I Developing Quantum Expressions using QUBO

rpthomps
Messages
182
Reaction score
19
TL;DR Summary
I want to build an expression to solve the two ways to sum to the value of 8 using a set of five numbers 1 , 2, 3, 4, 5 and the criteria is only three numbers can be chosen.
Hi there, I would like some help developing a QUBO expression where a Quantum Annealing approach would find the two ways of summing the 5 numbers {1 2 3 4 5) to 8 by selecting 3 of the numbers. I am basing this off of a dwave.sys video example I found on their site.

My initial kick at the can, looks likes this:

(x1+2x2+3x3+4x4+5x5-8)2+(x1+x2+x3-3)2

I saw a chart in a paper with penalties so I guess, I would also subtract (x1x2+x2x3+x1x3)

What I would like is another expression of a similar vein with the solution so I could analyze it an understand what is happening. Any thoughts/help would be appreciated.
 
Physics news on Phys.org
Here is a QUBO expression that will find the two ways of summing the 5 numbers {1, 2, 3, 4, 5) to 8 by selecting 3 of the numbers: QUBO: minimize (x1 + 2x2 + 3x3 + 4x4 + 5x5 - 8)^2 + (x1 + x2 + x3 - 3)^2 + (x1x2 + x2x3 + x1x3)where x1, x2, x3, x4, x5 are binary variables (0 or 1). The first two terms in the QUBO expression are the objective function. The third term is the penalty term, which penalizes any solutions that have more than three variables set to 1. The solution to this QUBO expression is x1 = 1, x2 = 1, x3 = 1, x4 = 0, x5 = 0. This corresponds to {1,2,3} as the three numbers that sum to 8.
 
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
Back
Top