Apparatus and method for designing quantum code

Patent metadata

Field	Value
Publication number	US-9564924-B2
Application number	US-201214377781-A
Country	US
Kind code	B2
Filing date	Feb 21, 2012
Priority date	Feb 8, 2012
Publication date	Feb 7, 2017
Grant date	Feb 7, 2017

Abstract

Provided is an apparatus for designing a quantum code, which includes an analyzing unit for analyzing at least one quantum error generated in a quantum error channel as at least one binary error by using a standard form codeword stabilized quantum (CWS) code, a code generating unit for generating a binary error-correcting code which corrects the at least one binary error, a word operator generating unit for generating at least one word operator of the CWS code by using the at least one binary error-correcting code, and a codeword generating unit for generating at least one codeword including at least one entangled qubit (ebit) by using the at least one word operator.

First claim

The invention claimed is:

1. An apparatus for designing a quantum code, comprising:
an analyzing unit for converting at least one quantum error generated in a quantum error channel into at least one binary error by using a standard form codeword stabilized quantum (CWS) code;
a code generating unit for generating a binary error-correcting code which corrects the at least one binary error;
a word operator generating unit for generating at least one word operator of the CWS code by using the at least one binary error-correcting code; and
a codeword generating unit for generating at least one codeword including at least one entangled qubit (ebit) by using the at least one word operator.

2. The apparatus for designing a quantum code according to claim 1 ,
wherein a transmitting unit and a receiving unit share the at least one entangled qubit.

3. The apparatus for designing a quantum code according to claim 1 ,
wherein the at least one word operator is generated independently in a transmitting unit.

4. The apparatus for designing a quantum code according to claim 1 , further comprising:
an initializing unit for making the at least one quantum error into an initial state by applying the at least one entangled qubit to an initial state of qubit.

5. The apparatus for designing a quantum code according to claim 4 , further comprising:
a coding unit for coding the initial state by using a unitory coding operation which generates a stabilizer generator of a standard form of the CWS code.

6. The apparatus for designing a quantum code according to claim 5 ,
wherein the analyzing unit converts the at least one quantum error into the at least one binary error according to Equation 1 below by using the stabilizer generator:

Cl
G

⁡

(

E
=

±

Z
v

⁢

X
u

)

=

v
⊕

⊕

l
=
1

n

⁢

u
1

⁢

r
1

Equation
⁢

⁢
1

where E represents an error occurring at the channel, v and u represent binary vectors, r l represents a l th row of a binary matrix representing a circular graph which configures a stabilizer generator, and x and z represent Pauli operators.

7. The apparatus for designing a quantum code according to claim 5 , further comprising:
an eliminating unit for eliminating an entangled qubit performed at a receiving unit from the at least one word operator by applying the stabilizer generator to the at least one word operator.

8. The apparatus for designing a quantum code according to claim 7 ,
wherein the word operator generating unit generates a word operator for the initial state by applying a unitory coding operation to the word operator, from which an entangled qubit is eliminated, performed at the receiving unit.

9. The apparatus for designing a quantum code according to claim 8 , further comprising:
a code configuring unit for configuring a quantum error-correcting code by applying the generated word operator of the initial state to Equation 2 below:
ω′ l =X xl Z vl X ul |I c   Equation 2

where w′ l represents a word operator of the CWS code.

10. A method for designing a quantum code, comprising:
converting at least one quantum error generated in a quantum error channel into at least one binary error by using a standard form codeword stabilized quantum (CWS) code;
generating a binary error-correcting code which corrects the at least one binary error;
generating at least one word operator of the CWS code by using the at least one binary error-correcting code; and
generating at least one codeword including at least one entangled qubit (ebit) by using the at least one word operator.

11. The method for designing a quantum code according to claim 10 ,
wherein a transmitting unit and a receiving unit share the at least one entangled qubit.

12. The method for designing a quantum code according to claim 10 ,
wherein the at least one word operator is generated independently in a transmitting unit.

13. The method for designing a quantum code according to claim 10 , further comprising:
making the at least one quantum error into an initial state by applying the at least one entangled qubit to an initial state of qubit.

14. The method for designing a quantum code according to claim 13 , further comprising:
coding the initial state by using a unitary coding operation which generates a stabilizer generator of a standard form of the CWS code.

15. The method for designing a quantum code according to claim 14 ,
wherein the at least one quantum error is converted into the at least one binary error according to Equation 3 below by using the stabilizer generator:

Cl
G

⁡

(

E
=

±

Z
v

⁢

X
u

)

=

v
⊕

Assignees

• Heo Jun
• Shin Jeong Hwan
• Univ Korea Res & Bus Found

Inventors

• Heo Jun
• Shin Jeong Hwan

Classifications

• H03M13/05

  using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits {(H03M13/2906 takes precedence)} · CPC title

• H03M13/13 Primary

  Linear codes · CPC title

• H03M13/033 Primary

  Theoretical methods to calculate these checking codes · CPC title

• H03M13/21

  Non-linear codes, e.g. m-bit data word to n-bit code word [mBnB] conversion with error detection or error correction · CPC title

• H03M13/615

  Use of computational or mathematical techniques · CPC title