Takahiro Inagaki

A coherent Ising machine for 2000-node optimization problems

Taking the pulse of optimization Finding the optimum solution of multiparameter or multifunctional problems is important across many disciplines, but it can be computationally intensive. Many such problems defined as computationally difficult can be mathematically mapped onto the so-called Ising problem, which looks at finding the minimum energy configuration for an array of coupled spins. Inagaki et al. and McMahon et al. show that an optical processing approach based on a network of coupled optical pulses in a ring fiber can be used to model and optimize large-scale Ising systems. Such a scalable architecture could help to optimize solutions to a wide range of complex problems. Science, this issue pp. 603 and 614 An optical-based processor is developed to solve a broad class of complex optimization problems. The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

Large-scale Ising spin network based on degenerate optical parametric oscillators

Solving combinatorial optimization problems is becoming increasingly important in modern society, where the analysis and optimization of unprecedentedly complex systems are required. Many such problems can be mapped onto the ground-state-search problem of the Ising Hamiltonian, and simulating the Ising spins with physical systems is now emerging as a promising approach for tackling such problems. Here, we report a large-scale network of artificial spins based on degenerate optical parametric oscillators (DOPOs), paving the way towards a photonic Ising machine capable of solving difficult combinatorial optimization problems. We generate >10,000 time-division-multiplexed DOPOs using dual-pump four-wave mixing in a highly nonlinear fibre placed in a cavity. Using those DOPOs, a one-dimensional Ising model is simulated by introducing nearest-neighbour optical coupling. We observe the formation of spin domains and find that the domain size diverges near the DOPO threshold, which suggests that the DOPO network can simulate the behaviour of low-temperature Ising spins. More than 10,000 time-division-multiplexed degenerate parametric oscillators are generated using phase-sensitive amplification in a nonlinear optical fibre. They can be used to simulate a coherent Ising machine that could solve difficult computing problems.

A soft X-ray free-electron laser beamline at SACLA: the light source, photon beamline and experimental station

The status of a soft X-ray free-electron laser beamline at SACLA is reported.

Topological defect formation in 1D and 2D spin chains realized by network of optical parametric oscillators

A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this Ising machine for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice, and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear growth stage and a nonlinear saturation stage. These predictions are compared against recent data for a 10,000-spin 1D Ising machine.

Compact 110 MW modulator for C-band high gradient accelerator

The C-band high gradient accelerator of SACLA is driven by 72 units of 50 MW klystrons and 110 MW modulators. They are tightly placed in each 4 m space intervals in a 400 m-long klystron gallery. Therefore the modulator has to be very compact and reliable. SACLA is the X-ray free electron laser (XFEL) facility, which requests very tight tolerances of 100 ppm on amplitude and 0.2 degree on phase of the accelerating field. Then the voltage fluctuation and timing jitter of the high-voltage pulse on the klystron cathode should be minimized. In order to meet these demands, we developed a compact, reliable, and stable modulator, which is a conventional linetype modulator with a novel architecture design. All the highvoltage components, including a PFN circuit, a thyratron tube, a pulse transformer, and reverse protection circuits, were installed in a compact steel tank, filled with insulation oil. This design provides good EM noise-shield performance, and superior operational stability. Timing jitter of the thyratron is less than 1 ns, and flatness of the high-voltage pulse is 2%, which provides acceptable effect on the RF phase and amplitude fluctuations. In order to stabilize the charging voltage of PFN capacitors, we developed an extremely stable inverter-type high-voltage charger. The pulse-to-pulse stability of the charging voltage is about 10 ppm in standard deviation, which leads sufficient stability on the accelerating field. Since 2011, 72 modulators have been operated in 8000-9000 hours, to provide a stable electron beam for XFEL. Thus the technology of the innovatively compact and stable modulator system was established.

A stable pulsed power supply for multi-beamline XFEL operations

Since an X-ray Free Electron Laser (XFEL) facility is a linac-based single-user machine, a multi-beamline mode of operation, which improves the efficiency of user experiments, is critical for accommodating users rapidly increasing demand for beamtime. A key supporting technology is a highly stable pulsed power supply (PS), which enables stable XFEL operations by precisely switching the beam route. We developed a high-power pulsed PS to drive a kicker magnet installed in a SACLAs beam switching system. SiC MOSFETs were adapted as switching elements to reduce the required size and to increase the electric power efficiency. The PS we developed provides two key capabilities: (i) a high current stability of 20 ppm (peak-to-peak) at a peak power of 0.24 MW and (ii) generation of controllable, bipolar, and trapezoidal current waveforms at 60 Hz. This paper describes the overall concept, the detailed design, the performance achieved, and the initial beam test results.

Pulse-by-Pulse Multi-XFEL Beamline Operation with Ultra-Short Laser Pulses

The parallel operation of multiple beamlines is an important issue to expand the opportunity of user experiments for linear accelerator based FELs. At SACLA, the parallel operation of three beamlines, BL1~3, has been open to user experiments since September 2017. BL1 is a soft x-ray beamline driven by a dedicated accelerator, which is a former SCSS test accelerator, and BL2 and BL3 are XFEL beamlines sharing the electron beam from the SACLA main accelerator. In the parallel operation, a kicker magnet with 10 ppm stability (peak-to-peak) switches the two XFEL beamlines pulse by pulse at 60 Hz. To ensure wide spectral tunability and optimize the laser performance, the beam energy and the electron bunch length are independently adjusted for the two XFEL beamlines according to user experiments. Since the electron bunch of SACLA has typically 15 fs (FWHM) in length and its peak current exceeds 10 kA, CSR effect at a dogleg beam transport to BL2 is quite significant. In order to suppress the CSR effect, an isochronous and achromatic beam optics based on two DBA structures was introduced. The parallel operation of the three FEL beamlines substantially increases user time at SACLA.

Current status and future plan of the soft x-ray beamline at SACLA (Conference Presentation)

SACLA was inaugurated in March 2012 with two beamlines: BL3 for hard X-ray FEL and BL1 for wide range spontaneous emission. To enhance the research opportunities in soft X-ray region, the SCSS test accelerator, which was a prototype linac of SACLA and decommissioned in 2013, was upgraded, relocated to the SACLA undulator hall, and connected to BL1. The commissioning of this upgraded BL1 had been started from September in 2015, and user operation was started from June 2016. Currently, SASE-FEL pulses in the photon energy range of 20 to 150 eV are available and average pulse energy is about 70 μJ at 100 eV. We are developing beam diagnostic systems such as an arrival timing diagnostics between the SXFEL and the synchronized optical laser. We have further upgrade plans of the accelerator and the beamline. In this presentation, I will report the latest status and future upgrade plans of this beamline.

Current status of the EUV/soft x-ray FEL beamline at SACLA(Conference Presentation)

SACLA was inaugurated in March 2012 with two beamlines: BL3 for hard X-ray FEL and BL1 for wide range spontaneous emission. Currently, all user experiments have been performed at BL3 and BL2 that was constructed as the second hard XFEL beamline. To enhance research opportunities with softer X-ray FEL, we decided to relocate the SCSS test accelerator, which was a prototype of SACLA and decommissioned in 2013, to the SACLA undulator hall, to connect to BL1, and to generate EUV and soft X-ray FEL independently of the SACLA linac. In addition, we started commissioning of the upgraded BL1 in September 2015, and successfully observe SASE lasing at a photon energy of 36 eV in October. We are now constructing the end station, and will start commissioning in June 2016. We will install two C-band accelerator units that increase an electron beam energy up to 750 MeV with a photon energy up to 100 eV in the summer of 2016. In this presentation, I will report the latest status of the beamline.

Commissioning Status of the Extreme-Ultraviolet FEL Facility at SACLA

To equip SACLA with wide ability to provide laser beams in EUV and soft X-ray regions to experimental users, we have constructed a new free electron laser facility for the SACLA beamline-1. Injector components, such as a thermionic electron gun, two buncher cavities, and their RF sources, were relocated from the SCSS test accelerator. At the downstream of a bunch compressor chicane, 3 C-band acceleration units were newly installed to effectively boost a beam energy up to 500 MeV. 3 invacuum undulators with a larger K-value of 2.1 were remodelled for increasing SASE intensity. Beam commissioning was started in autumn 2015. We carefully tuned an electron beam orbit and bunch compression processes to obtain 240 A at the peak along the injector and 2 bunch compressors. The bunch length was successfully compressed from 1 ns to 1 ps. After the tuning, the lasing of the EUV-FEL was realized. So far the FEL radiation with energy of about 25 uf06dJ and a 30 nm wavelength driven by a 500 MeV electron beams was observed. In this summer, we will install additional 2 C-band accelerator units to raise the maximum beam energy to 750 MeV for providing a laser at 13 nm.