A quantum neural network framework for scalable quantum circuit approximation of unitary matrices

In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of the neural networks are defined by product of exponential of...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Rohit Sarma Sarkar, Adhikari, Bibhas
Format: Article
Language:English
Subjects:
Approximation
Gates (circuits)
Lie groups
Mathematical analysis
Matrix algebra
Neural networks
Qubits (quantum computing)
Online Access:Get full text
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Summary:In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of the neural networks are defined by product of exponential of certain elements of the Standard Recursive Block Basis, which we introduce as an alternative to Pauli string basis for matrix algebra of complex matrices of order \(2^n\). The recursive construction of the neural networks implies that the quantum circuit approximation is scalable i.e. quantum circuit for an \((n+1)\)-qubit unitary can be constructed from the circuit of \(n\)-qubit system by adding a few CNOT gates and single-qubit gates.
ISSN:2331-8422