Quantum Multiplexer Simplification for State Preparation

TL;DR

This paper introduces an algorithm that simplifies quantum multiplexers in state preparation circuits, reducing circuit depth and gate count, especially for states with some unentanglement, leading to faster compilation times.

Contribution

The proposed method detects factorizability of quantum states to eliminate controls in multiplexers, improving efficiency over previous algorithms in runtime and compilation speed.

Findings

Reduces circuit depth and CNOT gates in quantum state preparation

Significantly improves runtime and compilation efficiency for larger qubit systems

Maintains competitive performance in circuit complexity compared to existing methods

Abstract

The initialization of quantum states or Quantum State Preparation (QSP) is a basic subroutine in quantum algorithms. In the worst case, general QSP algorithms are expensive due to the application of multi-controlled gates required to build the quantum state. Here, we propose an algorithm that detects whether a given quantum state can be factored into substates, increasing the efficiency of compiling the QSP circuit when we initialize states with some level of unentanglement. The simplification is done by eliminating controls of quantum multiplexers, significantly reducing circuit depth and the number of CNOT gates with a better execution and compilation time than the previous QSP algorithms. Considering efficiency in terms of depth and number of CNOT gates, our method is competitive with the methods in the literature. However, when it comes to run-time and compilation efficiency, our result is significantly better, and the experiments show that by increasing the number of qubits, the gap between the temporal efficiency of the methods increases.