Combining Perfect Shuffle and Bitonic Networks for Efficient Quantum Sorting

The emergence of quantum computers in the last decade has generated research interest in applications such as quantum sorting. Quantum sorting plays a critical role in creating ordered sets of data that can be better utilized, e.g., quantum ordered search or quantum network switching. In this paper, we propose a quantum sorting algorithm that combines highly parallelizable bitonic merge networks with perfect shuffle permutations (PSP), for sorting data represented in the quantum domain. The combination of bitonic networks with PSP improves the temporal complexity of bitonic merge sorting which is critical for reducing decoherence effects for quantum processing. We present space-efficient quantum circuits that can be used for quantum bit comparison and permutation. We also present a reconfigurable hardware quantum emulator for prototyping the proposed quantum algorithm. The emulator has a fully-pipelined architecture and supports double-precision floating-point computations, resulting in high throughput and accuracy. The proposed hardware architectures are implemented on a high-performance reconfigurable computer (HPRC). In our experiments, we emulated quantum sorting circuits of up to 31 fully-entangled quantum bits on a single FPGA node of the HPRC platform. To the best of our knowledge, our effort is the first to investigate a reconfigurable hardware emulation of quantum sorting using bitonic networks and perfect shuffle.