KR101768595B1 - Fault-tolerant conversion apparatus and method between stabilizer codes - Google Patents

Abstract

The present invention relates to conversion device and method using a fault-tolerant scheme between quantum error correcting codes. More specifically, the conversion device and method using a fault-tolerant scheme between quantum error correcting codes can convert quantum error correcting codes used as a conversion target to reference type codes, compare the quantum error correcting codes with the converted reference type codes to select gates needed for a conversion operation, and appropriately arrange the corresponding gates to control the influences of the quantum noises suitably through a conversion process. According to the present invention, the conversion device includes: a standard type converter which converts initial quantum error correcting codes and target quantum error correcting codes from general type codes to standard type codes; a reference type converter converting the initial quantum error correcting codes and target quantum error correcting codes converted to the standard type codes from standard type codes to reference type codes; a quantum operator selector which compares the initial quantum error correcting codes and target quantum error correcting codes converted to the reference type codes to select quantum operators; a quantum circuit designer which arranges the selected quantum operators to design a quantum circuit; and a quantum transducer which applies the designed quantum circuit to the initial quantum error correcting codes to calculate the target quantum error correcting codes.

Description

[0001] The present invention relates to a fault-tolerant conversion apparatus and method between stabilizer codes,

The present invention relates to an apparatus and a method for mutual conversion of error-correcting codes between quantum error correcting codes. More particularly, the present invention relates to an apparatus and method for mutually converting quantum error correcting codes, And more particularly, to an apparatus and method for mutual conversion between a quantum error correcting code and a defect tolerant method in which the gates are appropriately arranged so that the conversion process can well control the influence of quantum noise.

The quirky phenomena of quantum mechanics enable theoretically to communicate with significantly faster computing and absolute security than classical digital computing and communication technologies.

However, there are many difficulties in applying the principles of quantum mechanics to the realization of computing and communication, and quantum noise is a typical problem.

The quantum information represented by the superposition of 0 and 1 is completely collapsed by the fine quantum noise. A typical technique to overcome the quantum noise problem is fault-tolerant quantum information processing using a quantum error-correcting code.

The quantum information must be encoded using a quantum error correction code throughout the processing of the quantum information, and the encoded quantum information must be manipulated using the quantum gates which are designed to be fault tolerant, and the quantum error should be periodically checked and corrected.

Here, the expression " fault tolerant " means that some of the quantization noise will not affect the overall computing result even if it occurs.

Quantum information processing systems, including quantum computers, are made up of several components.

Each component has a different function. When quantum information is processed by a certain component, if the quantum information has a form matching the function of the component, information processing will be more effective and stable.

For example, when quantum information is stored in a memory, or when quantum information is transmitted over a communication channel, more information can be stored or transmitted if the quantum information is compressed.

On the other hand, other features of the information are required (will be required). Therefore, a technology capable of converting the form of quantum information as needed for effective and stable quantum information processing is required.

The form of quantum information is determined by the characteristics of the quantum error correction code used. When encoded with a quantum code having a high compression ratio, the encoded quantum information has a high compression ratio, and when encoded with a quantum error correcting code specific to a specific type of noise, the encoded quantum information has strong characteristics against the quantum noise.

In this regard, the conventional digital information processing does not require a code conversion technique. When it is necessary to encode information encoded by code A with code B, it is necessary to decode and re-encode it into code B Because.

However, this method can not be used in quantum information. This is because, at the moment when the quantum information encoded with the quantum error correcting code is decoded, the quantum information is directly exposed to the noise and is completely collapsed by the fine quantum noise.

Therefore, the quantum error correction code must be coded by the quantum error correction code throughout the processing of quantum information. It is natural that the quantum information should be kept encoded in the quantum error correction code even during the code conversion process.

A conventional method for converting a quantum error correcting code is divided into a series of quantum gate applying methods and a structural characteristic utilizing technique of a quantum error correcting code.

A method of using structural characteristics of a quantum error correction code refers to a method of performing code conversion without special quantum operation between two quantum error correction codes structurally the same, that is, designed with the same principle.

When this method is used, a logical qubit of a quantum error correction code is used as an ancilla qubit of a code conversion process.

This method requires a quantum gate only to make an auxiliary qubit, so the complexity of the transformation is relatively low. However, the code to be converted is very limited.

On the other hand, a method of transforming a code by applying a series of quantum gates is that when a series of quantum gates are applied to the quantum information encoded with the quantum error correction code A, the quantum information is encoded into the quantum error correction code B That is, a method of applying a series of quantum gates to the quantum information encoded with the quantum error correction code A so that the quantum information has a form encoded with the quantum error correction code B. [

Since this method requires quantum gates for the transformation, the transformation complexity is higher than that of the previous method. However, since the transformation can be performed on various codes, utilization is high.

Korean Patent Publication No. 1020140071063 Korean Registered Patent No. 10-123386 Korean Patent Publication No. 10-2015-0097290 Korean Patent Registration No. 10-1517361

[1] Charles D. Hill, Austin G. Fowler, David S. Wang and Lloyd C Hollenberg, "Fault-tolerant quantum error correction code conversion", Quantum Information and Computation, Vol. 13, 5 & 6, 2013. Jonas T. Anderson, Guillaume Duclos-Cianci, and David Poulin, "Fault-Tolerant Conversion between the Steane and Reed-Muller Quantum Codes", Physical Review Letters, 113, 080501, 2014.

In order to solve the above problems, the present invention first converts the quantum error correcting codes to be converted into a reference type, selects a gate necessary for conversion by comparing them, And to provide an apparatus and method for mutual conversion of a quantum error correcting code to a defect tolerant system, in which the influence from quantum noise is well controlled.

According to an aspect of the present invention, there is provided a method of converting an initial quantum error correction code and a target quantum error correction code from a standard type to a standard type; A reference type converter for converting an initial quantum error correction code and a target quantum error correction code from a standard type to a reference type; A quantum operator selector for selecting quantum operators by comparing an initial quantum error correction code converted to a reference type with a target quantum error correction code; A quantum circuit designer for designing a quantum circuit by arranging selected quantum operators; And a quantum converter for applying the designed quantum circuit to an initial quantum error correcting code to calculate a target quantum error correcting code.

In addition, the reference converter according to an aspect of the present invention applies a standard Hadamard gate to the r + 1 to nk qubit of the initial quantum error correction code and the target quantum error correction code, Conversion.

In addition, the quantum operator selector of one aspect of the present invention implements quantum operators with a controlled NOT (NOT-NOT) gate.

In addition, the quantum operator selector of one aspect of the present invention implements quantum operators with a controlled Z (Controlled-Z) gate.

(A) converting the initial quantum error correction code and the target quantum error correction code from the standard type to the standard type; (B) transforming an initial quantum error correction code and a target quantum error correction code from a standard type to a reference type by a reference type converter; (C) selecting quantum operators by comparing an initial quantum error correction code that is converted into a reference type by a quantum operator selector and a target quantum error correction code; (D) designing a quantum circuit by arranging quantum operators selected by a quantum circuit designer; And (E) applying a quantum circuit designed with a quantum transducer to an initial quantum error correcting code to calculate a target quantum error correcting code.

The reference converter of the step (B) of the other aspect of the present invention may be configured to apply a Hadamard gate to the r + 1 to nk qubit of the target quantum error correcting code and the initial quantum error correcting code, Converts standard types to reference types.

The quantum operator selector in step (C) of another aspect of the present invention implements quantum operators with a controlled NOT (NOT-NOT) gate.

The quantum operator selector in step (C) of another aspect of the present invention implements quantum operators with a controlled Z (Controlled-Z) gate.

In another aspect of the present invention, the quantum transducer in step (D) obtains a target quantum error correction code by applying a Gaussian operator and a Hadamard operator inverse to an initial quantum error correction code through quantum operators.

According to the present invention, the quantum information processing parts performing different functions convert the quantum information to be processed first into a form conforming to the function of the user, and then the corresponding quantum information processing is performed as quantum noise So that it can operate effectively and stably.

Further, according to the present invention, an advantage that is obtained in comparison with the existing research results (non-patent documents 1 and 2) in connection with the conversion of the quantum error correcting code is applicability.

The existing research results are a conversion method designed for specific quantum error correction codes, but the present invention can convert between all quantum error correction codes belonging to a stabilization code.

This is possible because the necessary quantum gates are selected based on the reference type called IABC type and they are arranged properly.

FIG. 1 shows a quantum error correction code conversion process by applying a quantum operator.
FIG. 2 is a block diagram of an apparatus for mutual conversion between a quantum error correcting code and a defect tolerant system according to an embodiment of the present invention.
FIG. 3 is a flowchart illustrating a method of mutual conversion of a fault tolerant scheme between quantum error correction codes according to an embodiment of the present invention.
(B) of Fig. (A) 4 indicates a normal type (g ^normal) of stabilizing reference numerals, Figure 4 shows a standard type (g ^standard) of the stabilizing code, (c) of Figure 4 is based on called IABC type type ( g ^IABC ).
5 (a) shows a symbol of a Hadamard gate and its matrix, and FIG. 5 (c) shows a NOT (Controlled-NOT) gate controlled in FIG. 4 (b) Controlled-Z gate.
FIG. 6 is a conceptual diagram of mutual conversion of a defect tolerance scheme between quantum error correction codes according to an embodiment of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS The above and other objects, features and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.

First, the terminology used in the present application is used only to describe a specific embodiment, and is not intended to limit the present invention, and the singular expressions may include plural expressions unless the context clearly indicates otherwise. Also, in this application, the terms "comprise", "having", and the like are intended to specify that there are stated features, integers, steps, operations, elements, parts or combinations thereof, But do not preclude the presence or addition of features, numbers, steps, operations, components, parts, or combinations thereof.

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.

FIG. 1 shows a quantum error correction code conversion process by applying a quantum operator.

Referring to FIG. 1, a quantum error correcting code conversion process by applying a quantum operator applies a series of quantum operators (C ₁ to C _n ) to a quantum error correction code A And obtains the encoded quantum information.

FIG. 2 is a block diagram of an apparatus for mutual conversion of a fault tolerant scheme between quantum error correcting codes according to an embodiment of the present invention. FIG. 3 is a block diagram of a mutual conversion apparatus of a defect tolerant scheme between quantum error correcting codes according to an embodiment of the present invention. Fig.

Referring to FIG. 2, the configuration of the error-correcting inter-conversion apparatus between quantum error correction codes according to an embodiment of the present invention includes a standard converter 100, a reference converter 200, a quantum operator selector 300, A quantum circuit designing apparatus 400 and a quantum transducer 500 are provided.

In general, a stabilizer code, which is a representative quantum error correction code, has a representation method called a normal form and a standard form.

In this regard, (a) in FIG. 4 represents the ^normal type (g ^normal ) of the stabilization code, and (b) in FIG. 4 represents the standard type (g ^standard ) of the stabilization code.

In the general form of the stabilization code, G _X and G _Z must satisfy the following Equation 1 as a binary matrix.

(1)

Where G is a parity check matrix, G _X is an X operator part of a parity check matrix, G _Z is a Z operator part of a parity check matrix, G is a parity check matrix, _X ^T is the transpose of G _X , and G _Z ^T is the transpose of G _Z.

In the standard form of the stabilization code, I is an identity matrix in which the diagonal values of the matrix are 1, 0 is a zero matrix in which all matrix elements are 0, and the rest A ₁ , A ₂ , B, C, D, to be. Here, A ₁ , A ₂ , B, C, D, and E are arbitrary matrices of the corresponding positions appearing when the first part of a parity check matrix is arranged as an identity matrix I.

The standard type converter 100 converts the two quantum error correction codes A to be converted (which may be called an initial quantum error correction code with another name) and B (which can be called an object quantization error correction code) into a Gaussian elimination method, To convert the normal form of the stabilizer code into a standard form (S100). (Here, in order to simplify the conversion process, the Gaussian operator A _S or B _S is applied to the general form .

In this way, the conversion of the code by the Gaussian elimination method by the standard type converter 100 is merely expressed differently in the same sign, and no physical change occurs.

In the present invention, in addition to the above-mentioned general type and standard type, a reference type called IABC type is defined and used. In this regard, FIG. 3 (c) shows a reference type (g ^IABC ) called IABC type.

The reference converter 200 converts the standard types of the stabilization codes into the IABC type (i.e., the reference type) by applying a Hadamard gate to the r + 1 to nk qubits of the quantum error correction codes A and B converted to the standard type, (S110) (Here, Hadamard operator A _IABC or B _IABC is expressed as a standard type in order to simplify the conversion process).

The Hadamard gate is a 1-cubic quantum gate, and the code converted by this gate has the same error correction capability as the code before conversion.

FIG. 5 (a) shows the symbols of the Hadamard gate and their matrices.

Here, the reason why the reference type (IABC type) is required is that it is a kind of reference point for finding the gate necessary for converting the two stabilization codes.

Meanwhile, the quantum operator selector 300 compares the two stabilization codes converted into the IABC type to select quantum operators C ₁ to C _n used for code conversion (S 120).

These quantum operators C ₁ ~C _n may have a controlled NOT (Not Controlled) or a controlled Z (Z).

(NOT-controlled) gate and a controlled Z-controlled gate can be confirmed in FIGS. 5 (b) and 5 (c).

For reference, a controlled NOT gate can be replaced with a controlled Z gate with the help of the Hadamard gate mentioned above.

In contrast, a controlled Z-controlled gate can be replaced with a controlled NOT-controlled gate with the help of a Hadamard gate.

Therefore, the quantum operator selector 300 can implement quantum operators with a controlled NOT (NOT-NOT) gate.

Or quantum operator selector 300 may implement quantum operators with a controlled Z (Controlled-Z) gate.

We compared the IABC types of the two stabilization codes to be converted and selected the quantum operators necessary for the transformation. It is very important to arrange the selected quantum operators appropriately.

The quantum circuit designer 400 arranges the selected quantum operators through a trial and error process to design a quantum circuit (S130).

Next, the quantum transducer 500 applies the quantum circuit formed through the above-described series of processes to the stabilization code A to obtain the stabilization code B.

At this time, if the quantum circuit is applied to the stabilization code A, it becomes the IABC type of the stabilization code B instead of the stabilization code B as shown in Fig.

Therefore, the quantum converter 500 needs to inversely apply the quantum gates necessary to obtain the IABC type of the stabilization code B as the last stage of code conversion. Through this process, quantized information finally encoded with the stabilization code B can be obtained. In order to simplify this conversion process, the inverse of the Hadamard operator is expressed by applying B _IABC ^-1 to the reference type, and the inverse transformation of the Gaussian operator is expressed by applying B _S ^-1 to the standard type.

Therefore, referring to FIG. 6, the stabilization code A to B is converted into a standard type by applying a Gaussian elimination method to the stabilization code A (expressed as applying a Gaussian operator A _S ), and then a Hadamard gate is applied the Hadamard converting the operator as represented by a _IABC) standard type to be applied if the following, applying a set of both the operator, will arise another stabilizing code by the operator both _{(A-> a 1 -> a} 2 -> ... -> A _n-1 -> B).

When a quantum circuit formed through the above-described series of processes is applied to the stabilization code A, the resulting quantum error correction code B becomes strictly IABC type (reference type) of the stabilization code B, rather than the stabilization code B.

The quantum transducer 500 applies the quantum gates required to obtain the standard form of the reference stabilization code B in inverse manner to obtain the standard stabilization code B. [

Then, the quantum transducer 500 applies the quantum gate required for the standard stabilization code B in reverse to obtain the general stabilization code B.

Through this process, quantized information finally encoded with the stabilization code B can be obtained.

As described above, in the apparatus according to the present invention, the quantum information processing parts, which perform different functions, first convert the quantum information to be processed into a form conforming to the function of the user, It enables effective and stable operation from noise.

Further, according to the present invention, an advantage that is obtained in comparison with the existing research results (non-patent documents 1 and 2) in connection with the conversion of the quantum error correcting code is applicability.

The existing research results are a conversion method designed for specific quantum error correction codes, but the present invention can convert between all quantum error correction codes belonging to a stabilization code.

This is possible because the necessary quantum gates are selected based on the reference type called IABC type and they are arranged properly.

The foregoing description is merely illustrative of the technical idea of the present invention, and various changes and modifications may be made by those skilled in the art without departing from the essential characteristics of the present invention. Therefore, the embodiments of the present invention are not intended to limit the scope of the present invention but to limit the scope of the present invention. The scope of protection of the present invention should be construed according to the following claims, and all technical ideas within the scope of equivalents thereof should be construed as being included in the scope of the present invention.

100: Standard type converter 200: Standard type converter
300: Quantum operator selector 400: Quantum circuit designer
500: Quantum transducer

Claims (9)

A standard converter for converting an initial quantum error correction code and a target quantum error correction code from a standard type to a standard type;
A reference type converter for converting an initial quantum error correction code and a target quantum error correction code from a standard type to a reference type;
A quantum operator selector for selecting quantum operators by comparing an initial quantum error correction code converted to a reference type with a target quantum error correction code;
A quantum circuit designer for designing a quantum circuit by arranging selected quantum operators; And
And a quantum transducer for calculating a target quantum error correcting code by applying the designed quantum circuit to an initial quantum error correcting code. delete The method according to claim 1,
Wherein the quantum operator selector is a quantum error correction code interleaver that implements quantum operators with controlled NOT (Controlled-NOT) gates. The method according to claim 1,
Wherein the quantum operator selector is a quantum error correction code interleaver for implementing quantum operators with controlled Z (Controlled-Z) gates. (A) converting a standard quantum error correction code and a target quantum error correction code from a standard type to a standard type by a standard type converter;
(B) transforming an initial quantum error correction code and a target quantum error correction code from a standard type to a reference type by a reference type converter;
(C) selecting quantum operators by comparing an initial quantum error correction code that is converted into a reference type by a quantum operator selector and a target quantum error correction code;
(D) designing a quantum circuit by arranging quantum operators selected by a quantum circuit designer; And
(E) applying a quantum circuit designed with a quantum converter to an initial quantum error correcting code to calculate a target quantum error correcting code. delete The method of claim 5,
Wherein the quantum operator selector in the step (C) is a quantum operator that implements quantum operators with a controlled NOT gate. The method of claim 5,
Wherein the quantum operator selector of the step (C) is implemented by a controlled Z (Controlled-Z) gate to implement quantum operators. The method of claim 5,
The quantum transducer of the step (E) includes a quantum error correcting code error correcting code for obtaining a target quantum error correcting code by inversely applying a Gaussian operator and a Hadamard operator to an initial quantum error correcting code through quantum operators Mutual conversion method.

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