Quantum Multiplexer Simplification for State Preparation

2024-09-09

ACM Transactions on Quantum Computing

AI Summary

In quantum state preparation (QSP), multi-controlled gates induce excessive circuit depth and CNOT count, severely hindering compilation efficiency and execution performance. To address this, we propose a quantum multiplexer simplification method based on substate decomposability detection—first jointly modeling quantum state factorization identification and control-qubit reduction in multiplexers. Our approach preserves output fidelity while systematically eliminating redundant control logic, without altering the target state representation. By automatically identifying and exploiting local separable structures, it reduces both circuit depth and CNOT count. Experimental evaluation demonstrates order-of-magnitude speedups in both compilation and execution time over state-of-the-art QSP algorithms; these gains scale with qubit count and are particularly pronounced for medium-scale, non-entanglement-dominant quantum state initialization tasks.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Detecting factorable quantum states to improve compilation efficiency
• Simplifying quantum multiplexers by eliminating control gates
• Reducing circuit depth and CNOT gates for faster execution

Innovation

• Detects quantum state factorization into substates
• Simplifies circuits by eliminating multiplexer controls
• Reduces CNOT gates and improves compilation time