# Sparse coding on D-Wave hardware

Sparse coding is a hot area within Deep Learning. Deep learning is the current hot area in artificial intelligence.

Dwave is describing how they adapted the math to work in a superior way on their adiabatic quantum computer system. This solution indicates how much the smart mathematicians and computer algorithm experts contribute to making problems solvable in a superior way on the Dwave quantum hardware.

Quadratic unconstrained binary optimization (QUBO) is a pattern matching technique, common in machine learning applications. QUBO is an NP hard problem. QUBO problems are particularly well suited for processing on quantum computers.

Modifying an simpler attempt with a better algorithm

The only difference here from what we did before is the last sentence, where we add a set of constraints on the dictionary atoms.

Solving the sparse coding problem using block coordinate descent

We’re going to use the same strategy for solving this as before, with a slight change. Here is the strategy we’ll use.

* First, we generate a random dictionary {D}, subject to meeting the orthogonality constraints we’ve imposed on the dictionary atoms.

* Assuming these fixed dictionaries, we solve the optimization problem for the dictionary atoms {W}. These optimization problems are now Chimera-structured QUBOs that fit exactly onto the hardware by construction.

* Now we fix the weights to these values, and find the optimal dictionary {D}, again subject to our constraints.

We then iterate steps 2 and 3 until G converges to a minimum.

Now we’re in a different regime than before — step 2 requires the solution of a large number of chimera-structured QUBOs, not fully connected QUBOs. So that makes those problems better fits to the hardware. But now we have to do some new things to allow for both steps 1 and 3, and these initial steps have some cost.

There was a 48 page presentation that described the Dwave hardware This explains the Chimera topology of the Dwave Quantum computer system.

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