SRBB-Based Quantum State Preparation

2025-03-17

AI Summary

This work addresses the fundamental challenge of scalable approximate quantum state preparation in multi-qubit systems. We propose a variational quantum circuit framework based on the Standard Recursive Block Basis (SRBB), introducing its hierarchical structure—previously unexplored in variational state preparation—to establish an explicit mapping between variational parameters and the topology of the SU(2ⁿ) Lie group. Leveraging constraints from its diagonal subalgebra, our approach significantly reduces CNOT count and circuit depth. Integrating a variational quantum neural network with a multi-objective loss function (fidelity, trace distance, Frobenius norm) and a hybrid Adam–Nelder-Mead optimizer, we achieve high-fidelity preparation in 4-qubit simulations and demonstrate feasibility on real quantum hardware. The method jointly optimizes resource efficiency and preparation accuracy, revealing the efficacy of geometry-driven circuit design while identifying scalability bottlenecks inherent to current architectures.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Intelligent Robots: State Estimation

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: Foundation models and LLMs for Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In this work, a scalable algorithm for the approximate quantum state preparation problem is proposed, facing a challenge of fundamental importance in many topic areas of quantum computing. The algorithm uses a variational quantum circuit based on the Standard Recursive Block Basis (SRBB), a hierarchical construction for the matrix algebra of the $SU(2^n)$ group, which is capable of linking the variational parameters with the topology of the Lie group. Compared to the full algebra, using only diagonal components reduces the number of CNOTs by an exponential factor, as well as the circuit depth, in full agreement with the relaxation principle, inherent to the approximation methodology, of minimizing resources while achieving high accuracy. The desired quantum state is then approximated by a scalable quantum neural network, which is designed upon the diagonal SRBB sub-algebra. This approach provides a new scheme for approximate quantum state preparation in a variational framework and a specific use case for the SRBB hierarchy. The performance of the algorithm is assessed with different loss functions, like fidelity, trace distance, and Frobenius norm, in relation to two optimizers: Adam and Nelder-Mead. The results highlight the potential of SRBB in close connection with the geometry of unitary groups, achieving high accuracy up to 4 qubits in simulation, but also its current limitations with an increasing number of qubits. Additionally, the approximate SRBB-based QSP algorithm has been tested on real quantum devices to assess its performance with a small number of qubits.

Problem

• Develops scalable algorithm for quantum state preparation.
• Uses SRBB to reduce CNOT gates and circuit depth.
• Tests algorithm on real quantum devices for accuracy.

Innovation

• Uses SRBB-based variational quantum circuits
• Reduces CNOTs and circuit depth exponentially
• Approximates states via scalable quantum neural networks