Ufuk Korkmaz

The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard quantum circuit model, and implementing them based on hardware. However, the ability to capture the non-linear behavior in neural networks using a computation process that usually involves linear quantum mechanics principles remains a major challenge in both categories. In this study, a hardware-efficient quantum neural network operating as an open quantum system is proposed, which presents non-linear behaviour. The model's compatibility with learning processes is tested through the obtained analytical results. In other words, we show that this dissipative model based on repeated interactions, which allows for easy parametrization of input quantum information, exhibits differentiable, non-linear activation functions.

Significant progress in the construction of physical hardware for quantum computers has necessitated the development of new algorithms or protocols for the application of real-world problems on quantum computers. One of these problems is the power flow problem, which helps us understand the generation, distribution, and consumption of electricity in a system. In this study, the solution of a balanced 4-bus power system supported by the Newton-Raphson method is investigated using a newly developed dissipative quantum neural network hardware. This study presents the findings on how the proposed quantum network can be applied to the relevant problem and how the solution performance varies depending on the network parameters.

The promising performance increase offered by quantum computing has led to the idea of applying it to neural networks. Studies in this regard can be divided into two main categories: simulating quantum neural networks with the standard quantum circuit model, and implementing them based on hardware. However, the ability to capture the non-linear behavior in neural networks using a computation process that usually involves linear quantum mechanics principles remains a major challenge in both categories. In this study, a hardware-efficient quantum neural network operating as an open quantum system is proposed, which presents non-linear behaviour. The model's compatibility with learning processes is tested through the obtained analytical results. In other words, we show that this dissipative model based on repeated interactions, which allows for easy parametrization of input quantum information, exhibits differentiable, non-linear activation functions.

Today, the competition to build a quantum computer continues, and the number of qubits in hardware is increasing rapidly. However, the quantum noise that comes with this process reduces the performance of algorithmic applications, so alternative ways in quantum computer architecture and implementation of algorithms are discussed on the one hand. One of these alternative ways is the hybridization of the circuit-based quantum computing model with the dissipative-based computing model. Here, the goal is to apply the part of the algorithm that provides the quantum advantage with the quantum circuit model, and the remaining part with the dissipative model, which is less affected by noise. This scheme is of importance to quantum machine learning algorithms that involve highly repetitive processes and are thus susceptible to noise. In this study, we examine dissipative information transfer to a qubit model called Cat-Qubit. This model is especially important for the dissipative-based version of the binary quantum classification, which is the basic processing unit of quantum machine learning algorithms. On the other hand, Cat-Qubit architecture, which has the potential to easily implement activation-like functions in artificial neural networks due to its rich physics, also offers an alternative hardware opportunity for quantum artificial neural networks. Numerical calculations exhibit successful transfer of quantum information from reservoir qubits by a repeated-interactions-based dissipative scheme.

We investigate the open dynamics of a probe qubit weakly interacting with distinct qubit environments bearing quantum information. We show that the proposed dissipative model yields a binary classification of the reservoir qubits' quantum information in the steady state in the Bloch qubit parameter space, depending on the coupling rates. To describe the dissipation model dynamics, we have adopted the collision model, in which the input information parameters of the reservoir qubits are easily determined. We develop a generalized classification rule based on the results of the micromaserlike master equation where the classification can be described in terms of the Bloch parameters. Moreover, we show that the proposed classification scheme can also be achieved through quantum parameter estimation. Finally, we demonstrate that the proposed dissipative classification scheme is suitable for gradient descent-based supervised learning tasks.

We investigate the open dynamics of a probe qubit weakly interacting with distinct qubit environments bearing quantum information. We show that the proposed dissipative model yields a binary classification of the reservoir qubits' quantum information in the steady state in the Bloch qubit parameter space, depending on the coupling rates. To describe the dissipation model dynamics, we have adopted the collision model, in which the input information parameters of the reservoir qubits are easily determined. We develop a generalized classification rule based on the results of the micromaser-like master equation where the classification can be described in terms of the Bloch parameters. Moreover, we show that the proposed classification scheme can also be achieved through quantum parameter estimation. Finally, we demonstrate that the proposed dissipative classification scheme is suitable for gradient descent based supervised learning tasks.