Low-Rank Combinatorial Optimization and Statistical Learning by Spatial Photonic Ising Machine.

The spatial photonic Ising machine (SPIM) [13D. Pierangeli et al., Large-Scale Photonic Ising Machine by Spatial Light Modulation, Phys. Rev. Lett. 122, 213902 (2019).PRLTAO0031-900710.1103/PhysRevLett.122.213902] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. The primitive version of the SPIM, however, can accommodate Ising problems with only rank-one interaction matrices. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, it acquires the learning ability of Boltzmann machines. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions. Thus, the proposed model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.

Spatial-photonic Ising machine by space-division multiplexing with physically tunable coefficients of a multi-component model.

This paper proposes a space-division multiplexed spatial-photonic Ising machine (SDM-SPIM) that physically calculates the weighted sum of the Ising Hamiltonians for individual components in a multi-component model. Space-division multiplexing enables tuning a set of weight coefficients as an optical parameter and obtaining the desired Ising Hamiltonian at a time. We solved knapsack problems to verify the system's validity, demonstrating that optical parameters impact the search property. We also investigated a new dynamic coefficient search algorithm to enhance search performance. The SDM-SPIM would physically calculate the Hamiltonian and a part of the optimization with an electronics process.

Quantitative analysis of nonlinear optical input/output of a quantum-dot network based on the echo state property.

The echo state property, which is related to the dynamics of a neural network excited by input driving signals, is one of the well-known fundamental properties of recurrent neural networks. During the echo state, the neural network reveals an internal memory function that enables it to remember past inputs. Due to the echo state property, the neural network will asymptotically update its condition from the initial condition and is expected to exhibit temporally nonlinear input/output. As a physical neural network, we fabricated a quantum-dot network that is driven by sequential optical-pulse inputs and reveals corresponding outputs, by random dispersion of quantum-dots as its components. In the network, the localized optical energy of excited quantum-dots is allowed to transfer to neighboring quantum-dots, and its stagnation time due to multi-step transfers corresponds to the hold time of the echo state of the network. From the experimental results of photon counting of the fluorescence outputs, we observed nonlinear optical input/output of the quantum-dot network due to its echo state property. Its nonlinearity was quantitatively verified by a correlation analysis. As a result, the relation between the nonlinear input/outputs and the individual compositions of the quantum-dot network was clarified.

Optical decomposition of DNA gel and modification of object mobility on micrometre scale.

DNA gels can be engineered to exhibit specific properties through the choice of DNA sequences and modification with dye molecules, and can therefore be useful in biomedical applications such as the detection of biomolecules. State transitions of DNA gels on the micrometre scale can generate a viscosity gradient, which can be used to modify the mobility of micrometre-sized objects. In this paper, we propose a method for changing the viscosity of DNA gels using optical decomposition. The use of light allows for decomposition on the micrometre scale, which can be used to achieve patterned viscosity changes within DNA gels. Decomposition was induced by thermal energy released through non-radiative relaxation of excited quenchers. We demonstrated the decomposition of DNA gels in response to irradiation patterns on the micrometre scale. In addition, as a result of changes in DNA gel viscosity due to decomposition, the mobility of polystyrene beads was shown to increase. This technique could provide a new optical approach for controlling the mobility of micrometre-sized objects.

Photothermal fabrication of microscale patterned DNA hydrogels.

This paper introduces a method for fabricating microscale DNA hydrogels using irradiation with patterned light. Optical fabrication allows for the flexible and tunable formation of DNA hydrogels without changing the environmental conditions. Our scheme is based on local heat generation via the photothermal effect, which is induced by light irradiation on a quenching species. We demonstrate experimentally that, depending on the power and irradiation time, light irradiation enables the creation of local microscale DNA hydrogels, while the shapes of the DNA hydrogels are controlled by the irradiation patterns.