Magnetic coprocessor and method of use

1. A method for solving a quadratic optimization problem, the method comprising:

associating each of a plurality of variables of a quadratic optimization problem with a nanomagnet of a nanomagnet array;

driving the nanoagnets of the nanomagnet array to an excited state;

allowing the nanomagnets of the nanomagnet array to enter a relaxed state after being driven to an excited state, wherein the nanomagnets magnetically couple with one another in the relaxed state to minimize the total magnetic coupling energy of the nanomagnet array; and

sensing a magnetic coupling of the nanomagnets of the nanomagnet array to solve the quadratic optimization problem.

2. The method of claim 1 , wherein associating each of a plurality of variables of a quadratic optimization problem with a nanomagnet of a nanomagnet array further comprises:

identifying a plurality of variables of quadratic optimization problem;

mapping a nanomagnet of the nanomagnet array to each of the variables of the quadratic optimization problem, wherein the distances between the nanomagnets that have been mapped to the variables of the quadratic optimization problem are such that a magnetic coupling energy of the nanomagnets is proportional to an energy relationship between the plurality of variables in the quadratic optimization problem.

3. The method of claim 1 , further comprising, selecting the nanomagnets of the nanomagnet array that have been mapped to the variables of the quadratic optimization problem and deselecting the nanomagnets of the nanomagnet array that have not been mapped to the variables of the quadratic optimization problem.

4. The method of claim 1 , wherein sensing a magnetic coupling of the nanomagnets of the nanomagnet array to solve the quadratic optimization problem, further comprises:

sensing a state of each of the plurality of nanomagnets of the nanomagnet array to identify one or more nanomagnets of the plurality of nanomagnets that are in a single domain state; and

mapping the single domain state nanomagnets back to the plurality of variables of the quadratic optimization problem to solve the quadratic optimization problem.

5. The method of claim 1 . wherein the quadratic optimization problem is selected from a group of quadratic optimization problems consisting of motion segmentation, correspondence, figure-ground segmentation, clustering, grouping, subgraph matching and digital graph matching.

6. The method of claim 1 . wherein sensing a magnetic coupling of the nanomagnets of the nanomagnet array to solve the quadratic optimization problem further comprises sensing the magnetic coupling of the nanomagnets of the nanomagnet array in parallel.

7. The method of claim 1 , wherein the nanomagnet array is a two-dimensional array and wherein each of the nanomagnets of the nanomagnet array is a disk-shaped magnetic tunnel junction (MTJ) nanomagnet.

8. The method of claim 1 , wherein the quadratic optimization problem is a quadratic optimization problem for identifying salient edge segments of an image, and wherein associating each of a plurality of variables of a quadratic optimization problem for identifying salient edge segments of an image with a nanomagnet of a nanomagnet array further comprises:

processing an image to identify a plurality of edge segments of the image;

calculating an affinity matrix for the plurality of edge segments of the image;

calculating a distance map matrix for the plurality of edge segments of the image;

generating the nanomagnet array based upon the affinity matrix and the distance map matrix; and

mapping each of the edge segments of the image to one of the nanomagnets of the nanomagnet array.

9. A system for solving a quadratic optimization problem, the system comprising:

a nanomagnet array comprising a plurality of nanomagnets;

read/write/drive circuitry coupled to the nanomagnet array;

a compiler coupled to the drive circuitry and the read/write/drive circuitry, the compiler configured for;

associating each of a plurality of variables of a quadratic optimization problem with a nanomagnet of the nanomagnet array;

instructing the read/write/drive circuitry to drive the nanomagnets of the nanomagnet array to an excited state;

allowing the nanomagnets of the nanomagnet array to enter a relaxed state after being driven to an excited state, wherein the nanomagnets magnetically couple with one another in the relaxed state to minimize the total magnetic coupling energy of the nanomagnet array; and

instructing the read/write/drive circuitry to sense a magnetic coupling of the nanomagnets of the nanomagnet array to solve the quadratic optimization problem.

10. The system of claim 9 , wherein associating each of a plurality of variables of a quadratic optimization problem with a nanomagnet of a nanomagnet array further comprises:

identifying a plurality of variables of a quadratic optimization problem;

mapping a nanomagnet of the nanomagnet array to each of the variables of the quadratic optimization problem, wherein the distances between the nanomagnets that have been mapped to the variables of the quadratic optimization problem are such that a magnetic coupling energy of the nanomagnets is proportional to an energy relationship between the plurality of variables in the quadratic optimization problem.

11. The system of claim 10 , wherein the compiler is further configured for selecting the nanomagnets of the nanomagnet array that have been mapped to the variables of the quadratic optimization problem and deselecting the nanomagnets of the nanomagnet array that have not been mapped to the variables of the quadratic optimization problem.

12. The system of claim 9 , wherein instructing the read/write/drive circuitry to sense a magnetic coupling of the nanomagnets of the nanomagnet array to solve the quadratic optimization problem, further comprises:

instructing the read/write/drive circuitry to sense a state of each of the plurality of nanomagnets of the nanomagnet array to identify one or more nanomagnets of the plurality of nanomagnets that are in a single domain state; and

mapping the single domain state nanomagnets back to the plurality of variables of the quadratic optimization problem to solve the quadratic optimization problem.

13. The system of claim 9 , wherein the nanomagnet array is reconfigurable by the magnetic coprocessor.

14. The system of claim 9 , wherein the nanomagnet array is a two-dimensional nanomagnet array.

15. The system of claim 9 , wherein the nanomagnet array is a two-dimensional spin-transfer torque magnetic random access memory (STT-MRAM) reconfigurable array.

16. The system of claim 9 , wherein each of the nanomagnets of the nanomagnet array is a disk-shaped magnetic tunnel junction (MTJ) nanomagnet.

17. The system of claim 9 , wherein the read/write/sense circuitry comprises a plurality of complementary metal-oxide semiconductor transistors.

18. The system of claim 9 , wherein the quadratic optimization problem is selected from a group of quadratic optimization problems consisting of motion segmentation, correspondence, figure-ground segmentation, clustering, grouping, subgraph matching and digital graph matching.

19. The system of claim 9 , wherein the quadratic optimization problem is a quadratic optimization problem for identifying salient edge segments of an image, and wherein associating each of a plurality of variables of a quadratic optimization problem for identifying salient edge segments of an image with a nanomagnet of a nanomagnet array, and wherein the compiler is further configured for:

processing an image to identify a plurality of edge segments of the image;

calculating an affinity matrix for the plurality of edge segments of the image;

calculating a distance map matrix for the plurality of edge segments of the image;

generating the nanomagnet array based upon the affinity matrix and the distance map matrix; and

mapping each of the edge segments of the image to one of the nanomagnets of the nanomagnet array.

20. One or more non-transitory computer-readable media having computer-executable instructions for performing a method of running a software program on a computing device for solving a quadratic optimization problem, the computing device operating under an operating system, the method including issuing instructions from the software program comprising:

communicatively accessing the operating system of the computing device;

associating each of a plurality of variables of a quadratic optimization problem with a nanomagnet of a nanomagnet array;

driving the nanotnagnets of the nanomagnet array to an excited state;

allowing the nanomagnets of the nanomagnet array to enter a relaxed state after being driven to an excited state, wherein the nanomagnets magnetically couple with one another in the relaxed state to minimize the total magnetic coupling energy of the nanomagnet array; and

sensing a magnetic coupling of the nanomagnets of the nanomagnet array to solve the quadratic optimization problem.