KR20140071063A - Apparatus and method for designing quantum error correction code - Google Patents

Abstract

Provided are an apparatus and method for designing a quantum error correction code capable of designing a binary error correction code by correcting a binary error analyzed through a quantum error using a CWS code after a base state is formed by applying a gauge qubit to an initial state of the CWS code and a gauge group is formed for the base state including the gauge qubit. Also, provided are the apparatus and method for designing the quantum error correction code, capable of writing a word operator of the CWS performed in a transmission terminal by using the binary error correction code and writing a codeword including the gauge qubit by using the word operator.

Description

[0001] APPARATUS AND METHOD FOR DESIGNING QUANTUM ERROR CORRECTION CODE [0002]

Embodiments of the present invention are directed to an apparatus and method for designing a quantum error correction code.

Nowadays, the development of quantum information communication technology which is aiming at high speed computation processing ability by quantum secure communication using quantum information and quantum computer parallel processing technique is accelerated.

The cubic information, which is the basic information amount of the quantum system using quantum information, is sensitive to the surrounding environment and can easily cause information to be distorted. The algorithm performed in the quantum system basically assumes that there is no error in the quantum information. Therefore, a quantum error correcting code for protecting quantum information is required, and a lot of studies on quantum error correcting codes are being carried out in various ways in the world.

Most studies on quantum error correcting codes currently underway are based on the existing error correcting code designing technique and the trend of creating a new quantum error correcting code. The quantum error correction code can be largely divided into a linear code and a nonlinear code according to the construction method.

Among the linear codes, a stabilizer code suggests a method of constructing a quantum error correcting code using a code satisfying a dual-containing condition in a conventional linear block code.

In recent years, a code design technique called a codeword stabilized quantum code (CWS code), which can describe both a linear code and a nonlinear code, has been introduced. The CWS code is a technique for designing a quantum error correction code using an existing error correction code Can be presented.

Most quantum error correction codes encode quantum information in a subspace, and a general quantum error correction coding technique can encode quantum information in a subsystem.

The operator quantum error correcting code can provide a design method of a quantum error correcting code using a subsystem and the operator quantum error correcting code can provide a design method for integrating a passive quantum error correcting code and an active quantum error correcting code Code design technique. A quantum error correction coding scheme capable of systematically designing nonlinear codes is needed.

An embodiment of the present invention aims to extend the CWS code to a quantum error correction code of a subsystem by applying an operator quantum error correction coding scheme to the CWS code scheme.

An embodiment of the present invention aims at constructing a nonlinear code systematically from an error correction code.

One embodiment of the present invention provides a method for designing a quantum error correction code, which can include both a subspace code and a subsystem code.

The apparatus for designing a quantum error correcting code according to an embodiment of the present invention includes a first state construction unit for constructing a base state by applying a gauge qubit to an initial state of a CWS (codeword stabilized quantum) code, A second state constructing unit for constructing a gauge group for the base state including the gauge qubit, a second state constructing unit for constructing a gauge group for the base state including the gauge qubit, A code designing unit for designing a binary error correcting code for correcting the binary error, a code designing unit for designating a word operator of the CWS code performed in the transmitter using the binary error correcting code, And a second state creating unit for creating a code word including the gauge qubit by using the word operator, .

According to an aspect of the present invention, the analysis unit may encode the basic state using a unitary operator that generates a stabilizer generator in a standard form of the CWS code.

According to an aspect of the present invention, the analysis unit may convert the quantum error into the binary error using the stabilizer S _i and the gauge group g _j .

According to an aspect of the present invention, the first state creating unit may perform a unitary coding operation on a first word operator that removes an operator performed at a receiving end using the ballast, and performs a unitary coding operation on a second word operator Lt; / RTI >

The method of designing a quantum error correcting code according to an embodiment of the present invention includes the steps of constructing a base state by applying a gauge qubit to an initial state of a codeword stabilized quantum (CWS) code, Constructing a gauge group for the base state including a Gauge qubit, generating a quantum error occurring in the quantum error channel using the CWS code as a binary error Analyzing the binary error correcting code, designing a binary error correcting code for correcting the binary error, creating a word operator of the CWS code performed in the transmitter using the binary error correcting code, And generating a codeword including the gauge qubit by using the gauge qubit.

According to an embodiment of the present invention, a CWS code can be extended to a quantum error correction code of a subsystem by applying an operator quantum error correction coding scheme to the CWS code scheme.

According to an embodiment of the present invention, a non-linear code can be structured systematically from an error correction code.

According to an embodiment of the present invention, it is possible to provide a method of designing a quantum error correction code, which can include both a subspace code and a subsystem code in a CWS code.

FIG. 1 is a block diagram illustrating the structure of a quantum error correction code designing apparatus according to an embodiment of the present invention. Referring to FIG.
2 is a diagram illustrating a process of measuring a qubit using a measurement operator according to an embodiment of the present invention.
3 is a diagram showing an example of a coding circuit of a qubit bit flip code according to an aspect of the present invention.
4 is a diagram illustrating an example of a coding circuit of a qubit phase flip code according to an aspect of the present invention.
5 is a diagram showing an example of a coding circuit of a Sho-code according to an aspect of the present invention.
6 is a flowchart illustrating a method of designing a quantum error correction code according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings and accompanying drawings, but the present invention is not limited to or limited by the embodiments.

In the following description of the present invention, a detailed description of known functions and configurations incorporated herein will be omitted when it may make the subject matter of the present invention rather unclear. The terminology used herein is a term used for appropriately expressing an embodiment of the present invention, which may vary depending on the user, the intent of the operator, or the practice of the field to which the present invention belongs. Therefore, the definitions of these terms should be based on the contents throughout this specification.

The apparatus for designing a quantum error correcting code according to an aspect of the present invention can expand a CWS code to a subsystem quantum error correction code by applying an operator quantum error correction coding scheme to a CWS code scheme.

The CWS code is a scheme that can systematically construct nonlinear codes from classical error correcting codes and is a quantum error correcting code using subspace.

The apparatus for designing a quantum error correcting code according to an aspect of the present invention is a device for designing a nonlinear code by applying an operator quantum error correcting coding technique to a CWS code scheme capable of systematically designing a nonlinear code so that a CWS code includes both a subspace code and a subsystem code And can be extended by a general quantum error correction code design technique.

FIG. 1 is a block diagram illustrating the structure of a quantum error correction code designing apparatus according to an embodiment of the present invention. Referring to FIG.

1, an apparatus for designing a quantum error correcting code according to an embodiment of the present invention includes a first state construction unit 110, a second state construction unit 120, an analysis unit 130, a code design unit 140, A first state creating unit 150, and a second state creating unit 160. The first state creating unit 150 and the second state creating unit 160 are the same.

The first state construction unit 110 constructs a base state by applying a gauge qubit to an initial state of a codeword stabilized quantum (CWS) code, and the second state construction unit 120 constructs a base state, And construct a gauge group for a base state including a qubit.

The first state configuration unit 110 may construct the basic state as shown in Equation 1 by applying the gauge qubit to the initial state of the n-qubit of the CWS code.

는 초기 상태의 기본 스테이트(base state)를 의미하며,

는 임의의 r-큐비트,

를 나타낸다.At this time,

Denotes a base state of an initial state,

Is an arbitrary r-qubit,

.

Here, the qubit corresponds to a basic unit of information used in the quantum information system, and one of the largest specific quantities of the quantum information can be superimposed on information compared with existing information in the quantum information system. For example, a cuboid can take several different states of the Hilbert space, and may exist in a superposition where the states overlap.

The analysis unit 130 analyzes a quantum error occurring in the quantum error channel using a CWS code as a binary error and the code design unit 140 designs a binary error correction code for correcting the binary error.

The analyzer 130 may encode the basic state using a unitary operator that generates a stabilizer generator in a standard form of the CWS code.

Here, the stabilizer S _i and the gauge group g _j may be constructed by the following equations (2).

은 이진 벡터를 나타낸다. 또한, 표기 상의 편의를 위해 수식의 아래 첨자는 연산자의 위치를 나타내며, 예를 들어

의 경우

와 같이 나타낼 수 있다.In this case, X and Z represent 2X2 Pauly operators,

Represents a binary vector. Also, for convenience in notation, the subscript of the expression represents the position of the operator, for example

In the case of

As shown in Fig.

는 하기 수학식 3와 같은 관계로 구성될 수 있다.The analyzer 130 may convert the quantum error into the binary error using the stabilizer S _i and the gauge group g _j . For example, quantum error E and binary error

Can be expressed by the following equation (3).

,

,

은 이진 벡터를 의미하며,

은 벡터 u의 원소 중

번째 원소를 의미한다.제1 상태 작성부(150)는 이진 오류 정정 부호를 이용하여 송신단에서 수행되는 CWS 코드의 워드 오퍼레이터(word operator)를 작성하고, 제2 상태 작성부(160)는 워드 오퍼레이터를 이용하여 게이지 큐비트를 포함한 코드 워드를 작성한다.At this time,

,

,

Means a binary vector,

Of the elements of the vector u

The first state creating unit 150 creates a word operator of the CWS code to be executed in the transmitter using the binary error correcting code and the second state creating unit 160 creates the word operator of the CWS code, To generate a code word including the gauge qubit.

The first state creating unit 150 may perform a unitary encoding operation on the first word operator that removes the operator performed at the receiving end using the ballast to generate a second word operator for the initial state of the CWS code.

가 하기 수학식 4를 만족하는 양자 오류 정정 부호를 구성할 수 있다.The second state creating unit 160 creates a second state,

Can constitute a quantum error correction code satisfying the following equation (4).

At this time, A and B on the word operator means a subsystem where each word operator operates.

The apparatus for designing a quantum error correcting code according to an aspect of the present invention can design a quantum error correcting code designed with a CWS code using a gauge qubit, by extending it with a subsystem quantum error correcting code.

2 is a diagram illustrating a process of measuring a qubit using a measurement operator according to an embodiment of the present invention.

The quantum information may stably exist and the quantum information may collapse into the ground state at the instant of measurement and may not be restored to the state before measurement. As shown in FIG. 2, ² and | b | ² , it can be collapsed into one of the bases constituting the information. The collapsed information does not have the information of 'a' or 'b' and may not be returned to the state before the measurement.

The apparatus for designing a quantum error correcting code according to an aspect of the present invention is characterized in that, from the viewpoint of a quantum error correcting code, in a process of encoding and restoring information in order to apply a quantum error correcting code in the quantum information system, A codeword can be generated without measuring the change to be taken and the information can be recovered from errors occurring in the channel.

3 is a diagram showing an example of a coding circuit of a qubit bit flip code according to an aspect of the present invention.

Referring to FIG. 3, the apparatus for designing a quantum error correction code can be represented by a coding circuit of a 3-qubit bit flip code, but is not limited thereto. For example, a coding circuit may be composed of two CNOT (Controlled NOT) gates, and a codeword can be generated by receiving as input a single qubit and an additional two qubit.

4 is a diagram illustrating an example of a coding circuit of a qubit phase flip code according to an aspect of the present invention.

Referring to FIG. 4, the apparatus for designing a quantum error correction code can be represented by a coding circuit of 3-qubit phase flip codes, but is not limited thereto. Here, the 3-qubit bit flip code corresponds to a quantum error correction code used in a quantum channel in which a single phase error occurs, and the decoding process of a 3 qubit bit flip code can be performed through four different measurement operators have.

5 is a diagram showing an example of a coding circuit of a Sho-code according to an aspect of the present invention.

The Shore code is the first quantum error correction code that can protect a qubit from any quantum error with a quantum error correction code that can simultaneously protect the qubit from bit flip errors and phase flip errors.

The Shore code can combine two different types of error correction codes to protect information from two different kinds of errors, and can combine two different types of error correction codes to obtain a new error correction code It is possible to design a quantum error correction code in the same manner as that of the conventional technique.

Referring to FIG. 5, the apparatus for designing a quantum error correction code can encode a qubit by a phase flip code, and generate a final codeword through a process of encoding a bit flip code again.

Hereinafter, a method of designing a quantum error correction code according to an embodiment of the present invention will be described.

6 is a flowchart illustrating a method of designing a quantum error correction code according to an embodiment of the present invention.

Referring to FIG. 6, the quantum error correcting code designing apparatus constructs a base state (610) by applying a gauge qubit to an initial state of CWS (codeword stabilized quantum) code.

The quantum error correction code designing apparatus configures a gauge group for a base state including a gauge qubit (620).

The quantum error correcting code designing apparatus analyzes a quantum error occurring in a quantum error channel using a CWS code as a binary error (630).

For example, a quantum error correction code designing apparatus can encode a basic state using a unitary operator that generates a stabilizer generator in a standard form of a CWS code. Also, the quantum error correction code designing apparatus can convert the quantum error into the binary error using the stabilizer S _i and the gauge group g _j .

The quantum error correction code designing apparatus designs a binary error correction code for correcting the binary error (640).

The quantum error correcting code designing apparatus generates a word operator of the CWS code to be performed at the transmitting end using the binary error correcting code (650).

The quantum error correcting code designing apparatus generates a code word including a gauge qubit by using a word operator (660).

The quantum error correction coding design apparatus can generate a second word operator for the initial state of the CWS code by performing a unitary coding operation on a first word operator that removes an operator performed at a receiving end using a ballast.

The method according to an embodiment may be implemented in the form of a program command that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions to be recorded on the medium may be those specially designed and configured for the embodiments or may be available to those skilled in the art of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape; optical media such as CD-ROMs and DVDs; magnetic media such as floppy disks; Magneto-optical media, and hardware devices specifically configured to store and execute program instructions such as ROM, RAM, flash memory, and the like. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

110: first state component
120: second state component
130:
140:
150: First state preparing section
160: Second state preparing section

Claims (17)

A first state constructor configured to construct a base state by applying a gauge qubit to an initial state of a codeword stabilized quantum (CWS) code;
A second state configuring a gauge group for the base state including the gauge qubit;
An analyzer for analyzing a quantum error occurring in the quantum error channel using the CWS code as a binary error;
A code designing unit for designing a binary error correcting code for correcting the binary error;
A first state creating unit for creating a word operator of the CWS code performed by the transmitter using the binary error correction code; And
A second state creating unit for creating a codeword including the gauge qubit by using the word operator,
And a quantization error correcting code designing unit. The method according to claim 1,
Wherein the first state configuration unit comprises:
And the gauge qubit is applied to an initial state of an n-qubit of the CWS code to construct the basic state as shown in Equation (1).
[Equation 1]

(Wherein,

Corresponds to the base state of the initial state,

Corresponds to r-qubits.) The method according to claim 1,
The analyzing unit,
And a unitary operator for generating a stabilizer generator of a standard form of the CWS code to code the base state. The method of claim 3,
The stabilizer ( _Si ) and the gauge group ( _gj )
The quantum error correcting code designing apparatus comprising an operator as shown in Equation (2).
&Quot; (2) "

(Wherein,

And

The

Corresponds to the Paulownian operator,

Corresponds to a binary vector.) The method of claim 3,
The analyzing unit,
Wherein the quantum error correcting code designing apparatus converts the quantum error into the binary error using the stabilizer ( _Si ) and the gauge group ( _gj ). 6. The method of claim 5,
Wherein the quantum error and the binary error are < RTI ID = 0.0 >
The quantum error correcting code designing apparatus comprising:
&Quot; (3) "

(Wherein each of the

,

Corresponds to a binary vector,

Vector

Of the elements

Corresponding to the first element.) The method of claim 3,
Wherein the first state creating unit comprises:
And a second word operator for an initial state of the CWS code by performing a unitary encoding operation on a first word operator that removes an operator performed by a receiver using the ballast. 8. The method of claim 7,
Wherein the second state creating unit comprises:
And the second word operator constitutes a quantum error correcting code satisfying the following equation (4): " (4) "
&Quot; (4) "

(Where each of A and B corresponds to a subsystem in which each of the word operators operates). Constructing a base state by applying a gauge qubit to an initial state of a codeword stabilized quantum (CWS) code;
Constructing a gauge group for the base state including the gauge qubits;
Analyzing a quantum error occurring in a quantum error channel using a CWS code as a binary error;
Designing a binary error correcting code for correcting the binary error;
Creating a word operator of the CWS code performed in the transmitter using the binary error correction code; And
Generating a codeword including the gauge qubit by using the word operator
The method comprising the steps of: 10. The method of claim 9,
Wherein configuring the base state comprises:
Applying the gauge qubit to the initial state of the n-qubit of the CWS code to construct the base state as shown in Equation (5)
The method comprising the steps of:
&Quot; (5) "

(Wherein,

Corresponds to the base state of the initial state,

Corresponds to r-qubits.) 10. The method of claim 9,
Wherein analyzing the quantum error as a binary error comprises:
Encoding the base state using a unitary operator that generates a stabilizer generator in a standard form of the CWS code;
The method comprising the steps of: 12. The method of claim 11,
The stabilizer ( _Si ) and the gauge group ( _gj )
A quantum error correcting code designing method composed of an operator as shown in Equation (6).
&Quot; (6) "

(Wherein,

And

The

Corresponds to the Paulownian operator,

Corresponds to a binary vector.) 12. The method of claim 11,
Wherein analyzing the quantum error as a binary error comprises:
Transforming the quantum error into the binary error using the stabilizer ( _Si ) and the gauge group ( _gj )
And a quantum error correcting code designing method. 14. The method of claim 13,
Wherein the quantum error and the binary error are < RTI ID = 0.0 >
A quantum error correcting code designing method comprising the following relationship.
&Quot; (7) "

(Wherein each of the

,

Corresponds to a binary vector,

Vector

Of the elements

Corresponding to the first element.) 12. The method of claim 11,
The step of creating the word operator comprises:
Generating a second word operator for an initial state of the CWS code by performing a unitary encoding operation on a first word operator that removes an operator performed by a receiver using the ballast;
The method comprising the steps of: 16. The method of claim 15,
The step of generating the codeword comprises:
The second word operator configuring a quantum error correcting code satisfying the following equation (8)
The method comprising the steps of:
&Quot; (8) "

(Where each of A and B corresponds to a subsystem in which each of the word operators operates). A computer-readable recording medium storing a program for performing the method of any one of claims 9 to 16.

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