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International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT)

Mimicking an Information Reservoir by Superconducting Quantum Circuits

Ufuk Korkmaz, Cem Sanga, Deniz Türkpençe

Published Oct 21, 2021• 5 citations
Publisher

Abstract

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.

DOI
10.1109/ismsit52890.2021.9604610

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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.
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.
Engineered dissipation provides a powerful route to controlling and stabilizing quantum states in open systems. Superconducting circuits are particularly suited to this approach due to their tunable coupling to dissipative environments. Here we realize programmable local reservoirs for superconducting qubits through parametrically driven coupling to readout resonators, creating energy-selective incoherent pump and loss. Using coupled superconducting qubits, we autonomously stabilize entangled single-excitation states with fidelity up to 90.8%. We probe the stabilization dynamics under varying initial conditions and bath parameters, and implement robust classical shadow estimation for accurate and scalable state characterization. Finally, we numerically study a configuration where the engineered pump and loss share a common dissipative mode, leading to reservoir-mediated interference and classically correlated steady states. Our results demonstrate a scalable and hardware-efficient framework for dissipative preparation and control of correlated many-body states in superconducting circuits.
Reservoir computing is a temporal information processing system that exploits artificial or physical dissipative dynamics to learn a dynamical system and generate the target time-series. This paper proposes the use of real superconducting quantum computing devices as the reservoir, where the dissipative property is served by the natural noise added to the quantum bits. The performance of this natural quantum reservoir is demonstrated in a benchmark time-series regression problem and a practical problem classifying different objects based on temporal sensor data. In both cases the proposed reservoir computer shows a higher performance than a linear regression or classification model. The results indicate that a noisy quantum device potentially functions as a reservoir computer, and notably, the quantum noise, which is undesirable in the conventional quantum computation, can be used as a rich computation resource.
We analyze numerically the performance of Quantum Reservoir Computing (QRC) for statistical and financial problems. We use a reservoir composed of two superconducting islands coupled via their charge degrees of freedom. The key non-linear elements that provide the reservoir with rich and complex dynamics are the Josephson junctions that connect each island to the ground. We show that QRC implemented in this circuit can accurately classify complex probability distributions, including those with heavy tails, and identify regimes in correlated time series, such as periods of high volatility generated by standard econometric models. We find QRC to outperform some of the best classical methods when the amount of information is limited. This demonstrates its potential to be a noise-resilient quantum learning approach capable of tackling real-world problems within currently available superconducting platforms. We further discuss how to improve our QRC algorithm in real superconducting hardware to benefit from a much larger Hilbert space.
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.