Method of simulating quantum computing system and quantum computing simulation system

1. A method of simulating, by a non-quantum computer, a quantum computing system having an error correction function, the method comprising:

generating, by the non-quantum computer, a quantum information density matrix;

generating, by the non-quantum computer, a coded density matrix by performing quantum error correction coding on the quantum information density matrix;

applying, by the non-quantum computer, simulated quantum computing to the coded density matrix and calculating a change in a first reliability of the coded density matrix;

applying, by the non-quantum computer, the simulated quantum computing to the quantum information density matrix and calculating a change in a second reliability of the quantum information density matrix;

determining, by the non-quantum computer, a unit time that calculates error rates and reliabilities of the coded density matrix and the quantum information density matrix;

determining, by the non-quantum computer, an operation time of the simulated quantum computing, based on the unit time and the change in the first reliability and the change in the second reliability; and

performing, by the non-quantum computer, quantum error correction in the simulated quantum computing based on the operation time,

wherein the simulated quantum computing includes an operation of two or more quantum gates on coded quantum information corresponding to the quantum information density matrix,

wherein the performing quantum error correction includes

performing, by the non-quantum computer, quantum error correction decoding on the coded quantum information, and

applying, by the non-quantum computer, a quantum operation opposite to each of types of errors that are determined based on the operation time, and

wherein the determining the unit time includes shortening the unit time to improve at least one of a resolution, an accuracy, or a reliability of time for error correction decoding that is performed by the simulated quantum computing system.

2. The method of claim 1 , wherein the calculating of the change in the first reliability includes:

calculating the change in the first reliability of the coded density matrix in units of the unit time.

3. The method of claim 2 ,

wherein the unit time is less than a respective operation time of the quantum gates.

4. The method of claim 2 , wherein the calculating of the change in the first reliability of the coded density matrix in units of the unit time includes:

applying an error of the unit time by the simulated quantum computing to the coded density matrix; and

applying a naturally occurring quantum error of the unit time to the coded density matrix.

5. The method of claim 4 , wherein the applying of the error of the unit time by the simulated quantum computing to the coded density matrix includes:

applying an error in an amplitude of the unit time by the simulated quantum computing to the coded density matrix; and

applying an error in a phase of the unit time by the simulated quantum computing to the coded density matrix.

6. The method of claim 4 , wherein the applying of the naturally occurring quantum error of the unit time to the coded density matrix includes:

applying an error in a naturally occurring amplitude of the unit time to the coded density matrix; and

applying an error in a naturally occurring phase of the unit time to the coded density matrix.

7. The method of claim 1 , wherein the calculating of the change in the second reliability includes:

calculating the change in the second reliability of the quantum information density matrix in units of a unit time.

8. The method of claim 1 , wherein the determining of the operation time of the simulated quantum computing, based on the change in the first reliability and the change in the second reliability includes:

detecting singularities based on a change in a difference between the first reliability and the second reliability; and

determining the operation time based on the singularities.

9. The method of claim 8 , wherein the detecting of the singularities includes:

detecting at least two singularities in which the difference between the first reliability and the second reliability is less than a threshold.

10. The method of claim 8 , wherein the detecting of the singularities further includes:

when a second singularity is detected after a first singularity is detected, ignoring the second singularity when a time difference between the first singularities and the second singularities is less than or equal to a threshold.

11. The method of claim 8 , wherein the determining of the operation time includes:

determining a time for which the first reliability is highest among the singularities as the operation time.

12. The method of claim 8 , wherein the determining of the operation time includes:

determining a time belonging to the singularities as the operation time.

13. The method of claim 8 , wherein the detecting of the singularities includes:

comparing of the change in the first reliability and the change in the second reliability in units of a reference operation time, and detecting the singularities, based on the comparison in units of the reference operation time.

14. The method of claim 13 ,

wherein the determining of the operation time includes;

determining an accumulative operation time of the quantum gates in which the accumulative operation time belongs to a time period between the singularities, among the two or more quantum gates, as the operation time.

15. A method of simulating, by a non-quantum computer, a quantum computing system having an error correction function, the method comprising:

generating, by the non-quantum computer, a quantum information density matrix;

applying, by the non-quantum computer, a selected one quantum gate to the quantum information density matrix in units of a unit time;

sequentially selecting, by the non-quantum computer, quantum gates and applying the selected quantum gates to the quantum information density matrix in units of the unit time; and

calculating, by the non-quantum computer, a change in reliability of the unit time of the quantum information density matrix as the quantum gates are applied; and

performing, by the non-quantum computer, quantum error correction in the simulated quantum computing system based on the calculated change in reliability,

wherein the performing quantum error correction includes

performing, by the non-quantum computer, quantum error correction decoding on coded quantum information corresponding to the quantum information density matrix,

applying, by the non-quantum computer, a quantum operation opposite to each of types of errors that are determined based on the calculated change in reliability; and

wherein the applying the selected one quantum gate includes shortening the unit time to improve at least one of a resolution, an accuracy, or a reliability of time for error correction decoding that is performed by the simulated quantum computing system.

16. The method of claim 15 , further comprising:

generating a coded density matrix by performing error correction coding on the quantum information density matrix;

sequentially selecting the quantum gates and applying the selected quantum gate to the coded density matrix in units of the unit time; and

calculating a change in a decoded reliability in units of the unit time of the coded density matrix as the quantum gates are applied.

17. The method of claim 16 , further comprising:

determining a time at which decoding is performed on the coded density matrix, based on the change in the reliability and the change in the decoded reliability.

18. The method of claim 16 , wherein the time is determined based on a unit of the operation time of each of the quantum gates.

19. A quantum computing simulation system comprising a non-quantum processor configured to implement the following modules to simulate a quantum computing system having an error correction function, the modules including instructions executable by the non-quantum processor:

a coding module configured to, when executed by the non-quantum processor, receive quantum information and quantum error correction coding information, and to perform error correction coding on the quantum information, based on the quantum error correction coding information to generate coded quantum information;

a memory module configured to, when executed by the non-quantum processor, perform simulated quantum computing by applying quantum gates to the coded quantum information in units of a unit time and by applying the quantum gates to the quantum information in units of the unit time;

an error correction module configured to, when executed by the non-quantum processor, generate decoded quantum information by performing error correction on the coded quantum information to which the quantum gates are applied, in units of the unit time; and

an evaluation module configured to, when executed by the non-quantum processor, calculate a change in a first reliability of the decoded quantum information in units of the unit time, and to calculate a change in a second reliability of the quantum information to which the quantum gates are applied, in units of the unit time;

wherein the evaluation module is further configured to, when executed by the non-quantum processor, determine an operation time to which the quantum gates are applied to the coded quantum information, based on a change in a difference between the first reliability and the second reliability;

wherein the performing quantum error correction includes

performing, by the non-quantum processor, quantum error correction decoding on the coded quantum information, and

applying, by the non-quantum processor, a quantum operation opposite to each of types of errors that are determined based on the operation time; and

wherein the determining the operation time includes shortening the unit time to improve at least one of a resolution, an accuracy, or a reliability of time for error correction decoding that is performed by the quantum computing simulation system.