Layout for a Ring Oscillator-Based Jitter Machine System

Abstract

To provide a ring oscillator-based Ising machine system.SOLUTION: One example includes an Ising machine system. The system includes a plurality of ring oscillators that are each configured to propagate an oscillation signal. Each of the ring oscillators can be cross-coupled with at least one other of the ring oscillators via a respective one of the oscillation signals to provide a respective phase coupling between the respective cross-coupled ring oscillators. The system also includes an Ising machine controller configured to generate control signals corresponding to parameters of an Ising problem and including a plurality of delay selection signals. The Ising machine controller can provide at least one of the delay selection signals to each of the ring oscillators. The delay selection signal can be configured to set a variable propagation delay of the ring oscillator to control the relative phase coupling of each of the ring oscillators to each of the at least one other of the ring oscillators.

Description

Technical Field

[0001] The present invention generally relates to computer systems, and more particularly to a layout for a ring oscillator-based annealing machine system.

Background Art

[0002] An annealing machine is a type of special computer system for solving various special problems known as annealing problems or non-deterministic polynomial-time hard (NP-hard) problems. An example of this is the "traveling salesman problem," which is a general term for optimization problems. Such annealing problems are evaluated based on the principle of the annealing model, i.e., the annealing problem Hamiltonian: H(σ)=-Σh i σ i -ΣJ ij σ i σ j Based on this, such a special annealing machine operates based on implementing a large number of variables and provides a high-quality answer to a specific combinatorial optimization problem extremely quickly. A typical annealing machine implements several elements (e.g., oscillators), and these elements interact with other elements in the annealing machine to provide cross-coupled effects. The cross-coupled effects can be implemented to solve the annealing problem based on the coupling effects of such cross-couplings.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Non-Patent Documents

[0004]

Non-Patent Document 1

Summary of the Invention

[0005] One example includes an edging machine system configured to solve the edging problem. The system includes a plurality of ring oscillators each configured to propagate an oscillation signal. Each of the plurality of ring oscillators includes a plurality of coupling stages. Each of the plurality of coupling stages can have a unique phase index number that matches the phase index numbers of the plurality of coupling stages of each of the other ring oscillators within each one of the plurality of ring oscillators. Each of the plurality of coupling stages, except for one coupling stage of each of the plurality of ring oscillators, is cross-coupled via the oscillation signal associated with each respective ring oscillator to a coupling stage having the same phase index number of one of the other ring oscillators, such that each of the plurality of ring oscillators is cross-coupled to each of the other ring oscillators by a single one of the plurality of coupling stages, and a respective phase coupling is provided between each of the cross-coupled ring oscillators.

[0006] Another example includes an edging machine system configured to solve an edging problem. The system includes a plurality of ring oscillators each configured to propagate an oscillation signal. Each of the plurality of ring oscillators includes a plurality of coupling stages. The plurality of coupling stages of the first ring oscillator among the plurality of ring oscillators can be fabricated in a linear physical arrangement along a first axis of a two-dimensional array. The plurality of coupling stages associated with the second ring oscillator among the plurality of ring oscillators can be fabricated in a linear physical arrangement along a second axis of the two-dimensional array that is orthogonal to the first axis. Each of the remaining ring oscillators can be fabricated in a physical L-shape. Each of the plurality of coupling stages can have a unique phase index number that matches the phase index number of each of the plurality of coupling stages of each of the other ring oscillators within each of the plurality of ring oscillators. Each of the plurality of coupling stages, except for one coupling stage of each of the plurality of ring oscillators, is cross-coupled via the oscillation signal associated with each of the plurality of ring oscillators to a coupling stage having the same phase index number of one of the other ring oscillators based on crossing each of the other ring oscillators within the two-dimensional array, such that each of the plurality of ring oscillators is cross-coupled with each of the other ring oscillators by a single one of the plurality of coupling stages, and each phase coupling is provided between each of the cross-coupled ring oscillators.

[0007] Another example includes an edging machine system configured to solve an edging problem. The system includes a plurality of ring oscillators each configured to propagate an oscillation signal. Each of the plurality of ring oscillators includes a plurality of coupling stages. Each of the plurality of coupling stages can have a unique phase index number that matches the phase index numbers of the plurality of coupling stages of each of the other ring oscillators within each of the plurality of ring oscillators. Each of the plurality of coupling stages, except for one coupling stage of each of the plurality of ring oscillators, is cross-coupled via an oscillation signal associated with each of the ring oscillators to a coupling stage having the same phase index number of one of the other ring oscillators, such that each of the plurality of ring oscillators is cross-coupled by a single one of the plurality of coupling stages to each of the other ring oscillators, and a respective phase coupling is provided between each of the cross-coupled ring oscillators. The propagation distance of the oscillation signal between a first coupling stage having a given phase index number and a second coupling stage having the next consecutive phase index number is equal for each of the plurality of ring oscillators.

Brief Description of the Drawings

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Modes for Carrying Out the Invention

[0009] The present invention generally relates to a computer system, and more particularly to a layout for a ring oscillator based annealing machine system. The annealing machine system can be implemented in any of a variety of applications to solve complex annealing problems such as optimization problems (e.g., the "traveling salesman problem"). The annealing machine system includes a plurality of ring oscillators each configured to propagate an oscillation signal. As an example, each of the plurality of ring oscillators can be formed from a complementary metal oxide semiconductor (CMOS) manufacturing technique including logic gates formed from CMOS, including, for example, application specific integrated circuits (ASICs) and / or field programmable gate arrays (FPGAs). Each of the plurality of ring oscillators can include a plurality of coupling stages each configured to receive an oscillation signal from one of the other ring oscillators and, similarly, to provide an oscillation signal to another ring oscillator. The oscillation signal of a given ring oscillator can affect the relative phase relationship between each of the ring oscillators. Accordingly, each of the plurality of ring oscillators can be coupled in a cross-coupled manner to at least one other ring oscillator to provide a respective dynamic phase coupling between each of the ring oscillators.

[0010] The annealing machine system can also include an annealing machine controller configured to generate a plurality of sets of control signals provided to the plurality of ring oscillators. As an example, the annealing machine controller can supply a set of control signals to each of the plurality of coupling stages of each of the plurality of ring oscillators. As an example, the control signals can include delay selection signals that can set a variable propagation delay of the ring oscillator to control a relative dynamic phase coupling to each of at least one other ring oscillator of each of the plurality of ring oscillators.

[0011] As an example, each of the plurality of ring oscillators can be manufactured in the same way and thus can include the same number of coupling stages. Each of the plurality of coupling stages in a given one of the plurality of ring oscillators can have a unique phase index number. Thus, cross-coupling of the coupling stages in separate ring oscillators can occur between coupling stages having the same phase index number in each pair of the plurality of ring oscillators. For example, the plurality of coupling stages can be arranged in a two-dimensional array, and two ring oscillators can include a plurality of coupling stages fabricated in a linear physical arrangement orthogonal to each other. The remaining ring oscillators can each be arranged in an L-shape having a coupling stage at the vertex. Thus, a given one ring oscillator can cross through coupling stages with the same phase index number as each of the other ring oscillators in the two-dimensional array, except for one coupling stage of each of the plurality of ring oscillators. The oscillation signal of each of the plurality of ring oscillators has an equal propagation distance between pairs of the same phase index number of coupling stages in order to provide an exact phase relationship between the oscillation signals. Further, based on the two-dimensional array arrangement of the plurality of coupling stages, the edging machine system can be fabricated in a compact manner such that there is less delay and less power consumption in the oscillation signal, thereby providing a more efficient design that can solve edging problems more quickly.

[0012] FIG. 1 shows an exemplary block diagram of an edging machine system 100. The edging machine system 100 can be implemented in any of a variety of specialized computing environments for solving edging problems that require the evaluation of a large number of variables. As an example, the edging machine system 100 can be implemented to solve complex optimization problems (e.g., the "traveling salesman problem").

[0013] The jittering machine system 100 includes a plurality of ring oscillators 102 and a jittering machine controller 104. The ring oscillator 102 can be implemented as any of various different types of ring oscillators. As an example, the ring oscillator 102 can be formed from a complementary metal-oxide-semiconductor (CMOS) manufacturing technique including logic gates formed from complementary metal-oxide-semiconductor (CMOS), such as application-specific integrated circuits (ASICs) and / or field-programmable gate arrays (FPGAs). Thus, each of the plurality of ring oscillators 102 can propagate the oscillation signals generally shown as a set of oscillation signals OSC in the example of FIG. 1. As an example, each of the plurality of ring oscillators 102 can be cross-coupled to another one of the ring oscillators 102 via its respective oscillation signal OSC, thereby providing dynamic phase coupling between the respective cross-coupled ring oscillators 102.

[0014] As described herein, the term "phase coupling" means that the phase characteristic of a given one of the plurality of ring oscillators 102 depends on the phase characteristic of another one of the plurality of ring oscillators 102. As an example, phase coupling can include a tendency towards phase alignment or phase anti-alignment between the respective oscillation signals OSC of the cross-coupled ring oscillators 102. Also, as described herein, since the jittering machine system 100 operates in a manner that substantially always changes with respect to the phase relationship between the ring oscillators, the phase coupling is called dynamic. As an example, the ring oscillator 102 can be controlled by various control signals such as a delay selection signal that can control the amount of delay in the oscillation of a given ring oscillator, and thus the oscillation period of a given ring oscillator. As described herein, the term "oscillation period" means the total time during which a given node of each ring oscillator changes from a first logic state to a second logic state and then changes back from the second logic state to the first logic state. For example, the ring oscillator 102 can be fabricated to provide an odd number of logic inversions during one cycle.

[0015] As an example, each of the plurality of ring oscillators 102 can be fabricated in substantially the same manner, and thus each ring oscillator can include the same number of coupling stages. Each of the plurality of coupling stages in a given one of the plurality of ring oscillators 102 can have a unique phase index number corresponding to the matching phase index number of another ring oscillator 102 to which the respective ring oscillator 102 is cross-coupled. Thus, cross-coupling of the coupling stages in separate ring oscillators 102 can occur between coupling stages having the same phase index number in each pair of ring oscillators 102.

[0016] For example, the plurality of coupling stages can be arranged in a two-dimensional array. As an example, at least two ring oscillators 102 can include a plurality of coupling stages fabricated in a linear physical arrangement orthogonal to each other, such that each of the two ring oscillators intersects in a cross-coupled set of coupling stages having the same phase index number. The remaining ring oscillators 102 can each be arranged in an L-shape having coupling stages at the vertices. As described herein, the term "L-shape" means a configuration in which the ring oscillator 102 has portions extending at right angles from the vertices and the coupling stages are disposed at the vertices. However, it will be appreciated that the legs of the L-shaped ring oscillator 102 can have the same length or different lengths relative to each other. Further, although the legs of the L-shaped ring oscillator 102 have been described as extending substantially orthogonally to each other, the legs can alternatively extend laterally relative to each other so as to define an acute or obtuse angle therebetween.

[0017] Accordingly, based on the remaining ring oscillators 102 being arranged in an L-shape, a given one of the ring oscillators 102 can cross via a coupling stage with the same phase index number as each of the other ring oscillators 102 in the two-dimensional array, except for one coupling stage of each of the plurality of ring oscillators 102. For example, the coupling stages at each vertex of each L-shaped ring oscillator 102 and the coupling stage at one end of the linear ring oscillator 102 can be decoupled from the other coupling stages. As an example, each of the plurality of uncoupled coupling stages can have a phase index number that is unique among the ring oscillators 102.

[0018] In the example of FIG. 1, the edging machine controller 104 is configured to provide a plurality of control signals, shown as “CTL,” to the ring oscillators 102. As an example, the plurality of control signals CTL can be supplied as a set to each of the plurality of ring oscillators 102 such that the plurality of control signals CTL correspond to the parameters of the edging problem to be solved by the edging machine system 100. As an example, the plurality of control signals CTL can include delay selection signals supplied to each of the plurality of ring oscillators 102. As another example, separate delay selection signals are provided to each of the plurality of coupling stages of each of the plurality of ring oscillators 102 such that the net oscillation period of each of the ring oscillators 102 at a given instant can be set based on the collective contribution of each of the delay selection signals provided to each of the plurality of coupling stages of a given ring oscillator 102. The plurality of control signals CTL can also include additional signals, such as selectively enabling the phase coupling of the coupling to other ring oscillator(s) 102 and / or selectively providing a reference clock and / or a simulated noise signal to the coupling stages for phase alignment to the reference clock and / or the simulated noise signal.

[0019] As an example, the variable delay of each of the plurality of coupling stages of each of the plurality of ring oscillators 102 set by the delay selection signal can impart variable strength or weight to the cross-coupling between the respective ring oscillators 102. The annealing machine system 100 further includes a phase sampler 106. The phase sampler 106 can be configured to monitor the logical state of each of the plurality of oscillation signals of each of the plurality of ring oscillators 102 to facilitate solving a given annealing problem. For example, to provide a solution to a given annealing problem, the annealing machine system 100 can operate over a duration (such as determined by any of various machine parameters or other circumstances such as empirical observations and / or real-time constraints), and the phases of the ring oscillators 102 can be sampled by the phase sampler 106 (such as via the oscillation signal OSC). The sampled phases of the ring oscillators 102 can be read by the phase sampler 106 as a set of data that can represent the solution to the annealing problem. The method of setting a variable delay for each of the plurality of coupling stages of the ring oscillators 102 can be provided in various ways as described in U.S. Patent No. 11,545,963, which is hereby incorporated by reference in its entirety.

[0020] Based on the two-dimensional array arrangement of the plurality of coupling stages of the plurality of ring oscillators 102, the annealing machine system 100 can be manufactured in a compact manner such that the delay in the oscillation signal is small and the power consumption of the annealing machine system 100 is low. For example, for each of the plurality of oscillation signals of each of the plurality of ring oscillators 102, the propagation distances between pairs of the same phase index numbers of the coupling stages between the ring oscillators 102 are equal to provide an accurate phase relationship between the oscillation signals. Thus, the ring oscillators 102 can have approximately equal Manhattan distances relative to each other between the coupling stages of any two phase index numbers. Thus, the compact design of the annealing machine system 100 can provide a more efficient design that can solve the annealing problem more quickly and with less power consumption.

[0021] Figure 2 shows a diagram of an exemplary ring oscillator 200. The ring oscillator 200 may correspond to one of the plurality of ring oscillators 102 in the example of FIG. 1. Accordingly, in the following description of the example of FIG. 2, reference is made to the example of FIG. 1.

[0022] The ring oscillator 200 includes a plurality of N coupling stages 202, where N is a positive integer. The plurality of coupling stages 202 are interconnected by inverters 204 that may each be implemented as CMOS inverters (e.g., having complementary pull-up and pull-down transistor switches). The ring oscillator 200 is configured to propagate an oscillation signal OSC. As an example, N can be an odd integer such that the oscillation signal OSC exhibits an odd number of logic inversions during one round of the ring oscillator 200.

[0023] In the example of FIG. 2, a plurality of oscillation signals OSC 1 ~OSC N are supplied from the plurality of coupling stages 202, and a plurality of oscillation signals OSC 1 ’~OSC N ’ are supplied from the plurality of inverters 204. Accordingly, a given Y-th oscillation signal OSC Y ’ corresponds to the inverted version of the respective Y-th oscillation signal OSC Y . Further, a given Y-th oscillation signal OSC Y supplied from the Y-th coupling stage 202 corresponds to the oscillation signal OSC Y-1 ’ supplied as an input to the respective Y-th coupling stage 202. As an example, the coupling stage 202 can provide a variable propagation delay of the oscillation signal OSC Y to provide the oscillation signal OSC Y-1 ’.

[0024] Furthermore, each of the plurality of coupling stages 202 has CTL 1 ~CTL Nis shown as receiving a set of control signals CTL. The plurality of control signals CTL can correspond to or can include a set of control signals CTL provided from the jogging machine controller 104. As described above, the control signal CTL can include a delay selection signal that can affect the propagation delay of the oscillator signal OSC through the coupling stage 202. Accordingly, the delay selection signal can affect the amount of delay between the oscillation signal OSC Y-1 ’ and the oscillation signal OSC Y and thus can affect the propagation delay amount of the oscillation signal OSC through each one of the plurality of coupling stages 202. Also, as described above, the control signal CTL can include various additional signals for controlling the operation of each of the plurality of coupling stages 202 and thus the ring oscillator 200. Accordingly, the control signal CTL can similarly include various additional signals for controlling the operation of each of the plurality of coupling stages 202 and thus the ring oscillator 200.

[0025] In the example of FIG. 2, a plurality of oscillation signals OSC 1 ’~OSC N ’ provided from each coupling stage 202 (e.g., via the inverter 204) are provided as a plurality of output oscillation signals OSC OUT1 ~OSC OUTN . Further, in the example of FIG. 2, each of the plurality of coupling stages also receives an input oscillation signal OSC IN1 ~OSC INN from another ring oscillator 102 shown as OSC IN . In the example of FIG. 2, each of the plurality of coupling stages 202 is numbered based on a unique phase index number and thus can be numbered from “1” to “N”. Accordingly, the oscillation signal OSC IN supplied to a given one of the plurality of coupling stages 202 can correspond to the oscillation signal OSC OUT supplied from a coupling stage having the same phase index number within a different ring oscillator 102. Similarly, the oscillation signal OSC OUTis supplied to coupling stages having the same phase index number within different ring oscillators 200. Accordingly, oscillator signals OSC IN and OSC OUT can provide cross-coupling to a coupling stage of a different ring oscillator 102 in a given one of the plurality of coupling stages 202. As an example, all of the plurality of coupling stages 202 can be cross-coupled to different ring oscillators 102, and as will be described in more detail herein, one of the plurality of coupling stages 202 is not coupled (cross-coupled) to any other coupling stage of another ring oscillator.

[0026] Further, in the example of FIG. 2, ring oscillator 200 includes a NAND gate 206 that interconnects the Nth coupling stage 202 and the first coupling stage 202. NAND gate 206 receives oscillator signal OSC N at a first input and receives the enable signal REN of the ring oscillator at a second input. The enable signal REN of the ring oscillator can correspond to an enable signal for the entire ring oscillator 200, and thus, ring oscillator 200 can be selectively enabled and disabled with respect to propagating oscillator signal OSC. As an example, the enable signal REN of the ring oscillator can be supplied as one of a plurality of control signals CTL supplied from the indexing machine control system 104 to ring oscillator 200. Accordingly, in response to assertion of the enable signal REN of the ring oscillator, ring oscillator 200 can provide an oscillator signal OSC as described herein. However, in response to de-assertion of the enable signal REN of the ring oscillator, ring oscillator 200 can be disabled such that the oscillator signal OSC stops propagating (e.g., maintains a static logic state between each of the plurality of coupling stages 202).

[0027] FIG. 3 shows an example of an edging machine coupling network 300. The edging machine coupling network 300 can correspond to a part of the edging machine system 100 in the example of FIG. 1. When explaining with the example of FIG. 3, the edging machine coupling network 300 includes a plurality of ring oscillators such as the ring oscillator 200 in the example of FIG. 2. Therefore, in the following description of the example of FIG. 3, refer to the examples of FIGS. 1 and 2.

[0028] The edging machine coupling network 300 includes a plurality of control stages 302 fabricated in a two-dimensional array. The plurality of control stages 302 are arranged in rows and columns shown as rows 304, 306, 308, 310, 312, 314, 316, 318, 320, 322, and columns 324, 326, 328, 330, 332, 334, 336, 338, 340, 342. Each of the plurality of control stages 302 includes a phase index number associated with each control stage, numbered from 1 to 10 in the example of FIG. 3. As will be described in more detail herein, most of the plurality of control stages 302 can represent pairs of control stages 302 each included in different ring oscillators.

[0029] In the example of FIG. 3, the plurality of ring oscillators are represented by lines connecting the plurality of coupling stages 302, and the lines are solid, dotted, dashed, dotted and dashed, and double-dotted and dashed lines to represent different ring oscillators, and thus oscillator signals propagating around a given ring oscillator. In the example of FIG. 3, the edging machine coupling network 300 includes ten different ring oscillators such that each type of line is replicated once to show two different ring oscillators. Each of the plurality of ring oscillators begins at a coupling stage having a phase index number "1" and is connected along the coupling stages having consecutive phase index numbers to the tenth and final coupling stage having a phase index number "10". Thus, in the example of FIG. 3, each of the plurality of ring oscillators intersects a different one of the ring oscillators at each of the coupling stages 302 having the same phase index number, except for one coupling stage. Thus, the coupling stage 302 at each intersection of two ring oscillators corresponds to two coupling stages 302, one for each of the two respective ring oscillators. As an example, the coupling stage 302 at a given intersection of two ring oscillators can be fabricated together to minimize the interconnection of oscillator signals for cross-coupling between the respective ring oscillators.

[0030] Accordingly, the injection machine coupling network 300 shows a set of X ring oscillators, where the set of X ring oscillators each has X coupling stages 302 and is cross-coupled to each of the remaining X - 1 ring oscillators. X is shown as a quantity of 10 in the example of FIG. 3, but X can be any quantity greater than 1. In the example of FIG. 3, the two-dimensional array of a plurality of coupling stages 302 includes a first ring oscillator having a coupling stage 302 with a phase index number of "1" in rows 320 and columns 332. The first ring oscillator extends linearly with respect to the coupling stages 302 in a first direction (vertically in the example of FIG. 3) to a coupling stage 302 having a phase index number of "10" in rows 304 and columns 332. The two-dimensional array of a plurality of coupling stages 302 includes a second ring oscillator having a coupling stage 302 with a phase index number of "1" in rows 314 and columns 324. The first ring oscillator extends linearly with respect to the coupling stages 302 in a second direction (horizontally in the example of FIG. 3) orthogonal to the first direction to a coupling stage 302 having a phase index number of "10" in rows 314 and columns 342.

[0031] The remaining ring oscillators of the edging machine coupling network 300 are fabricated in an L-shape such that each of the plurality of ring oscillators intersects each of the other ring oscillators at a coupling stage 302 of the same phase index number, and thus is cross-coupled. Accordingly, each of the plurality of ring oscillators is cross-coupled with each of the other ring oscillators to provide dynamic phase coupling with each of the other ring oscillators. To provide an appropriate phase relationship with each of the other ring oscillators, each of the plurality of ring oscillators can have a propagation length that is approximately equal for the entire loop formed by each respective ring oscillator that goes from a given one of the plurality of coupling stages 302 through all of the other coupling stages 302 and back to a given one of the plurality of coupling stages 302. For example, the oscillation signals of each of the plurality of ring oscillators within the edging machine coupling network 300 have an equal propagation distance between pairs of the same phase index number of the coupling stages between the ring oscillators within the edging machine coupling network 300 in order to provide an exact phase relationship between the oscillation signals. Accordingly, the ring oscillators within the edging machine coupling network 300 can have a substantially equal Manhattan distance with respect to each other between the coupling stages of any two phase index numbers.

[0032] FIG. 4 shows an example 400 of a ring oscillator. The ring oscillator is shown in the example of FIG. 4 as a first ring oscillator 402 and a second ring oscillator 404. The first and second ring oscillators 402 and 404 can correspond to two ring oscillators within the edging machine coupling network 300 in the example of FIG. 3. In particular, the first ring oscillator 402 can correspond to the ring oscillator in the example of FIG. 3 that has a coupling stage 302 with a phase index number of "1" at row 322 and column 332. The first ring oscillator 402 extends in a first direction along an L-shaped first leg to a coupling stage with a phase index number of "2" at the vertex of row 322 and column 334, and then extends in a second direction orthogonal to the first direction along an L-shaped second leg to a coupling stage with a phase index number of "10" at row 306 and column 334. Further, the first ring oscillator 402 includes a return path for the oscillation signal that couples the coupling stage with a phase index number of "10" back to the coupling stage with a phase index number of "1". Referring further to the example of FIG. 3, the first ring oscillator 402 can thus cross and thus cross-couple with each of the other ring oscillators at each of the plurality of coupling stages 302 at distinct respective phase index numbers, except for the coupling stage at the phase index number "2" at the vertex of the L-shape.

[0033] The second ring oscillator 404 can correspond to the ring oscillator in the example of FIG. 3 having the coupling stage 302 with a phase index number of "1" at row 318 and column 328. The second ring oscillator 404 extends in a first direction along the L-shaped first leg to the coupling stage with a phase index number of "6" at the vertex of row 318 and column 338, and then extends in a second direction orthogonal to the first direction along the L-shaped second leg to the coupling stage with a phase index number of "10" at row 310 and column 338. Also, the second ring oscillator 404 includes a return path for the oscillation signal that couples the coupling stage with a phase index number of "10" back to the coupling stage with a phase index number of "1". Referring further to the example of FIG. 3, the second ring oscillator 404 can thus cross and thus cross-couple with each of the other ring oscillators at each of the plurality of coupling stages 302 at a separate respective phase index number, except for the coupling stage at the phase index number "6" at the vertex of the L-shape. Thus, the second ring oscillator 404 can cross the first ring oscillator 402 at each of the respective coupling stages having a phase index number of "4" at row 318 and column 334 that are common to both the first ring oscillator 402 and the second ring oscillator 404.

[0034] The first and second ring oscillators 402 and 404 can have approximately equal distances with respect to the round-trip of the oscillation signals in each of the first and second ring oscillators 402 and 404, and thus, this can be the same distance as the remaining ring oscillators in the edging machine coupling network 300 in the example of FIG. 3. Thus, the ring oscillators of the edging machine coupling network 300 can provide an accurate nominal phase relationship between their respective oscillation signals when solving a given edging problem. As shown in the example of FIG. 3, the edging machine coupling network 300 includes ten ring oscillators, but the design principles described herein can be extended to provide much larger edging machines including dozens, scores, or more ring oscillators, as will be described in more detail herein. Further, the edging machine coupling network 300 can be manufactured in a CMOS manufacturing process. However, as will be described in the example of FIG. 5, a similar edging machine can be manufactured using a column-based FPGA implementation.

[0035] FIG. 5 shows an edging machine coupling network 500 of another example. The edging machine coupling network 500 can correspond to a part of the edging machine system 100 in the example of FIG. 1. When describing the example of FIG. 5, the edging machine coupling network 500 includes ring oscillators such as the ring oscillator 200 in the example of FIG. 2. Thus, in the following description of the example of FIG. 5, refer to the examples of FIGS. 1 and 2. As described in the example of FIG. 5, the edging machine coupling network 500 can be implemented using a column-based CMOS FPGA.

[0036] In the example of FIG. 3, the ring oscillator is represented by lines connecting a plurality of coupling stages 502, and the lines are solid, dotted, dashed, and dotted-dashed to represent different ring oscillators and thus oscillator signals propagating around a given ring oscillator. In the example of FIG. 5, the edging machine coupling network 500 includes four different ring oscillators. Each of the plurality of ring oscillators starts from a coupling stage 502 having a phase index number "1" and is connected along the coupling stages having consecutive phase index numbers up to the tenth final coupling stage having a phase index number "4". In the example of FIG. 5, the plurality of coupling stages 502 are provided in columns each corresponding to one of the phase index numbers. Thus, each of the plurality of ring oscillators intersects a different one of the plurality of ring oscillators having the same phase index number at each of the plurality of coupling stages except one. As a result, the coupling stage 502 at each intersection of two ring oscillators corresponds to two coupling stages 502, one for each of the two respective ring oscillators. As an example, the coupling stages 502 at a given intersection of two ring oscillators can be fabricated together to minimize the interconnection of oscillator signals for cross-coupling between the respective ring oscillators.

[0037] Accordingly, the edging machine coupling network 500 can operate in the same manner as described above with respect to the edging machine 300 in the example of FIG. 3. Thus, the edging machine coupling network 500 represents an alternative embodiment of the edging machine 300 shown in the example of FIG. 3. The edging machine coupling network 500 can be extended to include a significantly large number of ring oscillators, and thus the number of coupling stages having each respective phase index number can be increased.

[0038] As described above, the design principles described herein can be extended to provide much larger annealing machines that include dozens, hundreds, or more ring oscillators. FIG. 6 shows an annealing machine coupling network 600 of another example. The annealing machine coupling network 600 is fabricated to have a very large number Y of ring oscillators in a two-dimensional array, and each ring oscillator includes Y coupling stages. Similar to what was described above in the example of FIG. 3, each of the plurality of ring oscillators can be cross-coupled with each of the other ring oscillators at the same phase index number. Such a large number of ring oscillators can provide the calculation of significantly more complex annealing problems. However, since each ring oscillator is configured to propagate only a single oscillation signal, the amount of delay during the determination of the phase relationship between each oscillation signal and the oscillation signal of another ring oscillator can be large based on the amount of time required for each oscillation signal to make one round trip through each of the respective ring oscillators.

[0039] For example, in the example of FIG. 6, one of the plurality of ring oscillators is outlined by a dotted line at 602. Ring oscillator 602 includes 30 coupling stages, similar to all of the other ring oscillators within the annealing machine coupling network 600, and as a result, it takes a significant amount of time for the oscillation signal to propagate once around ring oscillator 602, and thus it may take a significant amount of time to solve the annealing problem based on the phase relationship between ring oscillator 602 and each of the other ring oscillators. Accordingly, the design principles of the annealing machines described herein can provide a significantly more efficient solution to the annealing problem based on reducing the latency of the oscillation signal between coupling stages and reducing the associated power consumption, but without making other changes, extending to annealing machines with a significantly larger number of ring oscillators may result in a diminishing marginal benefit.

[0040] FIG. 7 shows an edging machine coupling network 700 of another example. The edging machine coupling network 700 can correspond to an edging machine coupling network that is a modified version of the edging machine coupling network 600 in the example of FIG. 6. In the example of FIG. 7, the edging machine coupling network 700 includes separate array portions 702, 704, and 706 that collectively correspond to at least a portion of the edging machine. In the example of FIG. 7, the array portions 702, 704, and 706 are arranged in a one-dimensional array.

[0041] As an example, the edging machine coupling network 700 can be formed by dividing each of a plurality of ring oscillators in a large edging machine, such as the edging machine coupling network 600 in the example of FIG. 6, into several portions each included in one of the array portions such as array portions 702, 704, and 706. Thus, the ring oscillators within each array portion can be dedicated ring oscillators having a return path, and the connection to the ring oscillators in the next consecutive array portion is made via an intermediate coupling stage 708. Thus, each of the plurality of ring oscillators in a large-scale edging machine coupling network such as the edging machine coupling network 600 can be divided into separate ring oscillators.

[0042] Furthermore, the edging machine coupling network 700 includes additional coupling stages 710 at the ends of the array portions 702 and 706 that are not coupled to any other ring oscillators. The intermediate coupling stage 708 and the additional coupling stage 710 are provided to balance the operation of the individual ring oscillators that collectively form something equivalent to a larger ring oscillator (e.g., ring oscillator 602). Thus, the intermediate coupling stage 708 corresponds to the first coupling stage in the ring oscillators in both adjacent array portions such that it includes a return path to either another intermediate coupling stage 708 (for the ring oscillators in the second array portion 704, for example) or an additional coupling stage 710 (for the ring oscillators in the first and third array portions 702 and 706, for example).

[0043] In the example of FIG. 7, a plurality of ring oscillators in a given one of array portions 702, 704, and 706 can each propagate their respective oscillation signals in an opposite direction to a plurality of ring oscillators in the next adjacent array portion. As shown in the example of FIG. 7, the plurality of ring oscillators in array portion 702 propagate the oscillation signal in a clockwise direction, the plurality of ring oscillators in array portion 704 propagate the oscillation signal in a counterclockwise direction, and the plurality of ring oscillators in array portion 706 propagate the oscillation signal in a clockwise direction. Thus, the plurality of oscillation signals of the plurality of ring oscillators in each of array portions 702, 704, and 706 can interact with each other to provide a phase relationship between the plurality of ring oscillators in each of array portions 702, 704, and 706. In this way, a given one of the ring oscillators in each of array portions 702, 704, and 706 can operate in the same manner as one large ring oscillator across the entire large-scale Josephson machine coupling network, but can operate with a propagation time (e.g., about one-third of the propagation time) that is significantly shorter than that of each oscillation signal of the large-scale Josephson machine coupling network.

[0044] In the example of FIG. 7, the jitter machine coupled network 700 includes a first ring oscillator 712 in the first array portion 702, a second ring oscillator 714 in the second array portion 704, and a third ring oscillator 716 in the third array portion 706. Also, the ring oscillator 712 includes one of the additional coupling stages 710 and one of the intermediate coupling stages 708, and the ring oscillator 714 includes two of the intermediate coupling stages 708. Further, the ring oscillator 716 includes one of the additional coupling stages 710 and one of the intermediate coupling stages 708. In the example of FIG. 7, the intermediate coupling stage 708 is shown as being shared between adjacent array portions such that a single intermediate coupling stage 708 is included in both the first ring oscillator 712 and the second ring oscillator 714, and another single intermediate coupling stage 708 is included in both the second ring oscillator 714 and the third ring oscillator 716, as indicated by the dotted lines bounding the ring oscillators 712, 714, and 716. Thus, the ring oscillators 712, 714, and 716 can collectively correspond to the ring oscillator 602 in the example of FIG. 6.

[0045] The first ring oscillator 712 can propagate in the clockwise direction within the first array portion 702, the second ring oscillator 714 can propagate in the counterclockwise direction within the second array portion 704, and the third ring oscillator 716 can propagate in the clockwise direction within the third array portion 706. Thus, the first ring oscillator 712 can be cross-coupled to the second ring oscillator 714 via one intermediate coupling stage 708, and the second ring oscillator 714 can be cross-coupled to the third ring oscillator 716 via another intermediate coupling stage 708. Thus, the ring oscillators 712, 714, and 716 can collectively correspond to the ring oscillator 602 including 30 coupling stages. However, since the ring oscillators 712, 714, and 716 each propagate their respective oscillation signals to provide cross-coupling at each rotation, the ring oscillators 712, 714, and 716 can provide the phase relationship with other ring oscillators of the eddy current machine coupling network 700 in approximately one-third of the time of the ring oscillator 602 within the eddy current machine coupling network 600. Thus, the eddy current machine coupling network 700 can provide a faster and more efficient eddy current solution as compared to the eddy current machine coupling network 600.

[0046] FIG. 8 shows an eddy current machine coupling network 800 of another example. The eddy current machine coupling network 800 can correspond to a modified eddy current machine coupling network, such as the eddy current machine coupling networks 600 and 700 in each of the examples of FIGS. 6 and 7. In the example of FIG. 8, the eddy current machine coupling network 800 includes separate array portions 802, 804, 806, and 808 that collectively correspond to at least a portion of the eddy current machine. In the example of FIG. 8, the array portions 802, 804, and 806 are arranged in a two-dimensional array.

[0047] The Ezing machine coupling network 800 can be formed by copying the Ezing machine coupling network (e.g., array portions 802, 804, 806, and 808) multiple times into an array including vertical and horizontal mirror symmetries. Thus, the ring oscillators within each array portion can be dedicated ring oscillators with return paths. However, each of the multiple ring oscillators in a given one of the array portions 802, 804, 806, 808 can be cross-coupled to one ring oscillator in at least one orthogonally adjacent array portion, as shown by the cross-couplings between the array portions 802, 804, 806, 808 and the intermediate coupling stage 810. The array portions 802, 804, 806, 808 within the Ezing machine coupling network 800 are shown by way of example and can include significantly more ring oscillators, coupling stages, and / or array portions than shown in the example of FIG. 8.

[0048] The Ezing machine coupling network 800 can operate as a different type of Ezing machine architecture, in which the Ezing machine coupling network 800 operates as an array of fully connected portions with limited cross-couplings between portions. As an example, an Ezing machine coupling network configured similarly to the Ezing machine coupling network 800 can have a 10×10 array of portions, each portion including 16 ring oscillators. Thus, the Ezing machine coupling network would have 1600 oscillators, and as a result, the Ezing machine coupling network can implement 1600 unique variables. Thus, the number of other variables to which each variable can be connected is significantly reduced (e.g., only 15 - 18). Thus, the Ezing machine coupling network 800 represents an alternative to the Ezing machine coupling network 700.

[0049] What is described above are examples of the present invention. Of course, it is not possible to describe every possible combination of components or methods for the purpose of explaining the present invention, but those skilled in the art will recognize that many more combinations and substitutions of the present invention are possible. Accordingly, the present invention is intended to embrace all such changes, modifications, and variations that fall within the spirit and scope of the technical idea of the appended claims. In addition, when the present disclosure or the claims enumerate "a", "an", "a first", or "another" component, or equivalents thereof, it should be construed to include one or more such components, and does not necessarily require or exclude two or more such components. As used herein, the term "includes" means including but not limited to, and the term "including" means including but not limited to. The term "based on" means at least partially based on. The technical ideas that can be grasped from the above embodiments are described below as supplementary notes. [Supplementary Note 1] An edging machine system configured to solve edging problems, the edging machine system comprising a plurality of ring oscillators each configured to propagate an oscillation signal, each of the plurality of ring oscillators including a plurality of coupling stages, each of the plurality of coupling stages having a unique phase index number within one of each of the plurality of ring oscillators that matches the phase index number of each of the plurality of coupling stages of the other ring oscillators, each of the plurality of coupling stages being cross-coupled to a coupling stage having the same phase index number of one of the other ring oscillators via the oscillation signal associated with each of the plurality of ring oscillators, excluding one coupling stage of each of the plurality of ring oscillators, such that each of the plurality of ring oscillators is cross-coupled to each of the other ring oscillators by a single one of the plurality of coupling stages, and a respective phase coupling is provided between each pair of cross-coupled ring oscillators. [Supplementary Note 2] The propagation distance of the oscillation signal between a first coupling stage having a given phase index number and a second coupling stage having the next consecutive phase index number is equal for each of the plurality of ring oscillators, the system according to Supplementary Note 1. [Supplementary Note 3] The Manhattan distance of each of the plurality of ring oscillators is equal to the Manhattan distance of each of the other ring oscillators, the system according to Supplementary Note 1. [Supplementary Note 4] The plurality of coupling stages of the plurality of ring oscillators are arranged in a two-dimensional array, the system according to Supplementary Note 1. [Supplementary Note 5] Among the plurality of ring oscillators, the plurality of coupling stages of the first ring oscillator are fabricated in a linear physical arrangement along a first axis of the two-dimensional array, and the plurality of coupling stages associated with a second ring oscillator among the plurality of ring oscillators are fabricated in a linear physical arrangement along a second axis of the two-dimensional array that is orthogonal to the first axis. One of the plurality of coupling stages of the first ring oscillator among the plurality of ring oscillators physically intersects one of the plurality of coupling stages of the second ring oscillator among the plurality of ring oscillators having the same phase index number within the two-dimensional array. The system according to Supplementary Note 4. [Supplementary Note 6] Each of the remaining ring oscillators is fabricated in a physical L shape, and one of the plurality of coupling stages of each of the plurality of ring oscillators physically intersects one of the plurality of coupling stages of each of the other ring oscillators having the same phase index number within the two-dimensional array. The system according to Supplementary Note 5. [Supplementary Note 7] The coupling stage at the vertex of the physical L shape of each of the remaining ring oscillators is not coupled to another coupling stage of another ring oscillator among the plurality of ring oscillators. The system according to Supplementary Note 6. [Supplementary Note 8] The two-dimensional array includes a plurality of array portions, each of the plurality of array portions includes a separate plurality of ring oscillators, and each of the plurality of ring oscillators in a first array portion is cross-coupled to one of the plurality of ring oscillators in a second array portion to provide a phase coupling between the plurality of ring oscillators in the first array portion and the plurality of ring oscillators in the second array portion. The system according to Supplementary Note 5. [Supplementary Note 9] The plurality of array portions are physically arranged in a one-dimensional array, and the oscillation signals in each of the plurality of ring oscillators in one of the plurality of array portions propagate in a direction opposite to the oscillation signals in each of the plurality of ring oscillators in the next consecutive array portion in the one-dimensional array of the plurality of array portions. The system according to Supplementary Note 8. [Supplementary Note 10] The system according to appended note 8, wherein the plurality of array portions are physically arranged in a two-dimensional array, and each of the plurality of ring oscillators is cross-coupled via a coupling stage to one ring oscillator in each of the array portions that are orthogonally adjacent in the two-dimensional array of the plurality of array portions. [Appended note 11] The system according to appended note 1, further comprising an edging machine controller configured to generate a plurality of control signals corresponding to parameters of the edging problem and control relative phase coupling of each of the plurality of ring oscillators to the other ring oscillators. [Appended note 12] An edging machine system configured to solve an edging problem, the edging machine system comprising a plurality of ring oscillators each configured to propagate an oscillation signal, each of the plurality of ring oscillators including a plurality of coupling stages arranged in a two-dimensional array, the plurality of coupling stages of a first ring oscillator among the plurality of ring oscillators being fabricated in a linear physical arrangement along a first axis of the two-dimensional array, the plurality of coupling stages associated with a second ring oscillator among the plurality of ring oscillators being fabricated in a linear physical arrangement along a second axis of the two-dimensional array orthogonal to the first axis, each of the remaining ring oscillators being fabricated in a physical L-shape, each of the plurality of coupling stages having a unique phase index number that matches the phase index number of each of the plurality of coupling stages of each of the other ring oscillators within the two-dimensional array, each of the plurality of coupling stages, except for one coupling stage of each of the plurality of ring oscillators, is cross-coupled via the oscillation signal associated with each of the plurality of coupling stages to a coupling stage having the same phase index number of one of the other ring oscillators based on crossing the other ring oscillators, such that each of the plurality of ring oscillators is cross-coupled to each of the other ring oscillators by a single one of the plurality of coupling stages, and a respective phase coupling is provided between each of the cross-coupled ring oscillators. [Appended note 13] The propagation distance of the oscillation signal between a first coupling stage having a given phase index number and a second coupling stage having the next consecutive phase index number is equal for each of the plurality of ring oscillators, the system according to Supplementary Note 12. [Supplementary Note 14] The coupling stage at the physical L-shaped vertex of each of the remaining ring oscillators is not coupled to other coupling stages of other ring oscillators among the plurality of ring oscillators, the system according to Supplementary Note 12. [Supplementary Note 15] The two-dimensional array includes a plurality of array portions, and a first array portion is linked to a second array portion, and based on cross-coupling of the coupling stages of each of the plurality of ring oscillators of each of the first and second array portions, provides phase coupling between the plurality of ring oscillators of the first array portion and the plurality of ring oscillators of the second array portion, the system according to Supplementary Note 12. [Supplementary Note 16] An edging machine system configured to solve an edging problem, the edging machine system including a plurality of ring oscillators each configured to propagate an oscillation signal, each of the plurality of ring oscillators including a plurality of coupling stages, each of the plurality of coupling stages having a unique phase index number that matches the phase index number of each of the plurality of coupling stages of each of the other ring oscillators within each of the plurality of ring oscillators, each of the plurality of coupling stages being cross-coupled, via the oscillation signal associated with each respective ring oscillator, except for one coupling stage of each of the plurality of ring oscillators, to a coupling stage having the same phase index number of one of the other ring oscillators such that each of the plurality of ring oscillators is cross-coupled to each of the other ring oscillators by a single one of the plurality of coupling stages, and a respective phase coupling is provided between each pair of cross-coupled ring oscillators, and the propagation distance of the oscillation signal between a first coupling stage having a given phase index number and a second coupling stage having the next consecutive phase index number is equal for each of the plurality of ring oscillators, the edging machine system. [Supplementary Note 17] The plurality of coupling stages of the plurality of ring oscillators are arranged in a two-dimensional array, and the plurality of coupling stages of a first ring oscillator among the plurality of ring oscillators are fabricated in a linear physical arrangement along a first axis of the two-dimensional array, and the plurality of coupling stages associated with a second ring oscillator among the plurality of ring oscillators are fabricated in a linear physical arrangement along a second axis of the two-dimensional array orthogonal to the first axis, and one of the plurality of coupling stages of the first ring oscillator among the plurality of ring oscillators physically intersects one of the plurality of coupling stages of the second ring oscillator among the plurality of ring oscillators having the same phase index number in the two-dimensional array. The system according to Supplementary Note 16. [Supplementary Note 18] Each of the remaining ring oscillators is fabricated in a physical L-shape, and one of the plurality of coupling stages of each of the plurality of ring oscillators physically intersects one of the plurality of coupling stages of each of the other ring oscillators having the same phase index number in the two-dimensional array. The system according to Supplementary Note 17. [Supplementary Note 19] The coupling stage at the vertex of the physical L-shape of each of the remaining ring oscillators is not coupled to another coupling stage of another ring oscillator among the plurality of ring oscillators. The system according to Supplementary Note 18. [Supplementary Note 20] The two-dimensional array includes a plurality of array portions, and a first array portion is linked to a second array portion to provide phase coupling between the ring oscillators of the first array portion and the ring oscillators of the second array portion based on cross-coupling of the coupling stages of each of the plurality of ring oscillators of each of the first and second array portions. The system according to Supplementary Note 17.

Claims

1. 1. An Ising machine system configured to solve an Ising problem, the Ising machine system comprising a plurality of ring oscillators each configured to propagate an oscillation signal, each of the plurality of ring oscillators including a plurality of coupling stages, each of the plurality of coupling stages having a unique phase index number within a respective one of the plurality of ring oscillators that matches a phase index number of the plurality of coupling stages of each of the other ring oscillators, each of the plurality of coupling stages, except for one coupling stage of each of the plurality of ring oscillators, is cross-coupled to a coupling stage having the same phase index number of one of the other ring oscillators via the oscillation signal associated with the respective ring oscillator, each of the plurality of ring oscillators being cross-coupled to each of the other ring oscillators at a single respective one of the plurality of coupling stages to provide a respective phase coupling between respective cross-coupled ring oscillators.

2. 2. The system of claim 1, wherein a propagation distance of the oscillator signal between a first combining stage having a given phase index number and a second combining stage having a next consecutive phase index number is equal for each of the plurality of ring oscillators.

3. 2. The system of claim 1, wherein the Manhattan distance of each of the plurality of ring oscillators is equal to the Manhattan distance of each of the other ring oscillators.

4. The system of claim 1 , wherein the multiple coupled stages of the multiple ring oscillators are arranged in a two-dimensional array.

5. 5. The system of claim 4, wherein the multiple coupling stages of a first ring oscillator of the plurality of ring oscillators are fabricated in a linear physical arrangement along a first axis of the two-dimensional array, and the multiple coupling stages associated with a second ring oscillator of the plurality of ring oscillators are fabricated in a linear physical arrangement along a second axis of the two-dimensional array that is orthogonal to the first axis, and one of the multiple coupling stages of the first ring oscillator of the plurality of ring oscillators physically intersects one of the multiple coupling stages of the second ring oscillator of the plurality of ring oscillators having the same phase index number in the two-dimensional array.

6. 6. The system of claim 5, wherein each of the remaining ring oscillators is fabricated in a physical L-shape, and one of the multiple coupling stages of each of the plurality of ring oscillators physically intersects one of the multiple coupling stages of each of the other ring oscillators having the same phase index number in the two-dimensional array.

7. 7. The system of claim 6, wherein the coupling stage at the apex of the physical L-shape of each of the remaining ring oscillators is not coupled to other coupling stages of other ring oscillators of the plurality of ring oscillators.

8. 6. The system of claim 5, wherein the two-dimensional array comprises a plurality of array portions, each of the plurality of array portions comprising a separate plurality of ring oscillators, and each of the plurality of ring oscillators in a first array portion is cross-coupled to one of the plurality of ring oscillators in a second array portion to provide phase coupling between the plurality of ring oscillators of the first array portion and the plurality of ring oscillators of the second array portion.

9. 9. The system of claim 8, wherein the plurality of array portions are physically arranged in a one-dimensional array, and the oscillating signal in each of the plurality of ring oscillators of one of the plurality of array portions propagates in an opposite direction relative to the oscillating signal in each of the plurality of ring oscillators of a next successive array portion in the one-dimensional array of the plurality of array portions.

10. 9. The system of claim 8, wherein the plurality of array portions are physically arranged in a two-dimensional array, and each of the plurality of ring oscillators is cross-coupled via a coupling stage to one ring oscillator in each orthogonally adjacent array portion in the two-dimensional array of the plurality of array portions.

11. 2. The system of claim 1, further comprising an Ising machine controller configured to generate a plurality of control signals corresponding to parameters of the Ising problem to control a relative phase coupling of each of the plurality of ring oscillators to the other ring oscillators.

12. 1. An Ising machine system configured to solve an Ising problem, the Ising machine system comprising a plurality of ring oscillators each configured to propagate an oscillatory signal, each of the plurality of ring oscillators including a plurality of coupled stages arranged in a two-dimensional array, the plurality of coupled stages of a first ring oscillator of the plurality of ring oscillators being fabricated in a linear physical arrangement along a first axis of the two-dimensional array, the plurality of coupled stages associated with a second ring oscillator of the plurality of ring oscillators being fabricated in a linear physical arrangement along a second axis of the two-dimensional array that is orthogonal to the first axis, and each of the remaining ring oscillators being fabricated in a physical L-shape, and each of the plurality of coupled stages being fabricated in a linear physical arrangement along a first axis of the two-dimensional array that is orthogonal to the first axis, each of the plurality of coupling stages, except for one coupling stage of each of the plurality of ring oscillators, is cross-coupled to a coupling stage having the same phase index number of one of the other ring oscillators via the oscillation signal associated with each of the plurality of coupling stages based on crossing with the other ring oscillator, such that each of the plurality of ring oscillators is cross-coupled to each of the other ring oscillators with a single respective one of the plurality of coupling stages to provide a respective phase coupling between each cross-coupled ring oscillator.

13. 13. The system of claim 12, wherein a propagation distance of the oscillator signal between a first combining stage having a given phase index number and a second combining stage having a next consecutive phase index number is equal for each of the plurality of ring oscillators.

14. 13. The system of claim 12, wherein the coupling stage at the apex of the physical L-shape of each of the remaining ring oscillators is not coupled to other coupling stages of other ring oscillators of the plurality of ring oscillators.

15. 13. The system of claim 12, wherein the two-dimensional array comprises a plurality of array portions, a first array portion linked to a second array portion to provide phase coupling between the plurality of ring oscillators of the first array portion and the plurality of ring oscillators of the second array portion based on cross-coupling of coupling stages of each of the plurality of ring oscillators of each of the first and second array portions.

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