The subset sum problem (SSP) is a typical nondeterministic-polynomial-time (NP)-complete problem that is hard to solve efficiently in time with conventional computers. Photons have the unique features of high propagation speed, strong robustness, and low detectable energy level and therefore can be promising candidates to meet the challenge. Here, we present a scalable chip built-in photonic computer to efficiently solve the SSP. We map the problem into a three-dimensional waveguide network through a femtosecond laser direct writing technique. We show that the photons sufficiently dissipate into the networks and search for solutions in parallel. In the case of successive primes, our approach exhibits a dominant superiority in time consumption even compared with supercomputers. Our results confirm the ability of light to realize computations intractable for conventional computers, and suggest the SSP as a good benchmarking platform for the race between photonic and conventional computers on the way toward "photonic supremacy."
The subset sum problem (SSP) is a typical nondeterministic-polynomial-time (NP)-complete problem that is hard to solve efficiently in time with conventional computers. Photons have the unique features of high propagation speed, strong robustness, and low detectable energy level and therefore can be promising candidates to meet the challenge. Here, we present a scalable chip built-in photonic computer to efficiently solve the SSP. We map the problem into a three-dimensional waveguide network through a femtosecond laser direct writing technique. We show that the photons sufficiently dissipate into the networks and search for solutions in parallel. In the case of successive primes, our approach exhibits a dominant superiority in time consumption even compared with supercomputers. Our results confirm the ability of light to realize computations intractable for conventional computers, and suggest the SSP as a good benchmarking platform for the race between photonic and conventional computers on the way toward "photonic supremacy."
Nondeterministic-polynomial-time (NP)-complete problems are widely involved in various real-life scenarios but are still intractable in being solved efficiently on conventional computers. It is of great practical significance to construct versatile computing architectures that solve NP-complete problems with computational advantage. Here, we present a reconfigurable integrated photonic processor to efficiently solve a benchmark NP-complete problem, the subset sum problem. We show that in the case of successive primes, the photonic processor has genuinely surpassed electronic processors launched recently by taking advantage of the high propagation speed and vast parallelism of photons and state-of-the-art integrated photonic technology. Moreover, we are able to program the photonic processor to tackle different problem instances, relying on the tunable integrated modules, variable split junctions, which can be used to build a fully reconfigurable architecture potentially allowing 2N configurations at most. Our experiments confirm the potential of the photonic processor as a versatile and efficient computing platform, suggesting a possible practical route to solving computationally hard problems at a large scale.
NP-complete problems are widely and deeply involved in various real-life scenarios while still intractable to solve efficiently on conventional computers. It is of great practical significance to construct versatile computing architectures that solve NP-complete problems with computational advantage. Here, we present a reconfigurable photonic processor to efficiently solve a benchmark NP-complete problem, the subset sum problem (SSP). We show that in the case of successive primes, the photonic processor has genuinely surpassed commercial electronic processors launched recently by taking advantages of the high propagation speed and vast parallelism of photons and state-of-the-art integrated photonic technology. Moreover, we are able to program the photonic processor to tackle different problem instances relying on the tunable integrated modules, variable split junctions, which can be used to build a fully reconfigurable architecture potentially allowing 2N configurations at most. Our experiments confirm the potential of the photonic processor as a versatile and efficient computing platform, suggesting a possible practical route to solving computationally hard problems at large scale.
A variety of complicated computational scenarios have made unprecedented demands on the computing power and energy efficiency of electronic computing systems, including solving intractable nondeterministic polynomial-time (NP)-complete problems and dealing with large-scale artificial intelligence models. Optical computing emerges as a promising paradigm to meet these challenges, whereas current optical computing architectures have limited versatility. Their applications are usually either constrained to a specialized domain or restricted to general-purpose matrix computation. Here, we implement a fully-programmable integrated photonic processor that can be configured to tackle both specific computational problems and general-purpose matrix computation. We achieve complete end-to-end control of the photonic processor by utilizing a self-developed integrated programmable optoelectronic computing platform. For domain-specific computing, our photonic processor can efficiently solve two kinds of NP-complete problems: subset sum problem (far more than 2^N different instances) and exact cover problem. For general-purpose computation, we experimentally demonstrate high-precision optical dot product and further realize accurate image edge detection and MNIST handwritten image classification task with an accuracy of 97%. Our work enhances the versatility and capability of optical computing architecture, paving the way for its practical application in future high-performance and complex computing scenarios.
The Subset Sum Problem (SSP) is one of those combinatorial problems that are very easy to understand (take a bunch of integer numbers and verify whether there exists a subset of these numbers which sums up to a given target integer), but it can be very difficult to solve.The SSP is actually an NPcomplete problem, but it is "weakly" NP-hard, implying that there are instances of SSP that can be solved in polynomial time.For this particular problem, the instance hardness can be measured by evaluating the so-called "density" index, which basically compares the number of involved integer numbers to the number of bits we need for their binary representation.In our preliminary study on the use of adiabatic quantum computing for the SSP, we investigate the actual feasibility in solving hard instances of the problem.In fact, hard SSP instances are those requiring a large number of bits for the representation of the integers, while the analog nature of the quantum computer does not allow us to ensure highly accurate integer representations.Some preliminary computational experiments performed on D-Wave quantum annealer are presented and compared to standard solvers for classical computers.
In recent years, quantum information has rapidly evolved as a field with transformative potential in science and technology. It provides secure encryption for communication, accurate emulation of practical physical systems, streamlined and accelerated machine learning models, and advanced computational powers that outperform classical supercomputers in solving complex problems. These advancements are all reliant on the superposition and entanglement properties of qubits. While various candidates such as trapped ions or superconducting qubits have been proposed to realize quantum technologies, photons have demonstrated a prominent advantage due to their robustness against decoherence and noise, high clock cycle rate, fast and easy measurement, and room temperature working environment. In addition, photonic integrated chip (PIC) technology has developed rapidly since the beginning of the 21st century. The number of devices integrated on a single chip has increased rapidly, and its complexity has also increased. Quantum computing combined with integrated photonics is expected to solve bottleneck problems in practical situations. In this thesis, based on the silicon-on-insulator (SOI) platform, an optical computing chip and a large-scale quantum computing chip with various practical applications are specifically studied. In the first part of the thesis, a novel integrated diffractive optical network is studied, and a scheme is designed to realize parallel Fourier transform, convolution operations, and application-specific optical computing. Due to the utilization of on-chip compact diffractive cells (slab waveguides), the footprint and power consumption of the proposed architecture is reduced from quadratic scaling in the input data dimensions required for Mach-Zehnder interferometer (MZI)-based optical neural network (ONN) architectures to linear scaling for the improved deep neural networks. A 10-fold reduction in both footprint and energy consumption and equal high accuracy with previous MZI-based ONNs was experimentally achieved for computations performed on the Modified National Institute of Standards and Technology (MNIST) and Fashion-MNIST datasets. This reduction in the resource scaling from quadratic to linear has a profound impact on the realization of large-scale silicon-photonics computing circuits with current fabrication technologies. A quantum photonic microprocessor based on Gaussian Boson sampling (GBS) that offers dynamic programmability to solve various graph-related NP-complete problems is then demonstrated. The system with optical, electrical, and thermal packaging implements a GBS with 16 modes of single-mode squeezed vacuum states, a universal programmable 16-mode interferometer, and a single photon readout on all outputs with high accuracy, generality, and controllability. The developed system is applied to demonstrate applications in solving NP-complete problems, manifesting the ability of photonic quantum computing to realize practical applications for conventionally intractable computations. The GBS-based quantum photonic microprocessor is applied to solve task assignment, Boolean satisfiability, graph clique, max cut, and vertex cover. These demonstrations suggest an excellent benchmarking platform, paving the way toward large-scale combinatorial optimization. Finally, this thesis explores the application possibility of large-scale PICs in molecular simulation. A new algorithm utilizing states with zero displacements (vacuum-squeezed states) coupling to a linear network is proposed to calculate molecular vibronic spectra. With a large-scale PIC, molecular vibronic spectra are accurately simulated for formic acid and thymine with high reconstructed fidelity (>91%) and for naphthalene, phenanthrene, and benzene under the non-Condon regime. Our experimental demonstration will open pathways toward conducting large-scale molecular quantum simulations, a task surpassing classical computers’ capabilities.
Cognitive photonic networks are researched to efficiently solve computationally hard problems. Flexible fabrication techniques for the implementation of such networks into compact and scalable chips are desirable for the study of new optical computing schemes and algorithm optimization. Here we demonstrate a femtosecond laser-written optical oracle based on cascaded directional couplers in glass, for the solution of the Hamiltonian path problem. By interrogating the integrated photonic chip with ultrashort laser pulses, we were able to distinguish the different paths traveled by light pulses, and thus infer the existence or the absence of the Hamiltonian path in the network by using an optical correlator. This work proves that graph theory problems may be easily implemented in integrated photonic networks, down scaling the net size and speeding up execution times.