
Quantum Simulation of the Factorization Problem - CarolineW
https://arxiv.org/abs/1601.04896
======
reubenmorais
Here's a explanation for laymen of what this means:
[http://phys.org/news/2016-11-quantum-physics-
factor.html](http://phys.org/news/2016-11-quantum-physics-factor.html)

Some excerpts:

The researchers have shown that the arithmetic used in factoring numbers into
their prime factors can be translated into the physics of a device—a "quantum
simulator"—that physically mimics the arithmetic rather than trying to
directly calculate a solution like a computer does.

For now, the researchers do not know the technical complexity of building such
a device, or whether it would even be possible to factor very large numbers.

"We have shown that a quantum simulator able to factor numbers exists and, in
principle, it could be built," Martin said. "Whether the simulator is feasible
with current technology in a way that it can factor numbers of the same size
as the ones used in cryptography remains to be seen, but the avenue is now
open. The prospect of building such a device before a quantum computer is
built is something to be pondered seriously."

One of the most mathematically interesting aspects of the new work is that it
involves redefining the factorization problem by introducing a new arithmetic
function that could then be mapped onto the physics of the quantum simulator
and correspond to the energy values. In a sense, the researchers are rewriting
the math problem in terms of physics.

"The manuscript tries to bridge number theory with quantum physics," Rosales
said, noting that researchers have been trying to do this for several decades.
"Nowadays with the development of quantum information and computation and the
discovery of Shor's algorithm, the connection seems more intriguing and
important than ever."

~~~
rhaps0dy
I still don't quite understand:

"The method is 'analogue' in the sense that it is not like Shor's algorithm,
which is programmable in a quantum computer following the gate model. Instead,
it is the measurement of a carefully set quantum system that provides the
answer."

Isn't the gate model _also_ a carefully set quantum system, the measurement of
which provides the answer? Can someone shed some light on this please?

~~~
j1vms
As a rough way to understand this, take a look at the difference in operation
between an analog computer [0] and a digital computer. One of the main
differences is that an analog computer does not achieve a given "operation"
(e.g. integration of an input function) via a discrete heurestic (i.e. by
executing the calculation in steps using say numerical integration), but
rather the analog computer _embodies_ the operation itself via its underlying
physics.

Essentially, these researchers have proposed a way to tackle integer
factorization by creating a quantum system that embodies the calculation
itself, rather than performing discrete steps on an input to find its factors
as one would via, say, Shor's Algorithm on a "general-purpose" quantum
computer.

As is mentioned in GP post's link, this is potentially a significant result in
both pure math (quantum number theory) and applied cryptography.

[0]
[https://en.wikipedia.org/wiki/Analog_computer](https://en.wikipedia.org/wiki/Analog_computer)

------
e0m
Wow this is a huge deal. They devised a way to solve hard math problems (large
number factorization) with physics itself, and were able to validate it
against novel factorization algorithms. Mapping number theory to quantum
physics is no small feat. Really stretches what we think of when we say
"computing" an answer to a problem.

~~~
WhitneyLand
When you say solve problems using "physics itself", I think it's important to
clarify it's quantum physics.

Mapping math problems to classical physics has been done for quite a while,
for example
[http://www.nutsvolts.com/magazine/article/analog_mathematics](http://www.nutsvolts.com/magazine/article/analog_mathematics).

