  Compact quantum data representations are essential to the emerging field of
quantum algorithms for data analysis. We introduce two new data encoding
schemes, QCrank and QBArt, which have a high degree of quantum parallelism
through uniformly controlled rotation gates. QCrank encodes a sequence of
real-valued data as rotations of the data qubits, allowing for high storage
density. QBArt directly embeds a binary representation of the data in the
computational basis, requiring fewer quantum measurements and lending itself to
well-understood arithmetic operations on binary data. We present several
applications of the proposed encodings for different types of data. We
demonstrate quantum algorithms for DNA pattern matching, Hamming weight
calculation, complex value conjugation, and retrieving an O(400) bits image,
all executed on the Quantinuum QPU. Finally, we use various cloud-accessible
QPUs, including IBMQ and IonQ, to perform additional benchmarking experiments.

Quantum Physics