JP4176728B2 - Quantum circuit, quantum error correction apparatus, and quantum error correction method - Google Patents

Description

  In a quantum computer that applies a unitary operator to an input quantum state to cause a state transition and obtains a quantum state as an output result thereof, a code qubit group in which a quantum state that is transmission word information is encoded by a stabilizer code, Quantum circuit for converting to a state represented by a tensor product of a qubit representing the transmitted word information and a qubit in a superposition state of a plurality of bases. The present invention relates to a quantum error correction apparatus and a quantum error correction method that perform error correction and decode to recover the original quantum state.

  In a quantum computer or quantum cryptography that applies a unitary operator to an input quantum state to change the state and obtain output data as a result, manipulation of the quantum state is required. In general, a quantum state (operation system) to be operated is coupled with a quantum state (environment system) that cannot be intentionally operated, and the operation system is affected by the environment system and causes disturbance. As shown in Non-Patent Document 3, it is known that an arbitrary unitary operator can be configured as a combination (universal set) of some basic quantum gates.

  There is a quantum error correction technique as a technique for stably manipulating the quantum state. In general, quantum error correction is performed as follows. First, the quantum state is encoded. The encoded quantum state is affected by errors over time. For the quantum state after the influence of the error, if an error occurs, the error is estimated from a syndrome which is an output obtained by applying a certain relational expression to know what kind of error has occurred in the quantum state, and error correction is performed. If the error is within a correctable range, the corrected state becomes an encoded quantum state, and the encoded state is passed through a decoding circuit to recover the quantum state before encoding. As such a quantum error correction code, a stabilizer code described in Non-Patent Document 1 is used. The codeword of the stabilizer code is an eigenspace element of the commutative subgroup of the error group. An error group is a group formed by a set of operators having the same dimensions, which are constituted by tensor products of Pauli operators.

  Specifically, first, even if an error occurs in the code word in which the transmission word in the quantum state is encoded, the error can be corrected if the error is within a certain correctable range, The original codeword can be recovered. In this case, the codeword after error correction is decoded and returned to the transmission word. Here, in the quantum error correction, the state in which decoding is completed represents a state in which the qubit in which the transmission word is stored is entangled with other qubits.

  By the way, leaving the quantum state for a long time increases the noise generated in the quantum state. For this reason, it is preferable that the time required for the operation on the quantum state is as short as possible. Even when quantum error correction is performed on the encoded quantum state to return to the quantum state before encoding, it is preferable that the time required for the operation on the quantum state is as short as possible.

  As a technique for improving the efficiency of such quantum error correction, for example, the technique of Non-Patent Document 1 is raised. In the technique of Non-Patent Document 1, as an efficient decoding method for a 5-qubit code, an ancillary that is an auxiliary qubit is added to a codeword of 5 qubits that is an encoded quantum state. Then, each input of the qubits of the codeword (hereinafter referred to as “code qubit group”) at the start of decoding and the input from the ancilla are passed through the control NOT gate, and the output is output to the ancilla. Entanglement elimination is performed by applying a control NOT gate, and a tensor product of a quantum state representing a transmitted word and a superposition state is obtained.

D.Gottesman. D.Gottesman's thesis .http: // arxiv: org / archive / quant-ph / 9705052, 1997. A. Calderbank et.al.Quantum error correction and orthogonal geometry.http: // arxiv: org / archive / quant-ph / 9605005, 1996. A. Barenco et.al. Phys. Rev. A, 52, pp. 3457, 1995.

  However, in the technique of Non-Patent Document 1, in the quantum circuit that performs quantum error correction, an ancillary qubit is provided in addition to the qubit of the code word and the base discrimination information is output to the ancillary. There is a problem that the number of gates increases and the quantum circuit scale becomes excessive.

  The present invention has been made in view of the above, and it is possible to reduce the number of gates used for decoding to reduce the size of the quantum circuit, and to improve the efficiency of quantum error correction and quantum error. An object of the present invention is to provide a correction device and a quantum error correction method.

  In order to solve the above-described problems and achieve the object, the present invention encodes transmission word information as a quantum state, which is an element of a two-dimensional Hilbert space expressed by a linear combination of two bases, using a stabilizer coding scheme. A code qubit group that is a set of qubits representing the coded codeword information, and is a first code that is a quantum state in which the first base of the two-dimensional Hilbert space representing the transmission word information is coded A quantum state in which a quantum state and a second base of the transmission word information are encoded, and the first base is inverted to the second base for all qubits in the first code quantum state; The second base is expressed by a linear combination with a second code quantum state in a relationship of all qubits inverted by a NOT gate that inverts the first base to the first base, and Each of the bases included in the code quantum state is in a relationship of any one of the bases included in the first code quantum state with the all qubit inversion, and has a property of forming a pair of bases symmetrical with respect to all the qubit inversions. This is a quantum circuit that performs a decoding process for converting codeword information that has codeword information into a state represented by a tensor product of a qubit representing the transmission word information and a qubit represented as a superposition state of a plurality of bases. A plurality of control NOT gates acting on the code qubit group to perform a quantum operation, and whether the base of the code qubit group is a base included in the first code quantum state or the second Based on the number of 1 included in each base, base discrimination information that is information for determining whether the base is included in the quantum state is obtained, and is a part of the code qubit group. The base discriminating means for outputting to the qubits of the control and a control NOT gate using the specific qubit as the control qubit are acted on, so that the qubit expressing the transmission word information and the qubit other than the qubit including the transmission word information And an entanglement canceling means for canceling entanglement with the qubit.

  Further, the present invention provides a set of qubits that express codeword information obtained by encoding transmission word information as a quantum state, which is an element of a two-dimensional Hilbert space expressed by a linear combination of two bases, using a stabilizer coding scheme. A first code quantum state that is a quantum state obtained by encoding a first basis of a two-dimensional Hilbert space representing the transmission word information, and a second qubit group of the transmission word information A quantum state in which a base is encoded, wherein the first base is inverted to the second base for all qubits in the first code quantum state, and the second base is changed to the first base. Each of the bases included in the second code quantum state is represented by a linear combination with the second code quantum state in the relationship of all qubit inversions inverted by the NOT gate to be inverted. Code word information having a property of forming a pair of bases that are in a relation of all the qubit inversions to any one of the bases included in the code quantum state of the symmetric bit lines, and represents the transmission word information A quantum error correction apparatus including a quantum circuit that performs a decoding process for converting to a state represented by a tensor product of a qubit and a qubit expressed as a superposition state of a plurality of bases, wherein the quantum circuit includes: A plurality of control NOT gates acting on the code qubit group to perform a quantum operation, and whether the basis of the code qubit group is a basis included in the first code quantum state or the second quantum Base discrimination information, which is information for discriminating whether a base is included in a state, is obtained based on the number of 1s included in each base, and is a feature that is part of the code qubit group. The base discriminating means for outputting to the qubits of the control and a control NOT gate using the specific qubit as the control qubit are acted on, so that the qubit expressing the transmission word information and the qubit other than the qubit including the transmission word information And an entanglement canceling means for canceling entanglement with the qubit.

  Further, the present invention provides a set of qubits that express codeword information obtained by encoding transmission word information as a quantum state, which is an element of a two-dimensional Hilbert space expressed by a linear combination of two bases, using a stabilizer coding scheme. A first code quantum state that is a quantum state obtained by encoding a first basis of a two-dimensional Hilbert space representing the transmission word information, and a second qubit group of the transmission word information A quantum state in which a base is encoded, wherein the first base is inverted to the second base for all qubits in the first code quantum state, and the second base is changed to the first base. Each of the bases included in the second code quantum state is represented by a linear combination with the second code quantum state in the relationship of all qubit inversions inverted by the NOT gate to be inverted. Code word information having a property of forming a pair of bases that are in a relation of all the qubit inversions to any one of the bases included in the code quantum state of the symmetric bit lines, and represents the transmission word information A quantum encoding method for performing a decoding process for converting to a state represented by a tensor product of a qubit and a qubit expressed as a superposition state of a plurality of bases, wherein a plurality of code qubit groups The control NOT gate is operated to perform a quantum operation to determine whether the base of the code qubit group is a base included in the first code quantum state or a base included in the second quantum state. Basis discrimination information, which is information to be obtained, is obtained based on the number of 1 included in each basis, and is output to a specific qubit that is part of the code qubit group The untanglement between the qubit expressing the transmission word information and the qubits other than the qubit including the transmission word information is canceled by operating the control NOT gate using the specific qubit as the control qubit. An entanglement elimination step.

  According to the present invention, a quantum operation is performed by causing a plurality of control NOT gates to act on the code qubit group, and whether the basis of the code qubit group is a basis included in the first code quantum state or the second Based on the number of 1s included in each base, base discrimination information that is information for determining whether the base is included in the quantum state is obtained and output to a specific qubit that is part of the code qubit group. Since the control NOT gate using the specific qubit as the control qubit is operated, the entanglement between the qubit expressing the transmission word information and the qubit other than the qubit including the transmission word information is eliminated. The base discrimination and entanglement resolution can be realized with only codeword qubits and no ancillary qubits required, and the number of gates used for decoding It reduced it is possible to scale the scale of the quantum circuit. In addition, according to the present invention, a control NOT gate using a specific qubit in which the base discrimination information is output as a control qubit is applied to the qubit information of the codeword information, so that the queuing including the transmission word information is performed. Since the entanglement between the bit and the qubit other than the qubit including the transmission word information is eliminated, the code word information can be transmitted without the processing of applying the inverse operator of the unitary operator to the code qubit group. The information can be decoded, and the efficiency of quantum error correction can be improved.

  Exemplary embodiments of a quantum circuit, a quantum error correction apparatus, and a quantum error correction method according to the present invention will be explained below in detail with reference to the accompanying drawings.

(Embodiment 1)
FIG. 1 is a block diagram of a functional configuration of the quantum error correction apparatus 100 according to the first embodiment. The quantum error correction apparatus 100 according to the present embodiment includes an error correction circuit 110 and a decoding circuit 120 as shown in FIG.

  The error correction circuit 110 inputs codeword data obtained by encoding transmission word information representing a quantum state indicated by a linear combination of a plurality of bases into a quantum error correction code by a unitary operation, and adds the codeword data to the codeword data by syndrome measurement. This is a circuit that diagnoses the type of error that has occurred, that is, error syndrome, and corrects the error when it is within a correctable range.

  The decoding circuit 120 is a circuit that performs a decoding process on the quantum state of the codeword data that has been subjected to error correction, and returns the quantum state of the original transmission word information. Here, the quantum state is an element of the Hilbert space, and in particular, an element of the two-dimensional Hilbert space is called a qubit. The n qubit (n: a positive integer) is a quantum state, that is, n two-dimensional Hilbert spaces connected by a tensor product, and is expressed as a 2 n-dimensional Hilbert space.

  The quantum circuit used in this embodiment is a unitary operator. It has been found that any unitary operator can be constructed as a combination (universal set) of some basic quantum gates. An example of a universal set is a combination of an arbitrary rotation gate of 1 qubit and a conditional rotation gate of 2 qubits. In the present embodiment, transmission word information is composed of 1 qubit, codeword data is composed of 5 qubits, and both transmission word information and codeword data are binary quantum states expressed by two linear combinations. is there. Transmission word information | ψ> is expressed by equation (1), and codeword data | ψ> is expressed by equation (2). Here, the first quantum state in the present invention corresponds to | 0> in the equation (1), and the second quantum state in the present invention corresponds to | 1> in the equation (1).

In equations (1) and (2), states | 0> and | 1> are both bases of transmission word | ψ>, and | 0> = (1, 0), state | 1> = (0 , 1) is represented by an element of Hilbert space. The state | ψ ₀ > is obtained by encoding the basis | 0>, and | ψ ₁ > is obtained by encoding the basis | 1> of the transmission word information. Here, | Ψ ₀ > corresponds to the first code quantum state in the present invention, and | Ψ ₁ > corresponds to the second code quantum state in the present invention.

The code word data | Ψ> is further expressed by the following expression (3), and | Ψ ₀ > and | Ψ ₁ > are expressed by the expressions (4) and (5) using the basis, respectively. Therefore, the transmission word information | ψ> represented by the expression (1) is encoded into the code word data | Ψ> represented by the expression (6) when the expressions (4) and (5) are used. Become.

Here, in the expressions (4) and (5), the number of “1” is an even number in each basis of | Ψ ₀ >, and the number of “1” is an odd number in each basis of | Ψ ₁ >. ing. Also, each base of | Ψ ₀ > and a base at a corresponding position among | Ψ ₁ > bases are in an inverted relationship with each other. That is, when one base | 10010> of | Ψ ₀ > is seen, the number of “1” s is two and an even number. Also, in the base | 01101> of | Ψ ₁ > corresponding to the base | 10010> of | Ψ ₀ >, the number of “1” s is three and odd, and | 10010> of | Ψ ₀ > is just inverted. It has become a relationship.

  The decoding circuit 120 corresponds to the quantum circuit in the present invention, and includes a base discriminating circuit 121 and an entanglement eliminating circuit 122 as shown in FIG.

  The base discriminating circuit 121 is composed of a plurality of quantum gates, inputs a code qubit group, discriminates the type of base based on the quantity of “1” included in each base, and outputs it to a specific qubit of the code qubit group It is a quantum circuit.

  The entanglement elimination circuit 122 is composed of a plurality of quantum gates, and the base discriminating circuit 121 receives the code qubit group, discriminates the base type based on the quantity of “1” included in each qubit, and the code queue. A quantum circuit that outputs a specific qubit of a bit group.

Here, entanglement cancellation will be described. When | φ ₀ > is m qubit, | Φ> is n qubit, and | φ ₁ > is nm qubit, | Φ> is | φ ₀ > and | φ If it can be expressed by a tensor product of ₁ >, it can be said that the first m qubit of | Φ> can be separated from other nm qubits, and | Φ> can be expressed separately as in equation (7). If this is not possible, the first m qubit of | Φ> is said to be entangled with other nm qubits (entanglement).

  Taking the case of 2 qubits as an example, the quantum state represented by equation (8) is expressed as the tensor product of the first qubit and the second qubit, as in equation (9). Since it can be expressed, it is said that the first qubit and the second qubit are separated.

  On the other hand, the quantum state represented by equation (10) can be transformed as in equation (11), but as a tensor product of the first qubit and the second qubit as in equation (9). Since it cannot be expressed, it is said that the first qubit and the second qubit are entangled, that is, entangled.

  In a pair of bases symmetric with respect to all qubit inversions with respect to the 1st to (k-1) th qubits (k: an integer of 2 or more) from when the quantum state is expressed by the expression (12), entanglement Mentor has been resolved.

At this time, if the entanglement is canceled in a pair of bases symmetrical with respect to all qubit inversions with respect to the first to (k−1) th qubits from the equation (12), as in the equation (13) It can be deformed. That is, considering only the pair of bases having the common subscript j in | Ψ ₀ > and | Ψ ₁ >, it is described as a tensor product of the first to (k−1) th qubits and other qubits. Can do.

In other words, entanglement elimination refers to conversion of an entangled quantum state such as equation (10) into a separable form such as equation (9). The entanglement elimination circuit used in the above process separates the code word data output from the base discriminating circuit 121 by using the inversion relationship of the bases of the above-described code word data | Ψ> | Ψ ₀ > and | Ψ ₁ >. Converting to a format that can be done, entanglement elimination.

  FIG. 2 is an explanatory diagram showing a series of flow from encoding of transmission word information to decoding of code word data by the quantum error correction apparatus according to the present embodiment. The transmission word information of 1 qubit expressed by equation (1) is encoded, and codeword data of 5 qubit expressed by equation (2) is generated.

  This 5-qubit codeword data is affected by noise and an error occurs over time. The code word data of 5 qubits in which this error has occurred is input to the quantum error correction apparatus 100 of the present embodiment, error correction is performed by the error correction circuit 110, and the code word data subjected to error correction is decoded by the decoding circuit 120. Is restored to the original transmission word information of 1 qubit.

In the quantum error correction apparatus 100 of the present embodiment, the decoding circuit 120 base discrimination circuit 121 controls a specific qubit among the qubits of codeword data of 5 qubits and the other 4 qubits. Passing through (acting) a quantum gate of a control NOT classified as a torigate type as a qubit, discriminating each base constituting a code word, and base discriminating information (| Ψ ₀ > | 0> or | 1>) indicating whether it is the basis of | Ψ ₁ > or not is output to the specific qubit. Then, the specific qubit in which the base discrimination information is output is set as a control qubit, and the control CUt gate is set with 4 qubits other than the specific qubit as target qubits, and the specific qubit is expressed by Expression (1). The transmitted word information is output, and the superposition state in which the entanglement with the transmitted word information is eliminated in the other four qubits is output. As a result, it is possible to recover the transmitted word information by decoding the codeword data without causing the inverse operator of the unitary operator to act on the codeword data and eliminating the need for an extra qubit such as an ancillary and reducing the number of quantum gates. .

  Next, details of the decoding circuit 120 according to the present embodiment will be described. FIG. 3 is a circuit configuration diagram of the decoding circuit 120 according to the first embodiment.

  The base discriminating circuit 121 is provided with four control NOT gates. The base discriminating circuit 121 receives the value of each qubit of code word data of 5 qubits expressed by the equation (1). The fifth qubit is a specific qubit, the control qubit, each of the first to fourth qubits as the target qubit, the input of each of the first to fourth qubits and the fifth qubit The input of the qubit is calculated by the control NOT gate, and its output is output to the fifth qubit which is a specific qubit.

  Further, the entanglement cancellation circuit 122 is provided with four control NOT gates, the fifth qubit being a specific qubit is set as a control qubit, and the first to fourth qubits are targeted. It is a qubit. Therefore, the outputs of the first to fourth qubits and the output of the fifth qubit from the base discriminating circuit 121 are calculated by the control NOT gate, and the fifth qubit whose output is the control qubit. Is output. The decoded transmission word information is output to the fifth qubit of the entanglement cancellation circuit 122, and the superposition state is output to the first to fourth qubits.

  Here, the control NOT gate will be described. The control NOT gate is a quantum gate that calculates the exclusive OR of the input states of two qubits and outputs the result as two qubits, and is one of the torigates. 4A is a circuit diagram of the control NOT gate, and FIG. 4B is an explanatory diagram of a truth table of the control NOT gate. In addition, in the quantum circuit diagrams shown hereinafter including FIG. 4-1, a straight line indicates a qubit, and a symbol described on the straight line indicates a quantum gate.

In FIG. 4A, it is assumed that two qubit input states a ₁ and a ₂ are passed through a control NOT gate and output to two qubit output states b ₁ and b ₂ . Here, a ₁ is called a control qubit, and a ₂ is called a target qubit (or target qubit). As shown in the truth table of FIG. 4B, in the control NOT gate, the output value b ₁ is output with the control qubit a ₁ remaining as it is. On the other hand, when the control qubit a ₁ is “0”, the output to the target qubit a ₂ is not changed and the output state b ₂ is output as it is, but the control qubit a ₁ is “1”. ", The state of a ₂ is inverted and the output state b ₂ is output.

  Next, the operation of the decoding circuit 120 according to this embodiment shown in FIG. 3 will be described. Here, it is assumed that the decoding circuit 120 inputs code word data of 5 qubits expressed by Expression (2) obtained by encoding the transmission word expressed by Expression (1).

5, the code word data | 4 of each underlying [psi _0>, entanglement elimination circuit 122 | [psi> of | [psi _0> after passing through the four control NOT gate for each basis basal determination circuit 121 of the It is explanatory drawing which shows each base of | (PSI) ₀ > after passing through one control NOT gate.

Also, FIG. 6, the code word data | [psi> of | [psi _1> each basis is after passing through the four control NOT gate basal discrimination circuit 121 of | and each basis of [psi _1, entanglement elimination circuit 122 four control NOT gates were after passing | is an explanatory diagram showing each base of the [psi _1>.

As shown in FIG. 5, | after each underlying [psi _0> passes through the four control NOT gate basal discriminating circuit 121 acts a control NOT gate shown in FIG. 4-2, | Ψ _0> of There is no change in the first to fourth qubits of each base, and the fifth qubit is | 0> for all bases included in | Ψ ₀ >. For this reason, the state after each base of | Ψ ₀ > passes through the four control NOT gates of the base discriminating circuit 121 is expressed by equation (14).

On the other hand, as shown in FIG. 6, | after each basis of [psi _1> has passed through the four control NOT gate basal discriminating circuit 121 acts a control NOT gate shown in FIG. 4-2, | [psi ₁ The first to fourth qubits of each base of> are not changed, and are the fifth qubit | 1> for all bases included in | Ψ ₁ >. For this reason, the state after each base of | Ψ ₁ > passes through the four control NOT gates of the base discriminating circuit 121 is expressed by equation (15).

  For this reason, the state after the code word data | Ψ> passes through the four control NOT gates of the base discriminating circuit 121 is expressed by the equation (16).

Here, a specific example will be described. FIG. 7 is an explanatory diagram showing a change in state for each passage of the gate when the four control NOT gates of the base discriminating circuit 121 are passed with respect to the base | 10111> of | Ψ ₀ >.

  First, when the base | 10111> passes through the first control NOT gate (the leftmost gate in FIG. 3), the first qubit (control qubit) is “1” and the fifth qubit (target Since the qubit is “1”, the fifth qubit is inverted to “0” according to the truth table of FIG. 4-2 of the control NOT gate.

  Next, when the inverted base | 10110> passes through the second control NOT gate (second gate from the left side in FIG. 3), the second qubit (control qubit) is “0”, the fifth Since the qubit (target qubit) is “0” (changes from “1” to “0” by passing through the first gate), the fifth qubit remains in the state “0” as it is. is there.

  Next, when the base | 10110> passes through the third control NOT gate (the third gate from the left in FIG. 3), the third qubit (control qubit) is “1”, and the fifth cu Since the bit (target qubit) is “0”, the fifth qubit is inverted to “1”.

  Next, when the inverted base | 10111> passes through the fourth control NOT gate (fourth gate from the left side in FIG. 3), the fourth qubit (control qubit) is “1”, the fifth Since the qubit (target qubit) of “1” is “1”, the fifth qubit is inverted to “0”.

Similarly, for the other bases of | Ψ ₀ >, the fifth qubit is “0”, and as a result, | Ψ ₀ > (14) is expressed. That is, since the number of “1” s in the basis of | Ψ ₀ > is an even number, the first control qubit of | Ψ ₀ > when input to the base discriminating circuit 121 as shown in the example of FIG. When the state of the fifth qubit is “1”, the number of “1” s in the first to fourth qubits is an odd number, so the number of inversions by the control NOT gate is an odd number, and the fifth The state of the qubit is “0”. On the other hand, when the state of the fifth qubit that is the control qubit of | Ψ ₀ > at the time of input to the base discriminating circuit 121 is “0”, “1” in the first to fourth qubits is “1”. Since the number is an even number, the number of inversions by the control NOT gate is an even number. In this case as well, the state of the fifth qubit is “0”.

On the other hand, FIG. 8 is an explanatory diagram showing a change in state at each gate passage when the four control NOT gates of the base discriminating circuit 121 are passed with respect to the base | 11111> of | Ψ ₁ >.

  First, when the base | 11111> passes through the first control NOT gate, the first qubit (control qubit) is “1” and the fifth qubit (target qubit) is “1”. Therefore, the fifth qubit is inverted to “0”.

  Next, when the inverted base | 11110> passes through the second control NOT gate, the second qubit (control qubit) is “1”, and the fifth qubit (target qubit) is “0”. ”(Change from“ 1 ”to“ 0 ”by passing through the first gate), the fifth qubit is inverted to“ 1 ”.

  Next, when the inverted base | 11111> passes through the third control NOT gate, the third qubit (control qubit) is “1”, and the fifth qubit (target qubit) is “1”. Therefore, the fifth qubit is inverted to “0”.

  Next, when the inverted base | 11110> passes through the fourth control NOT gate, the fourth qubit (control qubit) is “1”, and the fifth qubit (target qubit) is “0”. Therefore, the fifth qubit is inverted to “1”.

Similarly, for the other bases of | Ψ ₁ >, the fifth qubit is “1”, and eventually | Ψ ₁ > is expressed by equation (15). That, | since the number of "1" in the basis of [psi _1> is an odd number, as in the example of FIG. 8, is input to the base determination circuit 121 the time | first as the control qubit for [psi _1> When the state of the fifth qubit is “1”, the number of “1” s in the first to fourth qubits is an even number, so the number of inversions by the control NOT gate is an even number, and the fifth The state of the qubit is “1”. On the other hand, when the state of the fifth qubit that is the control qubit of | Ψ ₁ > at the time of input to the base discriminating circuit 121 is “0”, “1” in the first to fourth qubits is “1”. Since the number is an odd number, the number of inversions by the control NOT gate is an odd number. In this case as well, the state of the fifth qubit is “1”.

The base discriminating circuit 121 uses the output to the fifth qubit as base discriminating information, and the even number and odd number of “1” in the base of | Ψ ₀ > and the base of | Ψ ₁ > as described above. By utilizing the difference property, the basis of | Ψ ₀ > is determined when the basis determination information is “0”, and the basis of | Ψ ₁ > is determined when the basis determination information is “1”.

However, in the expression (16) that is the output of the base discriminating circuit 121, the code word data | Ψ> is tangled, and therefore it cannot be decoded into the transmission word information from the expression (16). Here, as described above, each base in the state | Ψ ₀ > and each base in | Ψ ₁ > have a relationship that is inverted. For this reason, the entanglement elimination circuit 122 according to the present embodiment converts | Ψ _{1, j} > ₁ to ₄ in the equation (16) into | Ψ _{0, j} > ₁ to ₄ using this inversion relationship. Then, conversion is performed so that the code word data | Ψ> is expressed by Expression (17), entanglement is eliminated as shown by Expression (18), and transmission word information | ψ> is obtained from Expression (18). .

As shown in FIG. 3, since the base discriminating information that is the output of the base discriminating circuit 121 is input to the fifth qubit of the entanglement canceling circuit 122, each base of | Ψ ₀ > is entangled canceling. When input to each gate of the circuit 122, the fifth qubit is always the base discrimination information “0”. Also, each of the four control NOT gates of the entanglement elimination circuit 122 uses the fifth qubit from which this base discrimination information is output as the control qubit, and sets each of the first to fourth qubits as the target. Since the control qubit is always “0”, the state of the first to fourth qubits after each base of | Ψ ₀ > passes through each gate of the entanglement cancellation circuit 122 is As shown in FIG. 5, the output after passing through the four control NOT gates of the base discriminating circuit 121 is not changed from | Ψ _{0, j} > ₁ to _4, and the output of all qubits is | Ψ _{0, j} > ₁ to It is represented by a tensor product of ₄ and | 0>.

On the other hand, when each base of | Ψ ₁ > is input to each gate of the entanglement canceling circuit 122, the fifth qubit is always base discrimination information “1”. Therefore, since this control qubit is always “1”, the states of the first to fourth qubits after each base of | Ψ ₁ > passes through each gate of the entanglement cancellation circuit 122 are as shown in FIG. As shown in FIG. 5, the outputs after passing through the four control NOT gates of the base discriminating circuit 121 are all inverted from | Ψ _{1, j} > ₁ to ₄ , so that | Ψ _{0, j} > ₁ to _{4 is obtained} . Is represented by a tensor product of | Ψ _{0, j} > ₁ to ₄ and | 1>.

  This means that after the code word data | Ψ> passes through the four control NOT gates of the entanglement canceling circuit 122, the code word data | Ψ> is converted from the expression (16) to the expression (17) and is entangled. This means that it is expressed by equation (18), which means that it can be decoded into transmission word information | ψ>.

Here, in the decoding circuit of the conventional quantum error correction apparatus, both the base discriminating circuit and the entanglement canceling circuit are ancillary | 0> which is a qubit used in addition to 5 qubits corresponding to code word data. _Anc was provided. Each of the five qubits is provided with five control NOT gates each having the target qubit as an ancillary, and all the outputs of the respective gates are output to the ancilla. Whether the ancillary is the basis of | Ψ ₀ > or | Ψ ₁ >? The base discrimination information indicating is output. That is, when the ancilla is | 0> _anc , the basis is | Ψ ₀ >, and when the ancilla is | 1> _anc , the basis is | Ψ ₁ >. As a result, the output after the code word data represented by the equation (19) is passed through the base discriminating circuit is represented by the equation (20).

Further, in the entanglement elimination circuit, five control NOT gates are provided for each qubit in which the ancillary is a control qubit and each qubit of a code word of 5 qubits is a target qubit, and (21), (22 As shown in the equation, all five qubits of | Ψ ₁ > are inverted to cancel entanglement, and are decoded into transmission word information. For this reason, in this conventional decoding circuit using an ansila, the number of control NOT gates is required for all the qubits of the codeword data, and the size of the quantum circuit increases.

  On the other hand, in the quantum error correction apparatus according to the first embodiment, the base discriminating circuit 121 causes the control NOT gate to act on the qubits of the codeword data so that the number of “1” s in each base is even or odd. The base discrimination information for discriminating the type of each base included in the codeword gate is output to a specific fifth qubit in the qubit of the codeword data. An entanglement between the qubits including the transmission word information and the qubits other than the qubits including the transmission word information is performed by the entanglement cancellation circuit 122 by applying a control NOT using the fifth qubit as the control qubit. In the decoding circuit, there is no need to provide an ancillary in addition to the qubit of codeword data in the decoding circuit, and the number of control NOT gates can be reduced to reduce the circuit scale. Can be planned.

  Further, in the quantum error correction apparatus 100 according to the first embodiment, the entanglement canceling circuit 122 operates the control NOT using the fifth qubit as the control qubit, and transmits the qubit including the transmission word information and the transmission. Since entanglement with qubits other than qubits containing word information can be resolved and transmission word information can be decoded, it is not necessary to apply a unitary operator inverse operator to codeword data during decoding. Error correction efficiency can be improved.

  In the quantum error correction apparatus 100 according to the present embodiment, the specific qubit for outputting the base discrimination information is the fifth qubit of the codeword data, but the present invention is not limited to this. Any qubit of the word data can be a specific qubit.

(Embodiment 2)
In the quantum error correction apparatus 100 according to the first embodiment, since the entanglement cancellation is not canceled in all the qubits in the output state of the base discriminating circuit 121, the entanglement cancellation circuit 122 uses the first to fourth codeword data. The control NOT gate is operated on all the qubits using the fifth qubit, which is a specific qubit, as the control qubit. In the quantum error correction device according to the second embodiment, the entanglement cancellation is performed in the qubits in the output state of the basis discrimination circuit, and therefore, in the entanglement cancellation circuit 122, other than the qubits in part. The transmission word information is decoded by canceling entanglement for the qubits.

  FIG. 9 is a circuit diagram of the decoding circuit 920 according to the second embodiment. Similar to the first embodiment, the decoding circuit 920 according to the second embodiment includes a base discrimination circuit 921 and an entanglement elimination circuit 921.

  As shown in FIG. 9, the base discriminating circuit 921 is provided with four control NOT gates. Here, as in the first embodiment, the base discriminating circuit 921 receives the value of each qubit of the code word data of 5 qubits expressed by the equation (1). In the base discriminating circuit 921 according to this embodiment, the first control NOT gate is provided with the first qubit as the control qubit and the second qubit as the target qubit. The second control NOT gate is provided with the second qubit as the control qubit and the third qubit as the target qubit. The third control NOT gate is provided with the third qubit as the control qubit and the fourth qubit as the target qubit. The fourth control NOT gate is provided with the fourth qubit as the control qubit and the fifth qubit as the target qubit. That is, the first qubit becomes a control qubit in the first control NOT gate, and the second to fifth qubits become target qubits in successive control NOT gates. Each control NOT gate is provided so as to be.

  The entanglement elimination circuit 922 is provided with two control NOT gates as shown in FIG. The first control NOT gate has the fifth qubit as the control qubit and the first qubit as the target qubit, and the second control NOT gate has the fifth qubit as the fifth qubit. The qubit is the control qubit, and the third qubit is the target qubit. Then, transmission word information is output to the fifth qubit.

  In this embodiment, the fifth qubit becomes a specific qubit, and the base discriminating circuit 921 outputs the base discriminating information to the fifth qubit, and the entanglement cancellation circuit 922 outputs the fifth qubit. Transmission word information is output to the qubit.

Figure 10 is a code word data | 2 for each underlying [psi _0>, entanglement elimination circuit 922 | [psi> of | [psi ₀ each basis is after passing through the four control NOT gate basal determination circuit 921> It is explanatory drawing which shows each base of | (PSI) ₀ > after passing through one control NOT gate.

FIG. 11 shows each base of | Ψ ₁ > after each base of the code word data | Ψ> passes through the four control NOT gates of the base discriminating circuit 921 and two control NOTs of the entanglement canceling circuit 922. It is explanatory drawing which shows each base of | (PSI) ₁ > after passing through a gate.

Comparing the bases after passing through the two gates of the entanglement canceling circuit 922 in FIG. 10 and FIG. 11, the first to fourth qubits match, and the fifth of the respective bases of | Ψ ₀ > shown in FIG. It can be seen that the qubit is | 0>, and the fifth qubit of each base of | Ψ ₁ > shown in FIG. 11 is | 0>. This indicates that the expression (23) is established, and that the qubits of the transmission word information and other qubits are eliminated from entanglement.

Here, one of bases of | Ψ ₀ > is defined as | a ₁ a ₂ a ₃ a ₄ a ₅ >, and | a ₁ a ₂ a ₃ a ₄ a ₅ > Let the state be | a ′ ₁ a ′ ₂ a ′ ₃ a ′ ₄ a ′ ₅ >. Further, one base of | Ψ ₁ > and | a ₁ a ₂ a ₃ a ₄ a ₅ > and a base that is in a relation of all qubit inversions are | b ₁ b ₂ b ₃ b ₄ b ₅ >, Let | b ′ ₁ b ′ ₂ b ′ ₃ b ′ ₄ b ′ ₅ > be the state after passing four gates of the base discriminating circuit 921 of | b ₁ b ₂ b ₃ b ₄ b ₅ >.

At this time, | a ₁ a ₂ a ₃ a ₄ a ₅ > and | a ′ ₁ a ′ ₂ a ′ ₃ a ′ ₄ a ′ ₅ > have the relationships of the expressions (24) to (28). Also, | b ₁ b ₂ b ₃ b ₄ b ₅ > and | b ′ ₁ b ′ ₂ b ′ ₃ b ′ ₄ b ′ ₅ > hold, the expressions (29) to (33) hold.

Here, as described in the first embodiment, the basis of | Ψ ₀ > is defined as | a ₁ a ₂ a ₃ a ₄ a ₅ > and the basis of | Ψ ₁ > is defined as | b ₁ b ₂ b ₃ b ₄ b _{From the fact that 5} > is in an inversion relationship with each other and the meaning of the inversion relationship, equations (34) and (35) hold.

Assuming the relationship between the equations (34) and (35), when the relationship between a ′ _i and b ′ _i is obtained from the equations (24) to (33), equations (36) to (40) are established. It can be seen that the equations (41) and (42) are derived.

  From the equations (41) and (42), since the entanglement has already been eliminated for the second and fourth qubits when passing through the base discriminating circuit 921, the entanglement eliminating circuit 922 In order to eliminate entanglement only for the first, third, and fifth qubits in which entanglement has not been eliminated, two control NOT gates are provided as shown in FIG.

  As described above, in the quantum error correction device according to the second embodiment, the entanglement cancellation is performed in the qubits in the qubits in the output state of the base discriminating circuit 121. Since entanglement elimination is performed for qubits other than qubits, the number of control NOT gates can be further reduced to further reduce the circuit scale.

(Embodiment 3)
In the quantum error correction apparatus according to the third embodiment, entanglement cancellation is performed in the qubits that are part of the output state of the base discriminating circuit. It is another aspect which performs entanglement cancellation with respect to this and decodes transmission word information.

  FIG. 12 is a circuit diagram of the decoding circuit 1220 according to the third embodiment. Similar to the second embodiment, the decoding circuit 1220 according to the third embodiment includes a base discriminating circuit 1221 and an entanglement eliminating circuit 1221.

  As shown in FIG. 12, the base discriminating circuit 1221 is provided with four control NOT gates. Here, as in the first embodiment, the base discriminating circuit 1221 receives the value of each qubit of the code word data of 5 qubits expressed by the equation (1). In the base discriminating circuit 1221 according to the present embodiment, the first control NOT gate is provided with the first qubit as the control qubit and the second qubit as the target qubit. The second control NOT gate is provided with the second qubit as the control qubit and the third qubit as the target qubit. The third control NOT gate is provided with the fifth qubit as the control qubit and the fourth qubit as the target qubit. The fifth control NOT gate is provided with the fourth qubit as the control qubit and the third qubit as the target qubit.

  As shown in FIG. 12, the entanglement elimination circuit 1222 is provided with two control NOT gates. The first control NOT gate has the third qubit as the control qubit and the first qubit as the target qubit, and the second control NOT gate has the third qubit as the third qubit. The qubit is the control qubit and the fifth qubit is the target qubit.

  In this embodiment, the third qubit becomes a specific qubit, and the base discriminating circuit 1221 outputs the base discriminating information to the third qubit, and the entanglement canceling circuit 1222 outputs the third qubit. Transmission word information is output to the qubit.

13, the code word data | 2 for each underlying [psi _0>, entanglement elimination circuit 1222 | [psi> of | [psi _0> after each basis has passed the four control NOT gate basal determination circuit 1221 of the It is explanatory drawing which shows each base of | (PSI) ₀ > after passing through one control NOT gate.

Further, FIG. 14, the code word data | [psi> of | [psi _1> each basis is after passing through the four control NOT gate basal determination circuit 1221 | and each basis of [psi _1, entanglement eliminating circuit 1222 It is explanatory drawing which shows each base of | (PSI) ₁ > after passing through two control NOT gates.

Here, one of the bases of | Ψ ₀ > is defined as | a ₁ a ₂ a ₃ a ₄ a ₅ >, and the first two gates of the base discriminating circuit 1221 of | a ₁ a ₂ a ₃ a ₄ a ₅ > The state after the four gates of the base discriminating circuit 1221 of | a ′ ₁ a ′ ₂ a ′ ₃ a ′ ₄ a ′ ₅ > and | a ₁ a ₂ a ₃ a ₄ a ₅ >' ₁ a'' ₂ a'' ₃ a'' ₄ a'' ₅ >

Also, _one of the bases of | Ψ ₁ >, which is in a relation of | a ₁ a ₂ a ₃ a ₄ a ₅ > and all the qubits inversion | b ₁ b ₂ b ₃ b ₄ b ₅ >, | B ′ ₁ b ′ ₂ b ′ ₃ b ′ ₄ b ′ ₅ >, | b ₁ b ₂ after passing through the first two gates of the base discriminating circuit 1221 of | b ₁ b ₂ b ₃ b ₄ b ₅ > The state after passing through the four gates of the base discriminating circuit 1221 of b ₃ b ₄ b ₅ > is defined as | b ″ ₁ b ″ ₂ b ″ ₃ b ″ ₄ b ″ ₅ >.

At this time, | a ₁ a ₂ a ₃ a ₄ a ₅ > and | a ′ ₁ a ′ ₂ a ′ ₃ a ′ ₄ a ′ ₅ > have the relations of equations (43) to (47), and | a ₁ a ₂ a ₃ a ₄ a ₅ >, | a ′ ₁ a ′ ₂ a ′ ₃ a ′ ₄ a ′ ₅ > and | a ″ ₁ a ″ ₂ a ″ ₃ a ″ ₄ a ″ ₅ > Holds the relationship of the equations (48) to (52).

In addition, | b ₁ b ₂ b ₃ b ₄ b ₅ > and | b ′ ₁ b ′ ₂ b ′ ₃ b ′ ₄ b ′ ₅ > have the expressions (53) to (57), and | b ₁ b ₂ b ₃ b ₄ b ₅ >, | b ′ ₁ b ′ ₂ b ′ ₃ b ′ ₄ b ′ ₅ > and | b ″ ₁ b ″ ₂ b ″ ₃ b ″ ₄ b ″ ₅ > The relationship of the equations (58) to (62) is established.

Here, as in the second embodiment, the basis of | Ψ ₀ > is changed to | a ₁ a ₂ a ₃ a ₄ a ₅ > and the basis of | Ψ ₁ > is changed to | b ₁ b ₂ b ₃ b ₄ b ₅ > When the relationship of the inverted relationship to each other (34), the premise of equation (35), (43) - (62) determine the relationship of a '' _i and b '' _i from the equation (63) - (66 It can be seen that the following formulas (67) and (68) are derived.

  From the expressions (67) and (68), since the entanglement has already been eliminated for the second and fourth qubits when passing through the base discriminating circuit 1221, the entanglement elimination circuit 1222 In order to eliminate entanglement only for the first, third, and fifth qubits in which entanglement has not been eliminated, two control NOT gates are provided as shown in FIG.

  As described above, in the quantum error correction apparatus according to the third embodiment, the entanglement cancellation is performed on the basis discrimination circuit 1221 in a part of the qubits in its output state. Since entanglement elimination is performed for qubits other than qubits, the number of control NOT gates can be further reduced to further reduce the circuit scale.

  In the quantum error correction apparatus according to the first to third embodiments, an example in which codeword data of 5 qubits is input and decoded is shown, but the number of qubits is not limited to this, The present invention can be applied to decoding code word data of an arbitrary number of qubits.

  A quantum circuit, a quantum error correction device, and a quantum error correction method according to the present invention perform quantum error correction on codeword information obtained by encoding transmission word information representing a quantum state represented by a linear combination of a plurality of bases. A circuit that performs quantum error correction that decodes the original transmitted word information, and converts each qubit of the codeword information into a state represented by a tensor product of the qubits superimposed on the cubits of the transmitted word information. Thus, the present invention is useful for an apparatus including a decoding circuit that decodes transmission word information. As a basic gate realization method, for example, as described in the document “Katsuhiro Kitagawa, NMR Quantum Computer, Mathematical Sciences, No.424, 1998.”, nuclear spins caused by nuclear magnetic resonance (NMR) are described. The quantum circuit of the present invention can be applied when performing quantum computation using control.

  In addition, surplus in a superconducting electron pair box having a Josephson junction as in the document “T. Yamamoto et.al. Demonstration of conditional gate operation using superconducting charge qubits.Nature, vol.425, pp.941, 2003.” The quantum circuit of the present invention can be applied when quantum computation is performed by a method in which a superconducting electron pair is controlled by an electromagnetic pulse. As described above, the quantum circuit, the quantum error correction apparatus, and the quantum error correction method of the present invention can be realized using a natural law.

  In addition to the above-described nuclear spin manipulation by NMR and superconducting electron pair number manipulation by electromagnetic pulses, qubits and quantum gates can be realized by methods using photon polarization and phase difference, or solid-state EIT (Electromagnetically Induced Transparency) Some use the phenomenon. However, the present invention is not limited to the realization of qubits and quantum gates by nuclear spin manipulation by NMR and control of the number of superconducting electron pairs by electromagnetic pulses, but qubits and unitary as a Hilbert space defined mathematically. The present invention can be applied to all physical systems that can realize a quantum gate as an operator.

1 is a block diagram showing a functional configuration of a quantum error correction apparatus 100 according to a first embodiment. It is explanatory drawing which shows a series of flow from encoding of transmission word information to decoding of codeword data by the quantum error correction apparatus concerning this Embodiment. 1 is a circuit configuration diagram of a decoding circuit 120 according to a first embodiment. FIG. It is a circuit diagram of a control NOT gate. It is explanatory drawing which shows the truth table of a control NOT gate. Codeword data | [psi> of | [psi _0> after each basis has passed the four control NOT gate basal discrimination circuit 121 of | and each basis of [psi _0>, four control NOT gate entanglement elimination circuit 122 It is explanatory drawing which shows each base of | Ψ ₀ > after passing through. Codeword data | [psi> of | [psi _1> each basis is after passing through the four control NOT gate basal discrimination circuit 121 of | and each basis of [psi _1, four control NOT gate entanglement elimination circuit 122 It is explanatory drawing which shows each base of | Ψ ₁ > after passing. FIG. 11 is an explanatory diagram showing a change in state for each passage of the gate when four control NOT gates of the base discriminating circuit 121 are passed with respect to a base | 10111> of | Ψ ₀ >. FIG. 11 is an explanatory diagram showing a change in state for each passage of the gate when four control NOT gates of the base discriminating circuit 121 are passed with respect to a base | 11111> of | Ψ ₁ >. FIG. 6 is a circuit diagram of a decoding circuit 920 according to the second exemplary embodiment. Codeword data | [psi> of | [psi _0> after each basis has passed the four control NOT gate basal determination circuit 921 | and each basis of Ψ _0>, 2 two controlled-NOT gate entanglement elimination circuit 922 It is explanatory drawing which shows each base of | Ψ ₀ > after passing through. Codeword data | [psi> of | [psi _1> each basis basal discriminating circuit after passing through the four control NOT gate 921 for | and each basis of Ψ _1>, 2 two controlled-NOT gate entanglement elimination circuit 922 is an explanatory diagram showing each base of the [psi _1> | after passing the. FIG. 10 is a circuit diagram of a decoding circuit 1220 according to the third embodiment. Codeword data | [psi> of | [psi ₀ each basis is after passing through the four control NOT gate basal determination circuit 1221 of> | and each basis of Ψ _0>, 2 two controlled-NOT gate entanglement eliminating circuit 1222 It is explanatory drawing which shows each base of | Ψ ₀ > after passing through. Codeword data | [psi> of | [psi _1> each basis is after passing through the four control NOT gate basal determination circuit 1221 | and each basis of [psi _1, two control NOT gate entanglement eliminating circuit 1222 It is explanatory drawing which shows each base of | Ψ ₁ > after passing.

Explanation of symbols

DESCRIPTION OF SYMBOLS 100 Quantum error correction apparatus 110 Error correction circuit 120,920,1220 Decoding circuit 121,921,1221 Base discrimination circuit 122,922,1222 Entanglement cancellation circuit

Claims (7)

Code qubit group which is a set of qubits representing code word information obtained by encoding transmission word information as a quantum state, which is an element of a two-dimensional Hilbert space expressed by a linear combination of two bases, using a stabilizer coding scheme A first code quantum state that is a quantum state in which a first basis of a two-dimensional Hilbert space representing the transmission word information is encoded, and a quantum in which a second basis of the transmission word information is encoded. Inverted by a NOT gate that inverts the first base to the second base and inverts the second base to the first base for all qubits in the first code quantum state Each of the bases included in the second code quantum state is represented by the first code quantum state. Code word information having a property of forming a pair of bases symmetrical with respect to all qubit inversions, and a plurality of qubits representing the transmission word information A quantum circuit that performs a decoding process for converting to a state represented by a tensor product with a qubit expressed as a superposition state of a base of
A plurality of control NOT gates are applied to the code qubit group to perform a quantum operation, and whether the basis of the code qubit group is a basis included in the first code quantum state or the second quantum state A basis for determining basis discrimination information, which is information for discriminating whether a basis is included in each basis, based on the number of 1s included in each basis, and outputting to a specific qubit that is part of the code qubit group Discrimination means;
Entanglement for canceling entanglement between a qubit expressing the transmission word information and a qubit other than the qubit including the transmission word information by operating a control NOT gate using the specific qubit as a control qubit Resolving means,
A quantum circuit comprising: The base discriminating means includes a plurality of control NOT gates in which the specific qubit of the code qubit group is a target qubit, and the code qubit group other than the specific qubit is a control qubit, The basis NOT information which is the number of 1 included in each base is obtained by the control NOT gate and output to the specific qubit,
The entanglement elimination means includes a plurality of control NOT gates in which the specific qubit is a control qubit and a qubit other than the specific qubit is a target qubit, and is output to the specific qubit 2. The quantum circuit according to claim 1, wherein entanglement between a qubit expressing the transmission word information and other qubits is eliminated. The base discriminating means outputs a plurality of control discriminating information to the specific qubit by applying a plurality of control NOT gates to the code qubit group, and a quantum circuit that applies only a plurality of control NOT gates at the time of output. A plurality of connected control NOT gate groups, each of which is a set of two or more control NOT gates, in which the target qubit of each control NOT gate is the control qubit of the control NOT gate to be applied next; It is formed so as to be decomposable only by the control NOT gate group, and the output of the base discrimination process is the input to the entanglement canceling unit with respect to some qubits of the code qubit group excluding the specific qubit. Entanglement within a pair of bases that is symmetric with respect to all qubit inversions is eliminated, and all qubit inversions are Is intended to generate a qubit group entanglement is eliminated in symmetrical within a pair of base Te,
The entanglement elimination means sets a qubit other than a qubit group in which entanglement is eliminated in a pair of bases symmetrical with respect to all qubit inversions at the start of the decoding process as a target qubit, and A control NOT gate using the qubit as the control qubit is operated to eliminate entanglement between the qubit expressing the transmission word information and a qubit other than the qubit expressing the transmission word information. The quantum circuit according to claim 1. The base discriminating means includes a first control NOT gate having a first qubit as a control qubit and a second qubit as a target qubit in a code word data of 5 qubits; The second control NOT gate with the qubit as the control qubit, the third qubit as the target qubit, the third qubit as the control qubit, and the fourth qubit as the target qubit And the fourth control NOT gate with the fourth qubit as the control qubit and the fifth qubit as the target qubit, and the fifth qubit To output the basis discrimination information as the specific qubit,
The entanglement canceling means includes two control NOT gates in which the specific qubit is a control qubit, and the first qubit and the third qubit are target qubits, respectively. The quantum circuit according to claim 3, wherein the transmission word information is output to a qubit. The base discriminating means includes a first control NOT gate having a first qubit in the code word data of 5 qubits as a control qubit and a second qubit as a target qubit; The second control NOT gate with the third qubit as the target qubit, the fifth qubit as the control qubit, and the fourth qubit as the target cubit A third control NOT gate having a bit and a fourth control NOT gate having the fourth qubit as a control qubit and the third qubit as a target qubit, Outputting the basis discrimination information as the specific qubit in a bit,
The entanglement canceling means includes two control NOT gates in which the specific qubit is a control qubit, and the first qubit and the fifth qubit are target qubits. 4. The quantum circuit according to claim 3, wherein the transmission word information is output to a qubit. Code qubit group which is a set of qubits representing code word information obtained by encoding transmission word information as a quantum state, which is an element of a two-dimensional Hilbert space expressed by a linear combination of two bases, using a stabilizer coding scheme A first code quantum state that is a quantum state in which a first basis of a two-dimensional Hilbert space representing the transmission word information is encoded, and a quantum in which a second basis of the transmission word information is encoded. Inverted by a NOT gate that inverts the first base to the second base and inverts the second base to the first base for all qubits in the first code quantum state Each of the bases included in the second code quantum state is represented by the first code quantum state. Code word information having a property of forming a pair of bases symmetrical with respect to all qubit inversions, and having a plurality of qubits representing the transmission word information and a plurality of qubits, A quantum error correction apparatus including a quantum circuit that performs a decoding process for converting to a state represented by a tensor product with a qubit represented as a base superposition state,
The quantum circuit is
A plurality of control NOT gates are applied to the code qubit group to perform a quantum operation, and whether the basis of the code qubit group is a basis included in the first code quantum state or the second quantum state A basis for determining basis discrimination information, which is information for discriminating whether a basis is included in each basis, based on the number of 1s included in each basis, and outputting to a specific qubit that is part of the code qubit group Discrimination means;
Entanglement for canceling entanglement between a qubit expressing the transmission word information and a qubit other than the qubit including the transmission word information by operating a control NOT gate using the specific qubit as a control qubit Resolving means,
A quantum error correction apparatus comprising: Code qubit group which is a set of qubits representing code word information obtained by encoding transmission word information as a quantum state, which is an element of a two-dimensional Hilbert space expressed by a linear combination of two bases, using a stabilizer coding scheme A first code quantum state that is a quantum state in which a first basis of a two-dimensional Hilbert space representing the transmission word information is encoded, and a quantum in which a second basis of the transmission word information is encoded. Inverted by a NOT gate that inverts the first base to the second base and inverts the second base to the first base for all qubits in the first code quantum state Each of the bases included in the second code quantum state is represented by the first code quantum state. Code word information having a property of forming a pair of bases symmetrical with respect to all qubit inversions, and having a plurality of qubits representing the transmission word information and a plurality of qubits, A quantum encoding method for performing a decoding process for converting to a state represented by a tensor product with a qubit expressed as a superposition state of a base,
A plurality of control NOT gates are applied to the code qubit group to perform a quantum operation, and whether the basis of the code qubit group is a basis included in the first code quantum state or the second quantum state A basis for determining basis discrimination information, which is information for discriminating whether a basis is included in each basis, based on the number of 1s included in each basis, and outputting to a specific qubit that is part of the code qubit group A determination step;
Entanglement for canceling entanglement between a qubit expressing the transmission word information and a qubit other than the qubit including the transmission word information by operating a control NOT gate using the specific qubit as a control qubit A resolution step;
A quantum error correction method comprising:

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