A Molecular Computing Approach to Solving Optimization Problems via Programmable Microdroplet Arrays

Abstract

The search for novel forms of computing that show advantages as alternatives to the dominant von-Neuman model-based computing is important as it will enable different classes of problems to be solved. By using droplets and room-temperature processes, molecular computing is a promising research direction with potential biocompatibility and cost advantages. In this work, we present a new approach for computation using a network of chemical reactions taking place within an array of spatially localized droplets whose contents represent bits of information. Combinatorial optimization problems are mapped to an Ising Hamiltonian and encoded in the form of intra- and inter- droplet interactions. The problem is solved by initiating the chemical reactions within the droplets and allowing the system to reach a steady-state; in effect, we are annealing the effective spin system to its ground state. We propose two implementations of the idea, which we ordered in terms of increasing complexity. First, we introduce a hybrid classical-molecular computer where droplet properties are measured and fed into a classical computer. Based on the given optimization problem, the classical computer then directs further reactions via optical or electrochemical inputs. A simulated model of the hybrid classical-molecular computer is used to solve boolean satisfiability and a lattice protein model. Second, we propose architectures for purely molecular computers that rely on pre-programmed nearest-neighbour inter-droplet communication via energy or mass transfer.

Polaritonic XY-Ising machine

“…The term "pure" indicates that the system can operate at its own physical time-scale, i. e. picosecond scale for the polariton condensation. Among other pure physical simulators are the time-delay CIM [64] and the recently proposed pure molecular simulator [9]. The absolute coupling scheme with the hybrid-classical implementation as well as the relative coupling scheme with either of the proposed implementations would lead to the classical hybrid polariton simulators with an operational time limited by the frequency of the SLM.…”

“…The absolute coupling scheme with the hybrid-classical implementation as well as the relative coupling scheme with either of the proposed implementations would lead to the classical hybrid polariton simulators with an operational time limited by the frequency of the SLM. These approaches would be reminiscent of the CIM with a measurement feedback via FPGAs [2] or hybrid molecular simulator [9]. Table : Optimisation of the Ising and XY spin Hamiltonians with relative and absolute coupling models on unweighted MaxCut problems of size  and  with edge density ..…”

“…Various physical systems have recently emerged as unconventional computing platforms with a potential to successfully compete against the established state-ofthe-art classical techniques in solving large-scale combinatorial optimisation problems. Among the newly proposed computational machines are the coherent Ising machine (CIM) based on the degenerate Optical Parametric Oscillators (OPOs) [1][2][3], a CMOS-based Fujitsu digital annealer [4], an all-electronic oscillator-based Ising machine [5], a simulated bifurcation Toshiba machine [6], a spatial light modulator (SLM) based photonic Ising machine [7], an optical simulator with the injectionlocked multicore fibre lasers [8], and a molecular computing machine on a programmable microdroplet array [9]. All these approaches aim to achieve a much faster, more efficient, and more accurate way of solving a particular class of optimisation problems, namely the quadratic unconstrained binary optimisation (QUBO) problem.…”

Microwave Photonic Ising Machine

“…A large-scale Ising machine operates under room temperature can be achieved by using molecular spin, but it takes a long time of hundreds of seconds to optimize due to the limited speeds of molecular motions and chemical reactions (16). By the use of quantum superconducting or degenerate optical parametric oscillator (DOPO) spins, large-scale Ising machines have been implemented with computation acceleration.…”

“…Many Ising machines, e.g. based on trapped ions (12,13), superconducting circuits (14), molecules (15,16), and optical systems (17)(18)(19)(20)(21) have been reported. The key features of these Ising spins are shown in Fig.…”