We present numerical simulation of a six-qubit quantum reservoir network with an output implemented on a 5-dimensional decoherence-free subspace (DFS), working as a classifier between entangled and product states of the input quantum system, fed to the reservoir during a finite learning time. Since the dynamics of DFS is not affected by external fluctuations, no cooling is required, and the proposed model seems a promising candidate for future quantum artificial intelligence systems working at room temperatures and free of huge energy consumption.
We present numerical simulation of a six-qubit quantum reservoir network with an output implemented on a 5-dimensional decoherence-free subspace (DFS), working as a classifier between entangled and product states of the input quantum system, fed to the reservoir during a finite learning time. Since the dynamics of DFS is not affected by external fluctuations, no cooling is required, and the proposed model seems a promising candidate for future quantum artificial intelligence systems working at room temperatures and free of huge energy consumption.
The idea of coding the information in decoherence-free subspaces (DFS) to avoid decoherence in quantum computations has been receiving a lot of attention in circuit-based quantum computations, since first proposed by Zanardi & Rasetti [1] (Phys. Rev. Lett., 1997). Following [2] (Altaisky & Kaputkina, JISST, 2025), we study the possibility to harness DFS to quantum machine learning, where no explicit algorithm is present, but the quantum system learns to classify data. We have shown that a simple classification problem of distinguishing between 2-qubit product states and 2-qubit entangled states can be solved by 4-qubit quantum reservoir [3] (Ghosh, et al., npj Quantum Inf., 2019), the output of which we fed to decoherence-free subspaces.
The intersection of quantum information processing and machine learning has recently at-tracted considerable interest within the physics and artificial intelligence communities. From a physical perspective, quantum computing offers fundamentally new modes of information processing, enabled by superposition, interference, and entanglement, which can lead to ad-vantages in computational speed and resource efficiency over classical approaches. These developments have motivated the exploration of machine learning paradigms that lever-age quantum dynamics as a computational resource. In parallel, reservoir computing—a non–von Neumann and neuromorphic computing framework—has gained attention due to its reliance on high-dimensional dynamical systems, in-memory computation, and low en-ergy consumption. Quantum reservoir computing extends this paradigm by exploiting the intrinsic dynamics of quantum many-body systems, such as spin networks, to process tem-poral information. Despite growing interest in quantum reservoir architectures, the role of genuinely quantum resources, in particular entanglement, in determining their information-processing capabilities remains incompletely understood. In this thesis, we study a distributed spin-network reservoir in which two independent time series are injected into separate qubits. Using short-term memory capacity as an opera-tional measure, we analyze how information introduced at distinct sites propagates through the network and how different entanglement structures contribute to storing and combining past inputs. Focusing on bilinear memory tasks, which require reconstructing the product of the two inputs at various delays, we probe temporal memory. Due to the computational cost associated with simulating open quantum many-body dynamics, the present study focuses on a minimal spin-network architecture consisting of four qubits, with two qubits serving as input nodes that receive independent time series. Even for such moderate system sizes, the numerical integration of the open-system dynamics are computationally demanding. Nevertheless, this minimal setting already captures the essential mechanisms of distributed information processing in quantum reservoirs. By computing the logarithmic negativity across different bipartitions of the reservoir, we investigate how memory performance relates to the underlying entanglement structure. We find that the short-term memory capacity is maximized at relatively weak coupling strengths, where entanglement is present but remains moderate. Among the various bipar-titions, the entanglement between the two input qubits consistently plays the most promi-nent role in learning performance. In this optimal regime, the reservoir exhibits long-lived memory, while a characteristic reduction in performance at zero delay, observed across all frequencies, reflects the finite time required for information to propagate through the sys-tem. Taken together, these results indicate that effective learning in distributed quantum reservoir computing is enabled by moderate, well-structured entanglement, rather than by maximal correlations.
Quantum reservoir computing is a promising approach to quantum neural networks capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits are limited by low connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computation, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures.
Quantum reservoir computing is a promising approach for quantum neural networks, capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits suffer from limited connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits: with just two coupled quantum oscillators, we create a quantum reservoir comprising up to 81 neurons. We obtain state-of-the-art accuracy of 99 % on benchmark tasks that otherwise require at least 24 classical oscillators to be solved. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computing, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures, with billions of neurons implemented with only 10 coupled quantum oscillators.
We present a scheme to drive a finite-dimensional quantum system into the decoherence-free subspaces (DFS) by Lyapunov control. Control fields are established by Lyapunov function. This proposal works well for both closed and open quantum systems, with replacing the DFS by desired subspaces for closed systems. An example which consists of a four-level system with three degenerate states driven by three lasers is presented to gain further insight on the scheme. Numerical simulations for the dynamics of the system are performed and the results are good.
Today's quantum processors composed of fifty or more qubits have allowed us to enter a computational era where the output results are not easily simulatable on the world's biggest supercomputers. What we have not seen yet, however, is whether or not the complexity achievable with such quantum processors would ever be useful for any practical applications. In the quantum neural network approach, there has been an expectation that the Hilbert space can serve as a computational resource by providing a large feature space; however, it is not understood, nor illustrated in what way the Hilbert space provides that computational power. In this work we introduce a resource-efficient quantum neural network model with a focus on the role of the feature space the quantum processors can give. Then we apply it for classification tasks, showing a quantum advantage in terms of the physical resources needed to realize the neural network. To facilitate the Hilbert space as a large feature space, we utilize scale-free networks that can be generated in a discrete-time crystal model. The virtue of this approach is in both its theoretical simplicity and its practical applicability: our quantum neural network model is simple enough to identify the role of the Hilbert space as the feature space, and, furthermore, can be implemented with current technology. Our model does not require optimization of the quantum processor, and hence once the quantum processor has been set, it can be used for other different classification problems without any changes in the quantum processor itself.