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.
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.
Although the environmental effects, i.e., dissipation and decoherence seem to be the strongest adversaries in the quantum information realm, here, we address how dissipation can be harnessed for quantum state preparation and universal quantum computation. In this line, we propose a realistic scheme for hybrid classical-quantum neural networks based on dissipative two-qubit channels. In particular, we design a variational quantum circuit consisting of a set of universal quantum gates. We encode classical information in the initial states of a two-qubit system interacting with a global environment. This composite system plays the role of a dissipative quantum channel (DQC). A pooling layer concatenates the output states of the DQCs resulting in the outcome of the circuit. Both the DCQs and the pooling layer provide superposition and entanglement which are the key ingredients of any universal quantum computation protocol. Finally, we investigate the capability and adaptability of this model by doing some machine learning tasks. It is reasonable to postulate that a quantum computer based on DQCs may outperform a classical computer because, in contrast to the latter, the former is capable of producing atypical patterns through non-classical phenomena.
Among environmental effects, dissipation allows the stabilization of quantum resources, a fact that may accomplish key advantages over unitary quantum state manipulation. In this paper, we study an open quantum system composed of N two-mode Bose–Einstein condensates (BECs), namely, BEC qubits, interacting with their environments. Usually, the coupling of a system with its environment results in a dissipation process that washes out the quantum effects, but the environment may also play exactly the opposite role. Here, we show that the coupling of a BEC qubit with its local environments can be exploited to establish dissipative state engineering and dissipative quantum computation. Also, we discuss how to generate entanglement and transfer it using such macroscopic BEC qubits. Generally, the couplings can be manipulated such that the system is driven to a desired steady state. We demonstrate that the steady state of a BEC qubit just depends on the tunneling strength between its two modes and the features of the local environments. By preparing the proper physical conditions and adjusting the parameters involved in the model, it can be shown that the steady state of the system may coincide with its initial state. Also, the interaction between the BEC qubits and local environments can be engineered to provide physically controlled single- and two-qubit operations, which are necessary for performing dissipative universal quantum computation. With the prosperous development of quantum computing, such a system can be employed to implement quantum computers based on non-unitary operations.
Deep quantum neural networks may provide a promising way to achieve a quantum learning advantage with noisy intermediate-scale quantum devices. Here, we use deep quantum feed-forward neural networks capable of universal quantum computation to represent the mixed states for open quantum many-body systems and introduce a variational method with quantum derivatives to solve the master equation for dynamics and stationary states. Owning to the special structure of the quantum networks, this approach enjoys a number of notable features, including an efficient quantum analog of the back-propagation algorithm, resource-saving reuse of hidden qubits, general applicability independent of dimensionality and entanglement properties, as well as the convenient implementation of symmetries. As proof-of-principle demonstrations, we apply this approach to both one-dimensional transverse field Ising and two-dimensional ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ models with dissipation, and show that it can efficiently capture their dynamics and stationary states with a desired accuracy.
Quantum computing is one of the most exciting research areas of the last decades. At the same time, methods of machine learning have started to dominate science, industry and our everyday life. In this thesis we combine these two essential research topics of the 21st century and introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are capable of universal quantum computation and have low memory requirements while training. We start the discussion of this interdisciplinary topic by introducing artificial neural networks, which are a very common tool in classical machine learning. Next, we give an overview on quantum information. Here we focus on quantum algorithms and circuits, which are used to implement quantum neural networks. Moreover, we explain the opportunities and challenges arising with today's quantum computers. The discussion of the architecture and training algorithm of the DQNNs forms the core of this work. These networks are optimised with training data pairs in form of input and desired output states and therefore can be used for characterising unknown or untrusted quantum devices. We not only demonstrate the generalisation behaviour of these quantum neural networks using classical simulations, but also implement them successfully on actual quantum computers. To understand the ultimate limits for such quantum machine learning methods, we discuss the quantum no free lunch theorem, which describes a bound on the probability that a quantum device, which can be modelled as a unitary process and is optimised with quantum examples, gives an incorrect output for a random input. This gives us a tool to review the learning behaviour of quantum neural networks in general and the DQNNs in particular. Moreover we expand the area of applications of DQNNs in two directions. In the first case, we include additional information beyond just the training data pairs: since quantum devices are always structured, the resulting data is always structured as well. We modify the DQNN's training algorithm such that knowledge about the graph-structure of the training data pairs is included in the training process and show that this can lead to better generalisation behaviour. Both the original DQNN and the DQNN including graph structure are trained with data pairs in order to characterise an underlying relation. However, in the second extension of the algorithm we aim to learn characteristics of a set of quantum states in order to extend it to quantum states which have similar properties. Therefore we build a generative adversarial model where two DQNNs, called the generator and discriminator, are trained in a competitive way. Overall, we observe that DQNNs can not only be trained efficiently but also, similar to their classical counterparts, modified to suit different applications.
Abstract We study the dissipative stabilization of entangled states in arrays of quantum systems. Specifically, we are interested in the states of qubits (spin- 1 / 2 ) which may or may not interact with one or more cavities (bosonic modes). In all cases only one element, either a cavity or a qubit, is lossy and irreversibly coupled to a reservoir. When the lossy element is a cavity, we consider a squeezed reservoir and only interactions which conserve the number of cavity excitations. Instead, when the lossy element is a qubit, pure decay and a properly selected structure of XY-interactions are taken into account. We show that in all cases, in the steady state, many pairs of distant, non-directly interacting qubits, which cover the whole array, can get entangled in a stationary way, by means of the interplay of dissipation and local interactions.
Quantum state classification and entanglement quantification are of significant importance in the fundamental research of quantum information science and various quantum applications. Traditional methods, such as quantum state tomography, face exponential measurement demands with increasing numbers of qubits, necessitating more efficient approaches. Recent work has shown promise in using artificial neural networks (ANNs) for quantum state analysis. However, existing ANNs may falter when confronted with states affected by dephasing noise, especially with limited data and computational resources. In this study, we employ a machine-learning approach to investigate the disentanglement process in two-qubit systems in the presence of dephasing noise. Our findings highlight the limitations of general state-trained ANNs in classifying states under dephasing noise. Specialized ANN algorithms, tailored for classifying states and quantifying entanglement in such noisy environments, demonstrate excellent performance using only a subset of tomographic features.