Scott Aaronson's blog post today gave a list of interesting open problems/tasks in complexity. One in particular caught my attention:
Build a public library of 3SAT instances, with as few variables and clauses as possible, that would have noteworthy consequences if solved. (For example, inst...
@hadsed looks good to me. asked a question myself on adiabatic computing not long ago & managed to get votes. however! the issue of getting good quality responses is separate... =|
there are a few qm computing experts signed up on the site, & many good questions in the area, but participation is spotty...
In adiabatic quantum computation (AQC), one encodes the solution to an optimization problem in the ground state of a [problem] Hamiltonian $H_p$. To get to this ground state, you start in an easily coolable initial (ground) state with Hamiltonian $H_i$ and "anneal" (adiabatically perturb) towards...
this will be considered controversial by some, and even proponents of this angle will have to admit its in the early stages of research, but basically quantum computing seems to have many connections to parallelism and parallel computation. the references are right now scattered but an emerging t...
one other point. questions on adiabatic computer verge on the "dwave" arena, which is extremely controversial/contentious in the cs community....
due largely it seems to the singlehanded-yet-extreme efforts by "the foremost world dwave skeptic"...
it seems to me, hadsed, re your question, there is not much of a geometrical picture for much of anything in qm! and that is a deeper & more fundamental question/problem(?) than about adiabatic qm computing in particular...
@vzn good points. i do know that scott aaronson and peter shor hang out on physics sometimes too, but i'm not sure if they're very active anymore. my question had been up on physics for a while so i wondered if it might get better visibility here
i found a few papers that attempted an answer, but unfortunately im too noob to really understand them
I'm a fledgling computer science scholar, and I'm being asked to write a paper which involves integer factorization. As a result, I'm having to look into Shor's algorithm on quantum computers.
For the other algorithms, I was able to find specific equations to calculate the number of instructions...
Adiabatic quantum computation (AQC) relies on the adiabatic theorem to do calculations
and is closely related to quantum annealing
. First, a complex Hamiltonian is found whose ground state describes the solution to the problem of interest. Next, a system with a simple Hamiltonian is prepared and initialized to the ground state. Finally, the simple Hamiltonian is adiabatically evolved to the complex Hamiltonian. By the adiabatic theorem, the system remains in the ground state, so at the end the state of the system describes the solution to the problem.
AQC is a possible method to get ...
notice the wikipedia article says nothing about geometry or topology....
so, it could be that a geometric interpretation makes it more intuitive/accessible, or paradoxically, on the other hand, less accessable/more abstract.
are you familiar with bloch spheres? its a natural geometric interpretation for qm computing...
In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch.
Quantum mechanics is mathematically formulated in Hilbert space or projective Hilbert space.
The space of pure states of a quantum system is given by the one-dimensional subspaces of the corresponding Hilbert space (or the "points" of the projective Hilbert space).
In a two-dimensional Hilbert space this is simply the complex projective line, which is a geometrical sphere.
The Bloch sphere is a unit 2-sphe...
Scott Aaronson's blog post today gave a list of interesting open problems/tasks in complexity. One in particular caught my attention:
Build a public library of 3SAT instances, with as few variables and clauses as possible, that would have noteworthy consequences if solved. (For example, inst...
theory salon
theory salon