5

The earliest non-internal reference I can find is in NIPS 2009 from a Google/D-Wave effort1. You'll notice that the two Choi papers, in addition to not using the term "Chimera", do not describe a Chimera graph (and note that the name comes from D-Wave, not from graph theory). For a good early reference on Chimera, I recommend Bunyk et al., 20141 , which ...


3

There are multiple factors that affect an embedding's performance, including what Davide mentions. Depending on your background, the following interpretation of Davide's answer might be easier for you to understand: Early in the anneal, the Ising (classical/user-input/final) Hamiltonian has no effect, which means that two spins in a chain are not compelled ...


3

On parameter setting, check our work: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.031040 (Basically you want to make sure that the chains representing the logical qubit have a phase transition synchronized with the minimum gap). But in general this is a hard problem, and precision issues connected to the embedding characteristics are probably ...


2

I will assume you are asking about D-Wave's quantum annealer. If there is a part of the learning process that can fit the QUBO (Quadratic Unconstrained Binary Optimization) formulation, then yes. The problem however is what to consider as binary variables of your problem. In CNN, we have in general real-valued parameters that we tweak for training (using ...


2

Well first you will have to specify the MST in a QUBO/Ising formulation. In this article showing formulations for different types of problems, section 8.1 is about the MST with a maximal degree constraint. This paper contains results of Spanning Tree calculations. When you have the formulation, you map it on the Chimera Graph if the hardware size is not ...


1

The errors from quantum annealing apart from having crappy qubits will come from the imperfect instantiation of the qubit coupling. The first problem i.e having bad qubits can ultimately be mitigated by a kind of error correction look at Error-corrected quantum annealing with hundreds of qubits (Pudenz et al., 2014). But as it turns out the second problem ...


1

You can use a technique of reduction by substitution. Here we represent using ancilla representing a Boolean constraint $ z\Leftrightarrow x_1\wedge x_2 $ as a quadratic penalty function : $$P(x_1,x_2;z) = x_1 x_2 - 2(x_1+x_2)z + 3z$$ For a triplet interaction, you use it to reduce to pairwise : $$ x_1 x_2 x_3 = \min_z \bigl\{ z x_3 + M P(x_1,x_2;z) \bigr\},...


1

You need to introduce ancillary variables and minimize over them; which would enable you to have a QUBO form with only pairing terms. For example, if your binary variables are called $ x,y,z $ and you have a $ a*xyz $ term with the coefficient $ a$, you can use a technique of reduction by minimum selection where you introduce another variable $w$ such that ...


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