Abstract This study concerns with the evolution of entanglement in a quantum neural network (QNN) model that is locally in contact with data environments. As a valuable resource, duration of entanglement in quantum systems is extremely important. Therefore, the effect of various initial states on the occurrence or decay of entanglement are examined in the presence of information reservoirs. In this study, central spin model was investigated as a quantum version of neural networks inspired by biological models. The architecture of the model is based on a central spin system with two nodes where the nodes are coupled to independent spin baths. Numerical results show that initial state preparation has a profound effect on the fate of entanglement. The results show that the entanglement lifetime can be adjusted by engineering the reservoir states as well as the initial states of the system of interest. The results can be used to improve the performance of the formation or distribution of entanglement in realistic communication network states.
In this study, we propose a spin-star model for spin-(1/2) particles in order to examine the coherence dynamics of a quantum neural network (QNN) unit. Since quantum computing paradigm promises advantages over their classical counterparts, quantum versions of neural networks can be examined in this context. We focus on quantum coherence as a natural resource for quantum computing and investigate the central spin coherence of a spin star model in the time domain in a dissipative environment. More particularly, we investigate the extend to which the central spin coherence time would be prolonged under specific parameters and spin-coupling Hamiltonians in a Markov environment. We show that Ising-type spin coupling is not desirable since it rapidly diminishes the coherence time in a dissipative environment.
This paper investigates the potential of quantum neural networks (QNNs) enhanced by non-Markovian dynamics. Traditional Markovian QNNs suffer from limitations in capturing long-range dependencies, a crucial aspect in complex data processing. We propose a novel QNN architecture that incorporates quantum memory and entanglement to facilitate non-Markovian information processing. This approach allows the network to retain and utilize the entire past history of the input, fundamentally altering the dynamics of information flow. Through theoretical analysis and mathematical formulations, we demonstrate how this architecture can significantly improve the network's ability to learn and represent complex patterns, particularly those exhibiting long-range correlations. Specifically, we introduce a modified update rule leveraging the concept of quantum memory and entanglement, expressed as: $ \Delta w_{ij} = \alpha \cdot E[\rho(t)|x_1, x_2, ..., x_K] \cdot \langle \psi_i | \rho(t) | \psi_j \rangle - (1 - \alpha) \cdot w_{ij}$ Where: * $ \Delta w_{ij}$ is the change in the synaptic weight between neurons *i* and *j*. *
α is the learning rate. *
E[ρ(t)∣x1,x2,...,xK] represents the expected state of the quantum memory at time *t*, given the entire input sequence
x1,x2,...,xK. *
ρ(t) is the density matrix representing the quantum state at time *t*. *
⟨ψi∣ρ(t)∣ψj⟩ is the inner product between the quantum states
ψi and
ψj within the density matrix
ρ(t). *
wij is the current synaptic weight between neurons *i* and *j*. The core of our innovation lies in the utilization of quantum memory, modeled as a quantum state
ρ(t), which retains information about the entire past sequence. The entanglement between neurons further enables correlated updates, bypassing the limitations of Markovian models that only consider immediate dependencies. We explore the impact of varying the strength of entanglement and the capacity of the quantum memory on the network's performance using mathematical models. The results suggest a significant improvement in accuracy and convergence speed compared to standard Markovian QNNs when dealing with datasets exhibiting long-range dependencies. Further investigation into the scalability and practical implementation of this architecture is warranted.
This study examines the disentanglement evolution of a quantum neural network (QNN) model locally in contact with data environments. As a valuable resource, duration of entanglement in quantum systems is extremely significant. Therefore, the effect of various initial states to the generation or decay of entanglement has been investigated under pure and maximally mixed environmental states as two limit cases. Numerical results show that initial state preparation has a profound impact on the fate of entanglement even in the course of maximally noisy environments. The obtained results reveal that the decay of entanglement of the quantum neural network (with flip-flop type interaction) is affected by the initial preparation of the Bell state even in the presence of pure state environmental monitoring. Depending on the results it’s also suggested to begin with coherent product states since it provides robust entanglement generation with longer disentanglement time during the open quantum system evolution.
Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core challenge in understanding, implementing and ultimately using quantum neural networks is that they represent many-body systems with an exponentially large Hilbert space, in combination with a large parameter search space. Moreover, noise -- which is inherent to any quantum measurement -- sets practical limits for the estimation of training loss. Here, we study physics-informed large-scale quantum neural networks that are trained through a finite number of noisy loss function measurements. We show that this architecture permits the construction of nontrivial decision boundaries that enable the classification of quantum states through measuring an order parameter. Our approach can directly process quantum data that is output from quantum simulators and computers and is well suited for implementation on current hardware. Moreover, owed to a close link between the neural network dynamics and the evolution of Markovian open many-body quantum systems, one may expect a certain robustness to noise, which is ubiquitous in the current NISQ era.
This study is related to the fate of entanglement for initial separable states in a quantum neural network (QNN) model, which is in contact with the data environments locally. The duration of entanglement in quantum systems becomes extremely important when we consider it as a valuable resource. Thus, the effects of various initial states on the occurrence or decay of entanglement are investigated in the presence of information reservoirs. Especially in this study, central spin model has been examined as a quantum version of neural networks by taking inspiration from the biological models. Our model consists of a central spin system with two nodes to which the nodes are coupled to independent spin baths. Numerical results clearly show that different initial states have a profound effect on the fate of the entanglement. It also shows that the entanglement lifetime can be adjusted by regulating the reservoir states. The results can be used in realistic communication network situations to improve the performance of entanglement formation or distribution.