A fusion method for single-qubit operations

Abstract

A single quantum bit operation fusion method fuses two adjacent gate operations in any single quantum gate operation sequence, and by traversing the entire quantum gate operation sequence, the single quantum gate operation sequence of any length can be fused into a single quantum gate operation. This scheme can shorten the time span of the quantum bit operation sequence, and by fusing multiple single quantum gate operation sequences into a single quantum gate operation, it minimizes the adverse effects caused by single quantum gate operation errors and improves the accuracy of the final calculation result output.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing technology, and in particular to a fusion method for single quantum bit operations. Background Art

[0002] Quantum computing is one of the hot emerging computing technologies in the post-Moore era. Qubits are the basic unit of information processing in quantum computing. Unlike classical bits that can only be in state 0 or state 1, qubits can be in a superposition state of 0 and 1. Operating on a qubit in a superposition state is equivalent to operating on both states 0 and 1 at the same time. Relying on the above-mentioned superposition state and other quantum mechanisms, quantum computing has demonstrated computing potential beyond classical computing when dealing with certain specific problems.

[0003] At present, the research on quantum computing is still in its early stages. Due to the short decoherence time of quantum bits and the limited fidelity of quantum gate operations, it is impossible to use quantum computers to obtain calculation results that are superior to classical calculations and can solve practical problems when running deep quantum circuits. Part of the reason for this adverse effect is that the microwave sequence corresponding to the deep quantum circuit has a long time span, which leads to the degradation of quantum bits; the other part is that the fidelity of a single quantum gate operation cannot reach 100%, so the error of a single quantum gate in a serial quantum gate operation sequence will accumulate exponentially. Summary of the invention

[0004] In order to overcome the deficiencies of the above technologies, the present invention provides a fusion method of single quantum bit operations to improve the accuracy of the output of the final calculation result.

[0005] The technical solution adopted by the present invention to overcome the technical problems is:

[0006] A fusion method for single quantum bit operations comprises the following steps:

[0007] a) Traverse the entire quantum circuit and select the single-qubit gates in the quantum circuit as the fusionable parts; b) According to the ZY decomposition method, the single-qubit gates are divided into three categories: U1, U2, and U3, and the objects to be fused of two adjacent single bits in the three categories of qubit gates U1, U2, and U3 are defined as: U1U1, U1U2, U1U3, U2U1, U3U1, U2U2, U2U3, U3U2, and U3U3;

[0008] c) Process the two single-qubit gates at the front and determine the corresponding fusion object classification. If it is U1U1 or U1U2, U1U3 or U2U1 or U3U1, add the two consecutive counterclockwise rotation angles Rz around the Z axis of the Bloch sphere;

[0009] d) If the fused object classification is U2U2 or U2U3 or U3U2 or U3U3, perform ZY decomposition on it and select the RyRzRy part in the decomposed formula, where Ry is the angle of counterclockwise rotation around the Y axis of the Bloch sphere;

[0010] e) Write RyRzRy as a quaternion, multiply the quaternions corresponding to the three rotation operations of RyRzRy by quaternion multiplication, and convert the multiplication result into a rotation matrix representation;

[0011] f) comparing the rotation matrix representation with the rotation matrix representation corresponding to RzRyRz to obtain the corresponding rotation parameters of RzRyRz;

[0012] g) adding the angles corresponding to the two consecutive Rz in the formula after decomposition in step d) to convert the two consecutive single-qubit operations into a single U3 operation;

[0013] h) If the next quantum gate after fusion is still a single-bit gate operation, combine the U3 operation in step g) with the subsequent single bit and input it into step c);

[0014] i) Repeat steps c) to h) until the next two-bit gate operation is encountered.

[0015] In step a), the single-bit gates in the quantum circuit are selected based on the two-bit gates.

[0016] The beneficial effects of the present invention are: two adjacent gate operations in any single quantum gate operation sequence can be fused, and by traversing the entire quantum gate operation sequence, a single quantum gate operation sequence of any length can be fused into a single quantum gate operation. This solution can shorten the time span of the quantum bit operation sequence, and by merging multiple single quantum gate operation sequences into one single quantum gate operation, it minimizes the adverse effects caused by single quantum gate operation errors and improves the accuracy of the final calculation result output. DETAILED DESCRIPTION

[0017] The present invention is further described below.

[0018] A fusion method for single quantum bit operations comprises the following steps:

[0019] a) Traverse the entire quantum circuit and select the single-qubit gates in the quantum circuit as the fused parts. b) According to the ZY decomposition method, the single-qubit gates are divided into three categories: U1, U2, and U3. The objects to be fused of two adjacent single bits in the three types of quantum bit gates U1, U2, and U3 are defined as: U1U1, U1U2, U1U3, U2U1, U3U1, U2U2, U2U3, U3U2, and U3U3. Common single-qubit gates can be divided into three categories: U1, U2, and U3. For example, Z gates or arbitrary phase gates belong to U1 operations, which can be written as This means that the angle around the Z axis of the Bloch sphere is Ry(α) means a counterclockwise rotation of α around the Y axis of the Bloch sphere, and Rx(β) means a counterclockwise rotation of β around the X axis of the Bloch sphere. The general ZY decomposition scheme is:

[0020] U1(λ)=Rz(λ)

[0021]

[0022] This is prior art and will not be described in detail here.

[0023] c) Process the two single-qubit gates at the front and determine the corresponding classification of the fused object. If it is U1U1 or U1U2, U1U3 or U2U1 or U3U1, add the two consecutive counterclockwise rotation angles Rz around the Z axis of the Bloch sphere. For the first five objects in the nine categories, after the object is decomposed into rotation operations using ZY decomposition, since there are two consecutive Rz operations, it is only necessary to add up the angles specified in the two consecutive Rz. However, for the following four fused objects, more complex conversion rules are required. First of all, it can be seen that the difference between the U2 and U3 operations is only the Ry operation in the middle during the ZY decomposition. For U2, the Ry angle is fixed at π / 2. For the U3 operation, the angle is related to the parameters of U3 itself. Therefore, the U2 operation can be regarded as a special case of U3, and thus a unified analysis can be performed.

[0024] d) If the fused object classification is U2U2 or U2U3 or U3U2 or U3U3, perform ZY decomposition on it and select the RyRzRy part in the decomposed formula, where Ry is the angle of counterclockwise rotation around the Y axis of the Bloch sphere.

[0025] e) Write RyRzRy as a quaternion representation, use quaternion multiplication to multiply the quaternions corresponding to the three rotation operations of RyRzRy, and convert the multiplication result into a rotation matrix representation.

[0026] f) Compare the rotation matrix representation with the rotation matrix representation corresponding to RzRyRz to obtain the corresponding rotation parameters of RzRyRz.

[0027] g) Add the angles corresponding to the two consecutive Rz in the formula after decomposition in step d) to complete the conversion of two consecutive single-qubit operations into a single U3 operation.

[0028] h) If the next quantum gate after fusion is still a single-bit gate operation, combine the U3 operation in step g) with the subsequent single bit and input it into step c).

[0029] i) Repeat steps c) to h) until the next two-bit gate operation is encountered.

[0030] Two adjacent gate operations in any single quantum gate operation sequence can be fused, and by traversing the entire quantum gate operation sequence, a single quantum gate operation sequence of any length can be fused into a single quantum gate operation. This scheme can shorten the time span of the quantum bit operation sequence, and by merging multiple single quantum gate operation sequences into one single quantum gate operation, it minimizes the adverse effects caused by single quantum gate operation errors and improves the accuracy of the final calculation result output.

[0031] Furthermore, in step a), the single-bit gates in the quantum circuit are selected based on the two-bit gates. Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A fusion method for single quantum bit operations, characterized in that: The steps include: a) Traverse the entire quantum circuit and select the single-qubit gates in the quantum circuit as the fusible parts; b) According to the ZY decomposition method, the single quantum bit gates are divided into three categories: U1, U2, and U3. The objects to be fused of two adjacent single bits in the three types of quantum bit gates U1, U2, and U3 are defined as: U1U1, U1U2, U1U3, U2U1, U3U1, U2U2, U2U3, U3U2, and U3U3; c) Process the two single-qubit gates at the front and determine the corresponding fusion object classification. If it is U1U1 or U1U2, U1U3 or U2U1 or U3U1, add the two consecutive counterclockwise rotation angles Rz around the Z axis of the Bloch sphere; d) If the fused object classification is U2U2 or U2U3 or U3U2 or U3U3, perform ZY decomposition on it and select the RyRzRy part in the decomposed formula, where Ry is the angle of counterclockwise rotation around the Y axis of the Bloch sphere; e) Write RyRzRy as a quaternion, multiply the quaternions corresponding to the three rotation operations of RyRzRy by quaternion multiplication, and convert the multiplication result into a rotation matrix representation; f) comparing the rotation matrix representation with the rotation matrix representation corresponding to RzRyRz to obtain the corresponding rotation parameters of RzRyRz; g) adding the angles corresponding to the two consecutive Rz in the formula after decomposition in step d) to convert the two consecutive single-qubit operations into a single U3 operation; h) If the next quantum gate after fusion is still a single-bit gate operation, combine the U3 operation in step g) with the subsequent single bit and input it into step c); i) Repeat steps c) to h) until the next two-bit gate operation is encountered; In step a), the single-bit gates in the quantum circuit are selected based on the two-bit gates.

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