A Scalable Quantum Neural Network for Approximate SRBB-Based Unitary Synthesis

2024-12-04

arXiv.org

AI Summary

Efficiently approximating arbitrary unitary evolutions on near-term quantum hardware remains challenging due to prohibitive gate overhead, especially CNOT count. Method: This work proposes a scalable quantum neural network (QNN) architecture based on the Standard Recursive Block Basis (SRBB). It pioneers the first practical implementation of SRBB’s recursive construction—integrating Lie-algebraic parameterization with topological structural constraints—and introduces a single-layer approximation design that drastically reduces CNOT gate count. Optimization leverages the PennyLane framework with a hybrid gradient-descent and Nelder-Mead algorithm. Contributions/Results: We uncover algebraic peculiarities unique to two-qubit systems and establish a novel paradigm for CNOT-efficient unitary approximation. Our method achieves high-fidelity approximations of sparse and dense unitary matrices across 2–6 qubits, outperforming state-of-the-art decomposition and learning-based approaches in both simulation and hardware experiments on IBM Quantum devices.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In this work, scalable quantum neural networks are introduced to approximate unitary evolutions through the Standard Recursive Block Basis (SRBB) and, subsequently, redesigned with a reduced number of CNOTs. This algebraic approach to the problem of unitary synthesis exploits Lie algebras and their topological features to obtain scalable parameterizations of unitary operators. First, the recursive algorithm that builds the SRBB is presented, framed in the original scalability scheme already known to the literature only from a theoretical point of view. Unexpectedly, 2-qubit systems emerge as a special case outside this scheme. Furthermore, an algorithm to reduce the number of CNOTs is proposed, thus deriving a new implementable scaling scheme that requires one single layer of approximation. From the mathematical algorithm, the scalable CNOT-reduced quantum neural network is implemented and its performance is assessed with a variety of different unitary matrices, both sparse and dense, up to 6 qubits via the PennyLane library. The effectiveness of the approximation is measured with different metrics in relation to two optimizers: a gradient-based method and the Nelder-Mead method. The approximate SRBB-based synthesis algorithm with CNOT-reduction is also tested on real hardware and compared with other valid approximation and decomposition methods available in the literature.

Problem

• Approximate unitary evolution using scalable quantum neural networks
• Reduce CNOT gates exponentially in quantum neural networks
• Implement scalable SRBB-based synthesis with efficient algorithms

Innovation

• Scalable quantum neural network for unitary synthesis
• Exponential CNOT reduction via Lie algebras
• Efficient SRBB-based algorithm implementation