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arXiv:2211.16423 · Physical Review A

Quantum collisional classifier driven by information reservoirs

Ufuk Korkmaz, Deniz Türkpençe

Published Jan 30, 2023• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.107.012432

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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.
The dissipative model of quantum computation is proven to be equivalent to its circuit model. Particularly, multi-qubit gates require time-dependent control with optimized parameters for some specific problems. One such problem is the simulation of a quantum version of a perceptron that classifies quantum information as binary using the framework of open quantum systems. In this scheme, a probe qubit is in contact with multiple, distinct quantum information-bearing environments and returns a binary decision depending on its amplitude parameter in its steady state. We refer to these environments as quantum information reservoirs. We choose a standard quantum collisional model in which the reservoir parameters can be defined in detail. In this study, we present the analytical results of the proposed classifier with an application to the superconductor quantum circuits for a single information reservoir. We exploit the additivity of quantum dynamic maps for dissipative processes in the weak coupling regime where optimized time-dependent control is not required to achieve the classification result. We show that the current state-of-the-art for superconducting circuits allows for the physical implementation of dissipative quantum information processing in the presence of information reservoirs with realistic parameters.
In this study, we show that as a result of weak interaction of different information environments structured with a single probe qubit, these environments can perform binary classification of the information they contain. In this way, we refer to these environments as quantum information baths because they consist of sequences of identical qubits in certain pure quantum states. A micro-maser like master equation has been developed to clearly describe the system dynamics analytically and the quantum states of different information reservoirs. The model can also be treated as a quantum neuron, due to the single-qubit probe that makes a binary decision depending on the reservoir parameters in its steady state. The numerical results of the repeated interaction process based on the divisibility and additivity of the quantum dynamic maps are compared with the analytical results. Besides being a single quantum classifier, the model we present can also serve as a basic unit of a quantum neural network within the framework of the dissipative model of quantum computing.
Quantum machine learning (QML) aims to embed the power of quantum computation with learning theory. Quan-tum noise and finding the best recipe for encoding classical information into a quantum register could be seen as challenges to overcome for computational performance. Classification of quantum information is a subtask for QML. In this study, we adopt a dissipative route for quantum data classification and examine the developed theory on a gradient descent-based learning task. In particular, we follow repeated interactions based on open quantum dynamics where the binary decision is encoded on a steady state. Based on the analytical results, we develop a cost function for training an open quantum neuron. We demonstrate that the dissipation-driven protocol is suitable for a supervised learning scheme.
Abstract Entangled state preparation and preservation are the cornerstones of any quantum information platform. However , the strongest adversaries in quantum information science are unwanted environmental effects such as decoherence and dissipation. Here, we address how to control and harness the dissipation that arises from the coupling of a system with its environment, to provide stationary entangled states for quantum machine learning. To do so, we design a dissipative quantum channel, i.e., a two-qubit system interacting with a squeezed vacuum field reservoir, and study the output state of the channel by solving the corresponding master equation, especially, in the small squeezing regime. We show that the time-dependent output state of the channel is the so-called two-qubit X-states that generalize many families of entangled two-qubit states. Also, by considering a general Bell diagonal state as the initial state of the system we reveal that this dissipative channel generates two well-known classes of entangled mixed state and Werner-like states in the steady-state regime. Moreover, this channel provides an efficient way to determine whether a given initial state results in a stationary entangled state or not. Finally, we examine the potential application of the designed two-qubit channel for quantum machine learning. Integrating the non-unitary transformation of the two-qubit channel and parallel-processed neural computing establishes the requirements for a meaningful quantum neural network.
By using the non-Markovian master equation, we investigate the effect of the cavity and the environment on the quantum Fisher information (QFI) of an atom qubit system in a dissipation cavity. We obtain the formulae of QFI for two different initial states and analyze the effect of the atom–cavity coupling and the cavity–reservoir coupling on the QFI. The results show that the dynamic behavior of the QFI is obviously dependent on the initial atomic states, the atom–cavity coupling, and the cavity–reservoir coupling. The stronger the atom–cavity coupling, the quicker the QFI oscillates, and the slower the QFI decreases. In particular, the QFI will tend to be a stable value rather than zero if the atom–cavity coupling is large enough. On the other hand, the smaller the cavity–reservoir coupling, the stronger the non-Markovian effect, and the slower the QFI decays. In other words, choosing the best parameter can improve the accuracy of the parameter estimation. In addition, the physical explanation of the dynamic behavior of the QFI is given by means of the QFI flow.
This study concerns with the dynamics of a quantum neural network unit in order to examine the suitability of simple neural computing tasks. More specifically, we examine the dynamics of an interacting spin model chosen as a candidate of a quantum perceptron for closed and open quantum systems. We adopt a collisional model enables examining both Markovian and non-Markovian dynamics of the proposed quantum system. We show that our quantum neural network (QNN) unit has a stable output quantum state in contact with an environment carrying information content. By the performed numerical simulations one can compare the dynamics in the presence and absence of quantum memory effects. We find that our QNN unit is suitable for implementing general neural computing tasks in contact with a Markovian information environment and quantum memory effects cause complications on the stability of the output state.