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Sakarya University Journal of Science

Quantum Reservoir Parameter Estimation via Fisher Information

Ufuk Korkmaz, Deniz Türkpençe

Published Apr 25, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.16984/saufenbilder.1018716

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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.
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.
We find that the additivity of quantum information channels enables one to introduce a quantum classifier or a quantum decision maker. Proper measurement and sensing of temperature are of central importance to the realization of nanoscale quantum devices. Minimal classifiers may constitute the basic units for the physical quantum neural networks. We introduce a binary temperature classifier quantum model that operates in a thermal environment. In the present study, first the mathematical model was introduced through a two-level quantum system weakly coupled to the thermal reservoirs and it was demonstrated that the model faithfully classifies the temperature information of the reservoirs in the thermal steady state limit. A physical model by superconducting circuits composed of transmon qubits was also suggested.
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.
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.
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.