Systems and Methods for Quantum Global Optimization

• US 20200133947A1
• Filed: 10/25/2019
• Published: 04/30/2020
• Est. Priority Date: 10/25/2018
• Status: Active Grant

• Current Assignee: Georgia Tech Research Corporation (University System of Georgia)
• Original Assignee: Georgia Tech Research Corporation (University System of Georgia)
• Inventors: Wang, Yan
• Granted Patent: US 11,514,038 B2
• Time in Patent Office: Days
• CPC Class Codes: G06F 16/2453 Query optimisation
• CPC Class Codes: G06F 17/11 for solving equations , e.g. nonlinear equations, general mathematical optimization problems optimization specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06N 10/00 Quantum computing, i.e. information processing based on quantum-mechanical phenomena
• CPC Class Codes: G06N 3/126 Evolutionary algorithms, e.g. genetic algorithms or genetic programming

Abstract

A method for global optimization is disclosed. The method may include receiving a search request that may include an input. The method may further determine an amount of rotations necessary to perform the search request with a Grover Search algorithm. Then, the method may include determining that the amount of rotations is less than a predefined amount. Further, the method may generate one or more quantum walks. The one or more quantum walks and the Grover Search algorithm may be used to generated a global optimization algorithm. The method may then execute the global optimization algorithm to identify the input.

Claims

1. ) A method for global optimization, the method comprising:

receiving a search request comprising an input;

determining an amount of rotations necessary to perform the search request with a Grover Search algorithm;

determining that the amount of rotations is less than a predefined amount;

generating one or more quantum walks;

replacing the rotations in the Grover Search algorithm with the one or more quantum walks;

generating a global optimization algorithm based on the Grover search algorithm and the one or more quantum walks; and

executing the global optimization algorithm to identify the input.

2. ) The method of claim 1, wherein identifying the input with the global optimization algorithm has a first computational cost.

3. ) The method of claim 2, further comprising:

estimating a second computational cost for identifying the input using the Grover Search algorithm.

4. ) The method of claim 3, wherein the first computational cost is less than the second computational cost.

5. ) The method of claim 1, wherein generating the one or more quantum walks further comprises:

determining a functional integral by applying an equation (9) of;

6. ) The method of claim 5, wherein generating the one or more quantum walks further comprises:

applying an equation of;

7. ) The method of claim 6, further comprising:

updating the j^th element by applying the equation of;

8. ) The method of claim 7, further comprising:

determining a probability that j is observed by applying the equation of;

9. ) The method of claim 8, wherein:

Rc=[0,0,0,0,1,1,0,1,1,2,1,2,3,1,4,5,1,6,2,7,9,11,13,16,5,20,24,28,34,2,41, 49,4,60,72,0,88,105,125,3,149,22,133,219]

is the amount of rotations necessary to perform the search request with the Grover Search algorithm.

10. ) The method of claim 9, wherein the global optimization algorithm is represented by:

11. ) The method of claim 1, wherein executing the global optimization algorithm is performed by a quantum computer.

12. ) The method of claim 1, wherein executing the global optimization algorithm is performed by a quantum computer emulator.

13. ) A system for global optimization, the system comprising:

a quantum computer comprising;

a quantum transistor;

a fabric of programmable elements comprising a plurality of couplers and a plurality of qubits;

support circuitry;

a memory in communication with the quantum transistor, the fabric of programmable elements, and the support circuitry, storing instructions, that when executed cause the quantum transistor to;

receive a search request comprising an input;

determine an amount of rotations necessary to perform the search request with a Grover Search algorithm;

determine that the amount of rotations is less than a predefined amount;

generate one or more quantum walks;

replace the rotations in the Grover Search algorithm with the one or more quantum walks;

generate a global optimization algorithm based on the Grover search and the one or more quantum walks; and

execute the global optimization algorithm to identify the input.

14. ) The system of claim 13, wherein generating the one or more quantum walks further comprises:

determining a functional integral by applying an equation (9) of;

15. ) The system of claim 14, wherein generating the one or more quantum walks further comprises:

applying an equation of;

16. ) The system of claim 15, further comprising:

updating the j^th element by applying the equation of;

17. ) The system of claim 16, further comprising:

determining a probability that j is observed by applying the equation of;

18. ) The system of claim 17, wherein:

Rc=[0,0,0,0,1,1,0,1,1,2,1,2,3,1,4,5,1,6,2,7,9,11,13,16,5,20,24,28,34,2,41, 49,4,60,72,0,88,105,125,3,149,22,133,219]

is the amount of rotations necessary to perform the search request with the Grover Search algorithm.

19. ) The system of claim 18, wherein the global optimization algorithm is represented by:

20. ) A method for global optimization, the method comprising:

receiving a search request comprising an input;

determining a plurality of rotations necessary to perform the search request with a Grover Search algorithm;

generating one or more quantum walks based on the plurality of rotations;

replacing the plurality of rotations in the Grover Search algorithm with the one or more quantum walks;

generating a global optimization algorithm based on the Grover search algorithm and the one or more quantum walks; and

executing the global optimization algorithm to identify the input.