Quantum disentanglement and computation

F. J. Duarte

Borja Aizpurua, Sukhbinder Singh, Román Orús

We address the problem of implementing bottleneck layers from classical pretrained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid classical-quantum models. Our approach begins with a compression step in which the target linear layer is represented as an effective matrix product operator (MPO) without degrading model performance. The MPO is then further disentangled into a more compact form. This enables a hybrid classical-quantum execution scheme, where the disentangling circuits are deployed on a quantum computer while the remainder of the network—including the disentangled MPO—runs on classical hardware. We introduce two complementary algorithms for MPO disentangling: (1) an disentangling variational method leveraging standard tensor network optimization techniques and (2) an disentangling gradient-descent-based approach. We validate these methods through a proof-of-concept translation of simple classical neural networks for MNIST and CIFAR-10 image classification into a hybrid classical-quantum form.

F.J. Duarte

Josh Green, Joshua Snow, Jingbo B Wang

Quantum state preparation represents a critical bottleneck for a broad class of quantum algorithms. In this work, we introduce the Schmidt Spectrum Optimisation (SSO) algorithm as an efficient and scalable approach for preparing quantum states described by Matrix Product States (MPS). The SSO algorithm employs a preparation-by-disentangling strategy by optimising circuit layers of two-qubit gates to progressively remove entanglement from a target state. Each circuit layer is computed sequentially and efficiently on a classical computer using tensor network optimisation techniques. Once the target state has been successfully disentangled, a quantum state-preparation circuit is formed by reversing the sequence of optimised disentangling layers. Across benchmarks including random MPS and MPS approximations to the ground-states of local Hamiltonians, we find that the SSO algorithm significantly improves upon prior variational and disentangling-based approaches, highlighting its potential as a scalable framework for quantum state preparation.

Juan Yao

Abstract In this work, we report a novel quantum state reconstruction process based on the disentanglement algorithm. We propose a sequential disentanglement scheme, which can transform an unknown quantum state into a product of computational zero states. The inverse evolution of the zero states reconstructs the quantum state up to an overall phase. By sequentially disentangling the qubits one by one, we reduce the required measurements with only individual qubit measurement and identify the transformation unitary efficiently. Variational quantum circuit and reinforcement learning methods are used for the quantum circuit design for continuous and discrete quantum gates implementation. Demonstrations with our proposal for the reconstruction of the random states are presented. Our method is universal and imposes no specific ansatz or constraint on the quantum state.

Luis de la Peña, Ana Marı́a Cetto, Andrea Valdés Hernández