Hyperentanglement-based quantum reservoir computing

Claudio Conti

Keisuke Fujii, Kohei Nakajima

Bao‐Cang Ren, Deng Fu-Guo

Photon system is a promising candidate for quantum information processing, and it can be used to achieve some important tasks with the interaction between a photon and an atom (or a artificial atom), such as the transmission of secret information, the storage of quantum states, and parallel quantum computing. Several degrees of freedom (DOFs) of a photon system can be used to carry information in the realization of quantum information processing, such as the polarization, spatial-mode, orbit-angular-momentum, time-bin, and frequency DOFs. A hyperparallel quantum computer can implement the quantum operations on several DOFs of a quantum system simultaneously, which reduces the operation time and the resources consumed in quantum information processing. The hyperparallel quantum operations are more robust against the photonic dissipation noise than the quantum computing in one DOF of a photon system. Hyperentanglement, defined as the entanglement in several DOFs of a quantum system, can improve the channel capacity and the security of long-distance quantum communication, and it can also be conductive to completing some important tasks in quantum communication. Hyperentangled Bell-state analysis is used to completely distinguish the 16 hyperentangled Bell states, which is very useful in high-capacity quantum communication protocols and quantum repeaters. In order to depress the effect of noises in quantum channel, hyperentanglement concentration and hyperentanglement purification are required to improve the entanglement of the quantum systems in long-distance quantum communication, which is also very useful in high-capacity quantum repeaters. Hyperentanglement concentration is used to distill several nonlocal photon systems in a maximally hyperentangled state from those in a partially hyperentangled pure state, and hyperentanglement purification is used to distill several nonlocal photon systems in a high-fidelity hyperentangled state from those in a mixed hyperentangled state with less entanglement. In this reviewing article, we review some new applications of photon systems with multiple DOFs in quantum information processing, including hyperparallel photonic quantum computation, hyperentangled-Bell-state analysis, hyperentanglement concentration, and hyperentanglement purification.

Saud Čindrak, Brecht Donvil, Kathy Lüdge +1 more

We propose a scheme that can enhance the performance and reduce the computational cost of quantum reservoir computing. Quantum reservoir computing is a computing approach which aims at utilizing the complexity and high dimensionality of small quantum systems, together with the fast trainability of reservoir computing, in order to solve complex tasks. The suitability of quantum reservoir computing for solving temporal tasks is hindered by the collapse of the quantum system when measurements are made. This leads to the erasure of the memory of the reservoir. Hence, for every output, the entire input signal is needed to reinitialize the reservoir, leading to quadratic time complexity. Another critical issue for the hardware implementation of quantum reservoir computing is the need for an experimentally accessible means of tuning the nonlinearity of the quantum reservoir. We present an approach which addresses both of these issues. We propose artificially restricting the memory of the quantum reservoir by only using a small number inputs to reinitialize the reservoir after measurements are performed. This strongly influences the nonlinearity of the reservoir response due to the influence of the initial reservoir state, while also substantially reducing the number of quantum operations needed to perform time-series prediction tasks due to the linear rather than quadratic time complexity. The reinitialization length therefore provides an experimental accessible means of tuning the nonlinearity of the response of the reservoir, which can lead to significant task-specific performance improvement. We numerically study the linear and quadratic algorithms for a fully connected transverse Ising model and a quantum processor model. Published by the American Physical Society 2024

Daniel Mo Houshmand, Q | D∂rıα⟩

Reservoir computing exploits high-dimensional nonlinear dynamics to solve temporal prediction tasks with minimal training cost. We investigate Topological Quantum Reservoir Computing (TQRC), which proposes to harness the braiding dynamics of Fibonacci anyons as quantum reservoirs. Our comprehensive analysis reveals a fundamental tension: the very properties that make topological systems attractive for quantum computation (unitary evolution and information preservation) fundamentally oppose the Echo State Property (ESP) required for reservoir computing. We demonstrate rigorously that pure unitary TQRC violates the ESP: unitary evolution preserves distances in Hilbert space, preventing the fading memory necessary for reservoir computing. On Mackey-Glass time series benchmarks, pure unitary TQRC achieves NRMSE ≈ 1.0 (equivalent to random guessing). Introducing controlled dissipation recovers functional reservoir dynamics (best NRMSE = 0.44), but at the cost of sacrificing topological protection. Critically, we show that classical Echo State Networks outperform dissipative TQRC by 20× at equivalent state-space dimension (ESN NRMSE = 0.02 vs. TQRC NRMSE = 0.44 for d = 13). We identify four root causes: (1) probability readout constrains states to the simplex, (2) measurement destroys phase information, (3) | • | 2 provides weaker nonlinearity than tanh, and (4) structured braid matrices limit state-space utilization. These results constitute a no-go theorem for topological quantum reservoir computing: topological protection and reservoir computing functionality represent fundamentally competing requirements. This finding provides essential guidance for the quantum machine learning community, establishing that topological protection should not be pursued as a route to quantum reservoir computing advantage.