Shenzhen Quantum Institute makes important progress in compiling and optimizing quantum algorithms

Recently, Academician Yu Dapeng and Associate Researcher Yan Fei of the Shenzhen Institute of Quantum Science and Engineering, in collaboration with researcher Sun Xiaoming's team at the Institute of Computing, Chinese Academy of Sciences, have made new progress in the field of quantum algorithm implementation and quantum architecture. The research team proposed and experimentally implemented an easily scalable quantum version of the logic "with" (AND) gate, which significantly reduces the hardware cost of implementing with logic in quantum systems and lays the foundation for the implementation of a series of key quantum algorithms. The research results were published in Nature Physics on November 14, 2022, under the title "Scalable algorithm simplification using quantum AND logic".

Quantum computing has the potential to surpass classical computing in solving some problems, including database search and decomposition of large prime factors, which are widely used in social life. In order to run a particular quantum algorithm on a particular quantum computing device, the quantum circuit describing the algorithm needs to be first decomposed into a sequence of underlying quantum logic gate operations natively supported by the hardware. This compilation process is highly selective, and although all roads lead to Rome, the final performance results vary greatly. Optimized compilation strategies for quantum logic gate sequences can result in shorter sequences of physical operations, thus allowing quantum bits to perform more tasks in a limited lifetime. Therefore, in order to maximize the performance of quantum devices, optimization of the quantum lines describing quantum algorithms is an equally important aspect as enhancing the performance of the bits, and is of great importance to realize near-term applications.

a. QuAND gate and inverse QuAND gate decomposition methods and truth tables; b. Multi-bit control Z-gate decomposition lines

In this work, the research team proposes the concept of a quantum version of AND gate (Quantum AND, or QuAND for short). QuAND gates enrich the toolbox of quantum-based instruction sets and can significantly reduce the cost of decomposing large-scale quantum lines. For example, multi-bit Toffoli gates, quantum arithmetic lines and other important quantum lines that have wide applications in quantum algorithms.

8-bit superconducting quantum chip with content quantum bits (red, blue), tunable couplers (purple), control signal lines (orange) and other modules

The research team developed an 8-bit quantum processor based on superconducting quantum bits. The processor utilizes the latest highly scalable architecture of tunable couplers combined with fixed frequency bits, while simplifying the wiring scheme. In the experiments, high-fidelity QuAND gate operation was achieved by applying a selective drive to the coupler.

QuAND gate based 4-bit, 6-bit and 8-bit Toffoli gates

Line disassembly method and experimentally measured truth table

By cascading QuAND gates between different quantum bit pairs in a specific order and precisely calibrating the phase factors of the bits, the research team has successfully implemented how to construct multi-bit Toffoli gates of up to 8 bits using shallow lines. While conventional methods require the use of two-bit gates that are at least a square order of magnitude to the number of bits, the QuAND gate-based optimization method requires only a linear number. It is the dramatic reduction in gate operation overhead that enabled the experimental team to successfully implement the largest multi-bit Toffoli gate to date (the previous record was 4 bits). Based on this, the team used the implemented multi-bit Toffoli gate to demonstrate the Grover search algorithm, with a search space size of up to 64 and a much larger experimental scale than before.

Demonstration of Grover search algorithm based on multi-bit Toffoli gates

This work demonstrates how to construct non-traditional quantum logic gate operations on scalable quantum computing hardware to optimize the compiled results of quantum algorithms to executable quantum lines, illustrating the importance of tapping the manipulation potential of quantum hardware and enriching the set of logic gates, laying the foundation for future applications of larger scale and more meaningful quantum algorithms.

In the research results, J. Chu, a PhD student at the University of Southern Science and Technology, and Xiaoyu He, a PhD student at the Institute of Computing, Chinese Academy of Sciences, are the co-first authors of the paper, and the corresponding authors are Fei Yan, an associate researcher at the Quantum Research Institute, Xiaoming Sun, a researcher at the Institute of Computing, Chinese Academy of Sciences, and Dapeng Yu, an academician at the Quantum Research Institute. The research work was supported by the Department of Science and Technology of Guangdong Province, Shenzhen Science and Technology Commission, National Natural Science Foundation of China, Chinese Academy of Sciences, and Southern University of Science and Technology.

Links to related papers：

https://doi.org/10.1038/s41567-022-01813-7