm, the new approach factors integers in a reasonable amount of time.<\/p>\n
The work also points to new possibilities for implementing continuous methods in quantum computing. \u201cThis paper is saying, by using operations that feel very reasonable, they managed to achieve something that feels completely unreasonable,\u201d Chabaud said. \u201cThis is a pretty cool thing, and I was very enthusiastic when the results came out.\u201d<\/p>\n
Shor Enough<\/p>\n
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. \u201cIf 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,\u201d Chabaud said.<\/p>\n