SE546081C2 - Spinwave coherent ising machine - Google Patents

Abstract

A spinwave Coherent Ising computational machine comprising: a spinwave delay line that propagates a plurality of pseudo Ising spin pulses in the form of parametric spinwave oscillators, a spinwave-microwave transducer, an electronic phase-sensitive amplifier configured to cause phase degeneracy of a plurality of propagating spinwave pulses, a measuring unit configured to temporarily measure pseudo spins of the plurality of pseudo spin pulses, an interaction unit configured to temporarily implement magnitudes and phases of all the interactions relating to the plurality of pseudo Ising spin pulses; and, a pseudo Ising spin measuring unit which measures the pseudo Ising spins of the plurality of pseudo Ising spin pulses.

Description

Field of the Invention The disclosed invention generally relates to non-von-Neuman computing architectures and more particularly to a combinatorial spinwave Ising-model solver using the physical annealing method.

Background of the invention The Ising Model [Referencez 1] is an efficient computational tool that can be used to solve a variety of difficult computational problems time- and hardware-efficiently by using its physical implementation - Ising machine. Ising model manifests that if there is a magnetic structure that is made of an array of magnetic domains and each domain is either up or down c¿, cj: +1 or - 1 magnetic spin and they are coupled to each other through a magnetic field with a coefficient jl-j, one can calculate the energy of the whole system by simple summation of the product of each spin state in the pairs and their coupling: E = _ Ztgjfijfzcj (1) The Ising problem is to find for a given magnetic structure with particular coupling between elements, a unique configuration of spins (up or down) so that the whole magnetic structure has the lowest energy state. The Ising problems belong to the category of so-called NP-hard computational problems [2]. The term hard means that this problem is representative of the whole class of NP and can be mapped to an Ising machine and then solved with polynomial time.

An Ising machine can be implemented with a physical system that is made of an array of elements where each element has two well-defined and stable states that can be either +l or -l to represent an Ising spin and where each element can be connected to any other with a variable continuous coefficient. By setting different coefficients one can program this machine to solve a particular Ising problem. An Ising machine when turned on tends to go into the lowest energy state by flipping the states of individual spins. The final configuration of the spins coincides with the ground state of the Ising problem and represents its solution.

To date, Ising machines have been implemented with many physical paradigms, including quantum annealing [3-4], optical parametric oscillators [5-7], phase transition nano-oscillators [8], stochastic nanomagnets [9], electronic CMOS SRAM [l0], electronic LC oscillators [l l, l2], and spin-Hall nano-oscillators [13-l4]. All the concepts are characterized by different speeds, power consumption, number of supported spins, physical dimension, etc. but can still be divided into two distinct groups - spatially distributed oscillator arrays and time-multiplexed soliton systems as shown in figure lA and lB.

The most important parameters for Ising Machines are the time to solution and the number of supported spins, and these parameters are strongly interconnected. In FIG. lC we present time to solution as a function of annealing time and problem size N. For Ising Machines based on physical arrays of oscillators the main problem is interconnectivity because as the number of oscillators N grows the number of intersections between coupling lines increases dramatically as - O(N2). This problem is solved by grouping the elements with a sparse connection into a so-called chimera graph [l6]. However, it trades off the computational time-to-solution which in the case of the chimera graph connection scheme increases as - O(N2) (FIG.lC). It is the same growth rate as the computation speed of classical computers based on a von-Neuman architecture which means that there is no principal computational advantage in using Ising Machines built with spatially distributed oscillators.

For Coherent Ising Machines based on propagating light pulses the interconnectivity for a problem of all-to-all connected spins is easily solved with the time- multiplexing method. Computational problems with all-to-all connected spins are characterized by the computational time that grows as - O(N) when solved on physical Ising Machines. Therefore, the time multiplexing method makes computational time to solution for Ising problems with a large (>50) number of spins reasonable. The first time- multiplexing Ising Machine was implemented with optical parametric oscillators (OPOs) that are in the fonn of propagating light pulses in optical waveguides. The interconnectivity is implemented electrically (FIG.1B) by consecutive measurements of each propagating light pulses-OPOs and then adding to the additional small (r << 1) contributions according to the coefficients in Ising problem: fi = TZj/ijcj (2)111' Iij =5 (3) 1:/ij For the moment, time-multiplexed CIMs seem to be the most promising Ising Machine configuration for combinatorial problems With large (> 50 number of elements) due to -Û (N) computational speed. Even SHNO-based Ising Machines that are proj ected to provide unpresidential computational speed starting from tens of nanoseconds cannot compete With Coherent Ising Machines for a graph size above 50 as they belong to -0(N2) class of IM. The number of supported elements in Ising problems solved by optical CIMs Was progressively growing from 100 [5] spins through 2000 [6] and recently a CIM supporting 100000 spins Was reported [7]. However, despite clear progress in the number of supported spins, current CIMs are still not in the market as they have a considerable disadvantage of size, large power consumption, and, most importantly, costly optical infrastructure requiring optical tables, precise positioners, etc.

Summag of the invention Accordingly, the present invention preferably seeks to mitigate, alleviate or eliminate one or more of the above-identified deficiencies in the art and disadvantages singly or in any combination and solves at least the above mentioned problems by providing a spinWave Coherent Ising computational machine, SCIM, comprising:__~ t w-vvw- H-w- -\-~š»\~~\ v..> <- ø- \,;,._~._n~w..xv\.~ :uux-ßa- .n ~ -xl-:>»\*\'=\~'\-'~§ wc : »ar-VM fu. , sensitive amplifier. ïštie \;¿>š'=_:-.=.s .r configured to cause phase L a ._C- -.fl , -_ users-rio spin r>=:_=_sss_ degeneracy of a plurality of propagating spinwave pulses corresponding to a plurality of mgspins in the Ising model, and set an oscillation frequency corresponding _. _ 1 iïšïšfïíïfï “N si. i. __; _? ä.. ~ . .\\ < fm Ü Q I... n v Û _ f. Üx i _ f. to half a reference frequency; . . ' _ _ ~ "x w v* w f; -x ' \ ___. ._ .\ ä: .i :Ä t; ::..l.~. .l Kf' var: k-'x ' _a measuring unit O d u 6 S p f Û m. M r .m p 6 .m f O S .m p S O d u 6 S p 6 r u S a 6 m .r=~=ar~šå§=--measuring the phase of each of the plurality of pseudo spin x Å..

Y b S C ß u P n .l P S år. pulses each time the plurality of pseudo spin pulses circularly propagates in a ring circuit f measurement after one set of measurement is completed before another =“'crçsrnprisšsiasg- an interaction unitj '*~ set of measurement is restarted_ 'f ' " 'i configured to ~'šeša.v~ mi: f Ä x» w-smfw-»vs + \ fw >> w~§~~~~h~~ f iv... »mh _.\ at. . ____~_..~_\ hr,- a: m; _-\ på . khß-gw . ' t. .__ *w -w \-*\ fw »Magvhs M.

S m r fw r e P h .w h .w ...n n u g .m LL u P m o C .m a g .m M e n n a n a annealing by restarting the circulation of the plurality of pseudo Ising spin pulses and performs statistical analysis on the plurality of steady-state solution.

This disclosure relates to a novel architecture of Coherent Ising Machines (CIM) for solving combinatorial optimization problems. The key element of SpinWave CIM (SCIM) is a YIG spinwave delay line that is used as a waveguide where spinwave RF pulses propagate and are stored. The advantage of spinwave devices is the exceptionally slow group velocity of propagating spinwaves that is several orders lower than the speed of light. It allows miniaturizing of the CIM waveguide size down to the mm scale while keeping a high number of supported spins. Another advantage of the proposed invention in contrast to optical CIMs is that spinwaves can also be easily excited by and transduced back to electrical RF signals, which allows performing the compensation of propagation losses via low-power and power-efficient RF phase-sensitive and linear amplifiers. The transformation between spinwave RF pulses to electric RF pulses and back is implemented with wideband thin-wire transducers. The rapid measurement of RF circulating pulses is done electrically via homodyne IQ-demodulator and CORDIC algorithm implemented in microcontroller or FPGA that allows independent deduction of the phase and the amplitude of the RF pulses within pulse circulation time.

Further advantageous embodiments are disclosed in the appended and dependent patent claims.

Brief description of the drawings These and other aspects, features and advantages of which the invention is capable will be apparent and elucidated from the following description of embodiments of the present invention, reference being made to the accompanying drawings, in which Fig. lA. is a spatially distributed oscillator array Ising Machine.

Fig. IB is a time-multiplexed Ising Machine.

Fig. lC is a graph showing time to solution as a function of annealing time and problem size N, showing a comparison between existing solutions to the present disclosure, which is shown as the dashed line labelled Coherent Ising Machine Spinwaves GU.

Fig. 2A is a block diagram of a Spinwave Coherent Ising Machine comprising microwave delay lines and a microcontroller according to an aspect.

Fig. 2B is a block diagram of a Spinwave Coherent Ising Machine comprising an FPGA according to an aspect.

Fig. 3A shows the Szi-parameter of a YIG spinwave delay line.

Fig. 3B shows the delay time of the YIG spinwave delay line.

Fig. 4 shows the amplification of the phase-sensitive amplification block as a function of phase difference between circulating RF pulses and a reference signal.

Fig. 5 shows time traces of circulating RF pulses, their instantaneous phase and a control signal for RF switches.

Fig. 6 is a schematic of the transition between a non-optimal initial state and an optimal solution for MAX-CUT4 problem computed with the SCIM after 12 circulations.

Fig. 7A shows time traces of the circulating RF pulses and their instantaneous phase for the 1st circulation period.

Fig. 7B shows time traces of the circulating RF pulses and their instantaneous phase for an optimal solution computed at the 12th circulation period.

Fig. 8 shows the evolution of time traces and instantaneous phase for the 3” RF pulse within intermediate circulation steps at top and middle panel, correspondingly. Bottom panel shows the evolution of the instantaneous phase at the center of 1st, 2“d, 3fd and 4th RF pulse withing intermediate circulation steps.

Fig. 9 shows a SCIM comprising a plurality of ring circuits, each ring circuit connected to an FPGA.

Detailed description Figure 2A and 2B show a spinwave coherent Ising machine (SCIM). The key element of the SCIM is a spinwave delay line 21, 23 that supports up to N Ising spins in the form of propagating spinwave RF pulses. The spinwave delay line consists of a ferromagnetic material, such as YIG, spinwave waveguide 21 with an input 20 and an output 22 electromagnetic-spinwave transducers. The operating frequency fo of SCIM is set by phase-sensitive amplification block 1 via a reference frequency signal fref = fo 2. The losses in YIG spinwave waveguide are compensated by the phase-sensitive block and a linear amplifier 7. The phase of each circulating RF pulse cj is measured by deflecting 10% of power after a filter 6 with a directional coupler 8, power divider 9 and measuring the phase with an IQ-demodulator 10, 2-channel ADC 11, and a CORDIC algorithm implemented in microcontroller 13 as shown in fig. 2A.

The cable delay lines delay each circulating RF pulse by multiple of pulse repetition time introducing the coupling between Ising spins. The microcontroller 13 perfonns the computation of the Ising matrix (Equation 2,3) and sets the coupling between each Ising spin by controlling RF switches 16 in every delay channel, a phase shifter 19 and a Variable amplifier 25 which change the phase and amplitude of additional coupling RF pulses. Coupling RF pulses after a Variable amplifier 25 are added to the circulating RF pulses via power coupler 21. The microcontroller 13 controls RF switches Via control lines 12, performs an annealing procedure, and communicates with external systems Via data port As shown in the SCIM in figure 2B, the CORDIC algorithm may be implemented in an FPGA. ln such an architecture, the FPGA also performs the computation of the Ising matrix and sets the coupling between each Ising spin by controlling a phase shifter 17 and Variable amplifier 18 which change the phase and the amplitude of additional coupling RF pulses that are formed by the RF switch 16. Coupling RF pulses after an Variable amplifier 18 are added to the circulating RF pulses Via power coupler As shown in figure 2B, the SCIM comprising an FPGA comprises a microcontroller. The microcontroller 11 controls the FPGA, clock frequencies 9, performs an annealing procedure, and optionally communicates with extemal systems.

The number N of supported spins is proportional to the total delay time rdelay in a spinwaVe delay line and inversely proportional to the minimum possible spinwave RF pulse width Ip: _ Tdela N - T y <4) The minimum possible spinwaVe RF pulse duration is limited by the largest Value deriVed from the 3-dB bandwidth BI/VSW of the spinwaVe spectra and the delay time deViation Ardelay within BMW:BWSW ' (5) Afdelay 12,A particular Ising matrix (Equation 3) can be mapped into a SpinwaVe Coherent Ising Machine by setting an arbitrary time domain pattern of control signal for RF switches 16 so that each RF propagating pulse can be connected to any other RF pulses. In an architecture comprising cable delay lines, the number of cable delay channels should be M = N - 1 to support all-to-all connections. The delay time in cable delay lines CDLl 17 to CDL M is proportional to their index: TH. (6) 'f = CDL m fpulses where fpulses is a pulse repetition frequency.

FIG.3A shows the spinwave spectra of the YIG spinwave delay line in the forrn of Szl-parameter. The bandwidth of the spinwave generation spectrum is 60MHz measured at -3 dB level. FIG.3B shows the delay time of the YIG spinwave delay line [23]. The mean delay time rdemy is 270.62 ns. The limit of minimal pulse duration derived from bandwidth is 16.75 ns while the delay time deviation imposes a stronger limitation of 30. 19ns that results in 8 supported Ising spins , rounded down from 8.

Phase sensitivity is achieved by doubling the reference signal frequency via a frequency doubler 3 and combining it with an RF signal converted from spinwave RF pulses. The amplitude of the total signal after power divider/coupler 4 is set at a level that is close to the saturation point of an RF amplifier 5. The amplitudes of the signals at two inputs of a power divider/coupler 4 which have a relative phase close to 0° or l80° are added and the total signal amplification is affected by the saturation of the amplifier 5 more than if signals have a phase difference is close to 90° or 360°. The signal after an amplifier 5 is filtered by a highpass filter 6 with a cut of frequency fo to remove 2 fo signal after phase-sensitive amplification.

FIG. 4 shows the amplification of the phase-sensitive amplification block 1 as a function of a phase difference between the circulating RF pulses and the reference signal 2. The difference in amplification is denoted as APsA, which equals 6dB and represents the phase sensitivity of the block. The value of phase sensitivity can be adjusted by changing the amplitude of the reference signal at the input of the frequency multiplier.

FIG.5 shows time traces of control signal for RF switches, RF signal after RF amplifier 7, and instantaneous phase that is calculated from RF signal Vanipi. RF switch 26 is used to counteract the spreading of propagating RF pulses due to the delay time 90% deviation Ardelay of the YIG spinwave waveguide. tON is the switching time from the rising front of control signal CLsw 26 to the moment when RF switch 16 is open for 90%. Similarly, tåg? is the switching time from CLsw 26 falling front to the moment when RF switch 16 is open for 10%. RF switch 16 is used to form coupling RF pulses that are added to the circulating RF pulses and has similar parameters tågfß and tågïfï Fig. 9 shows a SCIM comprising a plurality of ring circuits. Each ring circuit comprises a respective spinwave delay line 21, and a phase sensitive amplifier 1. Each ring circuit is connected to the FPGA 15 forming at least the annealing and computing unit. Due to the reduced physical and power footprint of the present ring circuit, multiple ring circuits are practically feasible in a single SCIM. Each ring circuit may comprise a respective electric linear amplifier. The plurality of ring circuits enables an increased number of spins to be perfonned by the SCIM.

Examples 4 spin MAX-C UT solution The following illustrative example demonstrates the physical mechanisms and routes for obtaining a solution to a simple 4-spin MAX-CUT problem and is representative of embodiments of the schematic design, the physical parameters, and methods described herein are not meant to be limiting.

FIG. 6 shows a 4-spin MAX-CUT problem with nearest-neighbour connections which is described by the following Ising matrix: 0-100 00-j” I 0 0 0 -1 (7) -1 0 0 0 The initial state of the system is chosen randomly to be cj = {+1 -1 -1 -1}. Value +1 corresponds to 180° of the phase difference between the RF pulse and the reference signal 2, while value -1 corresponds to 0° of phase difference.

The problem (7) is mapped into the SCIM using a single cable delay line with a delay time that according to (6) equals to a pulse repetition period. The RF switch 16 is always open so that each RF pulse c,- is directionally coupled to an RF pulse cin via a single cable delay. In initial state, additional coupling RF pulses have the following values ß = {+1 of additional delayed coupling RF pulses according to table 1 below: -1 +1 +1}. Controlling components 19, 20 set the amplitude and phase fl- Amplitude Phase +1 1 180° -1 1 0° 0 0 180° or 0° TABLEThe measurement block composed of components 8, 9, 10, 11, 13 reads the instantaneous phase at the centre of each RF pulse, rounds its value, and processes the data as an intermediate state of the Ising system.

FIG.6 shows schematically the initial state that corresponds to the edge cut number of 2 which is a non-optimal solution for a MAX-CUT problem defined by (Eq. 7). After 12 circulations SCIM evolves to a state cj fmal = {+1 -1 +1 -1} Which represents an optimal solution. The microcontroller detects it as a stable state and sends cj fina, to the data port FIG.7 shows the time traces of circulating RF pulses and computed instantaneous phase for the 1st and 12"" circulation periods. The phase of spin 3 has changed from 0° (c3 = -1) to 180° (c3 = +1).

FIGS shows the evolution of times traces and computed instantaneous phase for the 3fd RF pulse within intermediate circulations steps. The instantaneous phase changes nonuniformly forming a temporal “domain wall” whose intermediate phase forces theformation of a dip in RF amplitude in the middle of the RF pulse which gradually propagates to the left and disappears leading to a uniformly distributed instantaneous phase of l80° (c3 = +1).

Although, the present invention has been described above with reference to specific embodiments, it is not intended to be limited to the specific form set forth herein. Rather, the invention is limited only by the accompanying claims.

In the claims, the term “comprises/comprising” does not exclude the presence of other elements or steps. Furthermore, although individually listed, a plurality of means, elements or method steps may be implemented by e.g. a single unit or processor. Additionally, although individual features may be included in different claims, these may possibly advantageously be combined, and the inclusion in different claims does not imply that a combination of features is not feasible and/or advantageous. In addition, GC 37 CG a singular references do not exclude a plurality. The temns , an”, “first”, “second” etc do not preclude a plurality. Reference signs in the claims are provided merely as a clarifying example and shall not be construed as limiting the scope of the claims in any way.

Claims (9)

1. CLAIMS A spinwave Coherent Ising computational machine, SCIM, comprising: a ring circuit, the ring circuit comprising: a spinwave delay line (23) that propagates a plurality of pseudo Ising spin pulses in the form of parametric spinwave oscillators, the spinwave delay line (23) comprising input and output electromagnetic-spinwave thin-Wire transducers (20, 22) for transforrning between spinwaves in the spinwave delay line (23) and electrical pseudo spin pulses; an electronic phase-sensitive amplifier (1) Wherein the phase-sensitive amplifier (1) receives a reference RF signal having a reference frequency and the propagating electrical pseudo spin pulses, the phase sensitive amplifier (1) comprising a frequency doubler (3) for doubling the frequency of the reference RF signal, and a signal coupler (4) for combining the reference RF signal With the electrical pseudo spin pulses, the phase sensitive amplifier (1) therein being configured to cause phase degeneracy of a plurality of propagating spinwave pulses corresponding to a plurality of electrical pseudo spins in the Ising model, and set an oscillation frequency corresponding to half the reference frequency; the SCIM comprising, in electrical connection With each ring circuit: a measuring unit (8, 9, 10, 11, ll* 13, 13*,14*,l5*) comprising an IQ demodulator, and an FPGA (15*) or microcontroller (13), the FPGA (15*) or microcontroller (13) configured to implement the CORDIC algorithm, Wherein the measuring unit receives electrical pseudo spin pulses from the ring circuit, and is configured to measure electrical pseudo spins of the plurality of pseudo spin pulses by measuring the phase of each of the plurality of pseudo spin pulses each time the plurality of pseudo spin pulses circularly propagates in a ring circuit and suspending measurement after one set of measurement is completed before another set of measurement is restarted; an interaction unit (11, 16, 17, 18, 19, l5*, 17*, 18*, 19*, 25, 26) Which receives each electrical pseudo spin pulse and sets the coupling between each electrical pseudo spin pulse in the ring circuit, the interaction unit comprising a variable amplifier (18, 25), power coupler (19, 21), RF switch (16) and either: a plurality of cable delay lines (17) connected according to the Ising model; or, an FPGA (15*) and phase shifter (l7ff“'_); wherein the cable delay lines (17), or the FPGA (15*) and phase shifter (17_°_*_) are configured to delay and couple each electrical pseudo spin pulse to additional RF pulses provided by the RF switch (16); and, an annealing and computing unit (1l*, 13, 15*) which performs annealing by restarting the circulation of the plurality of pseudo Ising spin pulses and performs statistical analysis on the plurality of steady-state solution. The SCIM according to claim 1, wherein the spinwave delay line (23) comprises a ferromagnetic wave propagating material in which the spin pulses propagate at a speed substantially less than the speed of light. The SCIM according to claims l or 2, comprising an electric linear amplifier (5) configured to compensate the amplitude losses of the plurality of propagating spinwave pulses. The SCIM according to any of claims 1 to 3, wherein the ferromagnetic wave propagating material comprises the phase sensitive amplifier (1) or wherein the SCIM comprises an additional ferromagnetic wave propagating resonator forming the phase sensitive amplifier (1). The SCIM according to any of claims 1 to 4, wherein the machine comprises a FPGA (15*), and wherein the FPGA (15*) is configured to map an Ising problem onto propagating spinwaves by connecting them via applying to eachRF pulse, an additional coupling RF pulse With an amplitude and phase defined by a coupling matrix. The SCIM according to claim 5, Wherein the measuring unit receives the propagated pseudo spin pulse after the measuring unit completes one set of measurement and before the measuring unit restarts another set of measurement. The SCIM according to any of claims 1 to 6, Wherein the parametric oscillators are time-multiplexed in a single spinwave delay line. The SCIM according to any of claim 1 to 7, Wherein the spinwave coherent Ising machine is configured to produce a set of numbers from a plurality of the Ising spins, Wherein the produced numbers contain information about statistics of stable states of the spinwave coherent Ising computational machine, and Wherein the produced numbers are generated from the phases of a plurality of pseudo spin pulses circularly propagating in the ring circuit. The SCIM according to any of claims 1 to 8, Wherein the SCIM comprises a plurality of ring circuits, each ring circuit comprising a respective spinwave delay line (23) and phase-sensitive amplifier (1).