# Quantum-parallel vectorized data encodings and computations on trapped-ions and transmons QPUs

**Authors:** Jan Balewski, Mercy G. Amankwah, Roel Van Beeumen, E. Wes Bethel, Talita Perciano, Daan Camps  
**arXiv:** [2301.07841](https://arxiv.org/abs/2301.07841)  
**Date:** 2023-01-19  
**Summary page:** https://www.summarizepaper.com/en/paper/2301.07841v1/

## Key points

- Compact quantum data representations are crucial in the emerging field of quantum algorithms for data analysis
- Researchers have introduced two new data encoding schemes: QCrank and QBArt
- QCrank encodes a sequence of real-valued data as rotations of the data qubits, enabling high storage density
- QBArt directly embeds a binary representation of the data in the computational basis and requires fewer quantum measurements, lending itself to well-understood arithmetic operations on binary data
- The proposed encodings have been demonstrated through various applications using different types of data, including DNA pattern matching, Hamming weight calculation, complex value conjugation, and retrieving an O(400) bits image - all executed on the Quantinuum QPU
- Both QCrank and QBArt are efficient in terms of time complexity compared to classical algorithms
- The proposed encodings can be implemented on any trapped-ion or transmon-based QPU architecture with uniformly controlled rotation gates

## Summary

In the emerging field of quantum algorithms for data analysis, compact quantum data representations are crucial. To this end, a team of researchers comprising Jan Balewski, Mercy G. Amankwah, Roel Van Beeumen, E. Wes Bethel, Talita Perciano, and Daan Camps have introduced two new data encoding schemes: QCrank and QBArt. These encoding schemes offer 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, which enables high storage density. On the other hand, QBArt directly embeds a binary representation of the data in the computational basis and requires fewer quantum measurements. This scheme lends itself to well-understood arithmetic operations on binary data. The researchers present several applications of these proposed encodings for different types of data. They 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. Furthermore, they use various cloud-accessible QPUs such as IBMQ and IonQ to perform additional benchmarking experiments. The results show that both QCrank and QBArt are efficient in terms of time complexity compared to classical algorithms. The authors note that their work is not limited to specific hardware platforms but can be implemented on any trapped-ion or transmon-based QPU architecture with uniformly controlled rotation gates. In summary, this research introduces two novel quantum-parallel vectorized data encoding schemes that offer high storage density and require fewer quantum measurements while enabling well-understood arithmetic operations on binary data. The proposed encodings have been demonstrated through various applications using different types of data and benchmarked against classical algorithms using cloud-accessible QPUs.