Efficient Computation Using Spatial-Photonic Ising Machines: Utilizing Low-Rank and Circulant Matrix Constraints

https://arxiv.org/abs/2406.01400

We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically affected by the rank and precision of the coupling matrices. By developing and assessing advanced decomposition techniques, we expand the range of problems SPIMs can solve, overcoming the limitations of traditional Mattis-type matrices. Our approach accommodates a diverse array of coupling matrices, including those with inherently low ranks, applicable to complex NP-complete problems. We explore the practical benefits of low-rank approximation in optimization tasks, particularly in financial optimization, to demonstrate the real-world applications of SPIMs. Finally, we evaluate the computational limitations imposed by SPIM hardware precision and suggest strategies to optimize the performance of these systems within these constraints.

Optimal quantum key distribution networks: capacitance versus security

The rate and security of quantum communications between users placed at arbitrary points of a quantum communication network depend on the structure of the network, on its extension and on the nature of the communication channels. In this work we propose a strategy for the optimization of trusted-relays based networks that intertwines classical network approaches and quantum information theory. Specifically, by suitably defining a quantum communication efficiency functional, we identify the optimal quantum communication connections through the network by balancing security and the quantum communication rate. The optimized network is then constructed as the network of the maximal quantum communication efficiency connections and its performance is evaluated by studying the scaling of average properties as functions of the number of nodes and of the network spatial extension.

https://www.nature.com/articles/s41534-024-00828-7

EIC Project HEISINGBERG launched !

The EU project HEISINGBERG has started!

This project is funded by the EIC-Pathfinder initiative of the European Innovation Council for innovative Quantum technologies.

The project leverages our Spatial Ising Machine (SPIM) device and aims at a new generation of programmable and quantum annealers.

For details, have a look at the HEISINGBERG website.

HEISINGBERG logo and website

See also

Hyperscaling in the Coherent Hyperspin Machine in PRL !

Classical and quantum systems are used to simulate the Ising Hamiltonian, an essential component in large-scale optimization and machine learning. However, as the system size increases, devices like quantum annealers and coherent Ising machines face an exponential drop in their success rate. Here, we introduce a novel approach involving high-dimensional embeddings of the Ising Hamiltonian and a technique called “dimensional annealing” to counteract the decrease in performance. This approach leads to an exponential improvement in the success rate and other performance metrics, slowing down the decline in performance as the system size grows. A thorough examination of convergence dynamics in high-performance computing validates the new methodology. Additionally, we suggest practical implementations using technologies like coherent Ising machines, all-optical systems, and hybrid digital systems. The proposed hyperscaling heuristics can also be applied to other quantum or classical Ising devices by adjusting parameters such as nonlinear gain, loss, and nonlocal couplings.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.017301

See arXiv post

Optimal quantum communication networks: capacitance versus security

https://arxiv.org/abs/2312.04221

The rate and security of quantum communications between users placed at arbitrary points of a quantum communication network depend on the structure of the network, on its extension and on the nature of the communication channels. In this work we propose a strategy of network optimization that intertwines classical network approaches and quantum information theory. Specifically, by suitably defining a quantum efficiency functional, we identify the optimal quantum communication connections through the network by balancing security and the quantum communication rate. The optimized network is then constructed as the network of the maximal quantum efficiency connections and its performance is evaluated by studying the scaling of average properties as functions of the number of nodes and of the network spatial extension.