UCLA

Efficient Quantum Block Encodings of non-unitary data are key for realizing quantum advantagefor linear algebraic operations. Dense, low entropy matrices, which have a low amount of unique values with the distribution of values concentrated largely on one value, have a variety of applications such as DNA analysis. To enable efficient block encodings of dense, low entropy data, we introduce a new paradigm for developing quantum block encodings by reducing the block encoding problem to controlled quantum state preparation and quantum state preparation problems. Through this reduction, we are able to construct three novel block encoding algorithms that incorporate the elements of state preparation algorithms. We then evaluate these algorithms on dense, low entropy data and find that our three block encoding algorithms significantly reduce circuit depth with little ancilla and additional CNOT cost.