Error improvement method for programmable photon integrated loop

Abstract

The invention discloses an error improvement method for a programmable photon integrated loop, which can realize error improvement without measuring the manufacturing error of each 3dB beam splitter in the loop in advance. For a triangular loop, a variable vector is input from the left side of the loop, parameters of a basic unit are adjusted to enable an output result of a specific port on the rightmost side of the loop to be the same as an output result under an ideal condition, so that error improvement can be realized, and the whole loop does not need to add additional components; for a rectangular loop, a small number of internal power monitors need to be added in the loop, a variable vector is input from the left end and the right end of the loop, and parameters of a basic unit are adjusted, so that the output result of the specific internal power monitor in the loop is the same as the output result of an ideal condition. According to the method, the improvement effect on the loop error is remarkable, the loop fidelity after the error is improved is greatly improved compared with the loop fidelity before the error is improved and is close to 100%, and the loop fidelity is not obviously reduced along with the increase of the order of the target matrix and the error of the 3dB beam splitter.

Description

Technical Field

[0001] The present invention relates to an error compensation control method for a photonic integrated waveguide grid structure, in particular to an error improvement method for a programmable photonic integrated circuit, and is applied to the field of optical signal processing technology. Background Art

[0002] A programmable photonic integrated circuit (PPIC) is a photonic integrated waveguide grid structure formed by taking Mach-Zehnder interferometers (MZIs) with phase-shift adjustable functions on the upper and lower arms as tunable basic units (TBUs), and expanding multiple such TBUs spatially in a certain manner. Through software programming, the circuit can be reconfigured to flexibly implement various different optical signal processing functions, and has wide applications in fields such as microwave photonics, machine learning, and quantum information processing. In the field of machine learning, the PPIC can be used as a forward transmission grid to achieve any optical linear transformation. However, during the process of the PPIC implementing optical linear calculations, errors in any phase shifter and 3dB beam splitter will cause deviations in the overall circuit calculations. When the scale of the photonic integrated circuit increases, the errors of the components will continuously accumulate, resulting in large errors. Among them, the manufacturing error of the 3dB beam splitter has a particularly obvious impact compared with the error of the phase shifter. Therefore, improving and compensating for the manufacturing error of the 3dB beam splitter is crucial for large-scale PPICs.

[0003] In the related research of PPIC, researchers generally adopt an asymmetric Mach-Zehnder interferometer structure circuit (ASMZIC). Its basic unit is usually an asymmetric Mach-Zehnder interferometer (ASMZI) composed of two 3dB beam splitters and two phase shifters. One phase shifter is located on one arm of the interferometer and is called an internal phase shifter; the other phase shifter is located outside the two arms of the interferometer and is called an external phase shifter. In 2021, the Bell team proposed a symmetric Mach-Zehnder interferometer structure circuit (SMZIC) by moving the external phase shifter into another interferometer arm to form a symmetric Mach-Zehnder interferometer (SMZI), and pointed out that this circuit structure greatly reduces the optical depth of the circuit and reduces the propagation loss compared with the ASMZIC structure. However, there is currently no relevant report on the research related to the manufacturing error of its 3dB beam splitter.

[0004] The prior art [1] (see Optica, 2015, 2(8): 747-750) constructed a dual Mach-Zehnder interferometer structure (DMZI) by adding another ASMZI to each basic unit structure ASMZI. On this basis, a PPIC was constructed with the DMZI as the TBU and a corresponding configuration method was proposed, which can improve the beam splitter manufacturing error in the range of splitting ratios from 85:15 to 15:85. Although this method has an obvious improvement effect on the beam splitter manufacturing error, the use of the DMZI increases the optical path and insertion loss of the loop.

[0005] The prior art [2] (see Optics Letters, 2020, 45(9): 2632-2635) proposed a new PPIC structure using a single tunable beam splitter and a single phase shifter as the TBU and designed a corresponding matrix implementation method. This new PPIC structure has good fault tolerance for the manufacturing error of the beam splitter. When the splitting ratio of the beam splitter changes in the range of 52:48 to 32:68 due to the manufacturing error, the accuracy of matrix calculation of this loop will not decrease significantly. However, this loop cannot achieve the decomposition of any matrix, thus limiting its practical application.

[0006] The prior art [3] (see Optica, 2021, 8(10): 1247-1255) proposed a local optimization method for improving the 3dB beam splitter error for ASMZIC, that is, correcting the manufacturing error of the 3dB beam splitter in each basic unit of the loop. The idea of this method is to split the transmission matrix of ASMZI with 3dB beam splitter error into the form of multiplying the transmission matrix of ASMZI in the ideal case by two phase shifter matrices. Structurally, this transformation is equivalent to adding a phase shifter before and after the original ASMZI. Although this method realizes the improvement of the 3dB beam splitter error, this method requires measuring the manufacturing error of each 3dB beam splitter in the loop in advance, which leads to a large number of internal power monitors in the loop, making the overall loop more complex and not conducive to the expansion of the loop scale.

[0007] The prior art [4] (see Photonics Research, 2013, 1(1): 1-15) proposed an algorithm for improving a 3dB beam splitter in a loop without measuring its manufacturing error. The basic idea is to add a power monitor at the lower output port or the upper input port of each ASMZI in the loop. In the actual process, by monitoring the output power of each ASMZI in real time, the parameters of the ASMZI are adjusted in turn to make the output result of the right port of the ASMZI close to the output result under ideal conditions, so as to improve the manufacturing error of the 3dB beam splitter of the ASMZI. Since this method requires adding the same number of internal power monitors as the number of ASMZIs in the loop, the overall loop is still relatively complex, which is not conducive to the expansion of the loop scale.

[0008] In summary, in the research on improving the manufacturing error of the 3dB beam splitter of PPIC, there are still various problems or deficiencies at present. In addition, the current research on improving the manufacturing error of the 3dB beam splitter is all carried out for ASMZIC, and there is no relevant report on the research of SMZIC. Summary of the Invention

[0009] In order to solve the problems of the prior art, the present invention provides an error improvement method for a programmable photonic integrated circuit, and provides an error compensation method for SMZIC that does not require measuring the manufacturing error of each 3dB beam splitter in the loop in advance, so as to improve the fidelity of the loop; and the programmable photonic integrated circuit structure of the present invention does not need to add too many other components, the loop structure is simple, the error improvement effect is remarkable, and the application range is wide.

[0010] In order to achieve the above object of the invention, the inventive concept of the present invention is as follows:

[0011] Considering from the perspective of the construction of SMZIC, when there is a 3dB beam splitter error, in the process of constructing the structure by sequentially setting the target matrix elements to zero, by inputting a specific vector to the left side of the loop and adjusting the phase shift parameters of the corresponding components, the output result on the right side of the loop is made the same as the output result under ideal conditions, so as to realize the improvement and compensation of the 3dB beam splitter error of SMZIC.

[0012] According to the above inventive concept, the present invention adopts the following technical solutions:

[0013] An error improvement method for a programmable photonic integrated circuit, starting from the perspective of constructing a symmetric Mach-Zehnder interferometer structure loop SMZIC, sets an auxiliary matrix as the target matrix; successively zeros each element in the upper triangular and lower triangular parts of the target matrix to improve the manufacturing error of the 3dB beam splitter, and successively zeros the elements of the target matrix for structure construction; during the process of zeroing the elements of the target matrix for structure construction, specifically when zeroing an element, first calculates the relevant component parameters required for loop construction under ideal conditions and updates the matrix; then inputs the corresponding column vector on the left or right side of the loop and adjusts the parameters of the phase shifter and basic unit to make the output result of a specific port of the loop the same as the output result under ideal conditions; then repeats the process of zeroing the elements of the target matrix for structure construction until each element of the auxiliary matrix is also zeroed to obtain a diagonal matrix, and makes the phases of the matrix elements of the diagonal matrix equal, so as to achieve improvement compensation for the 3dB beam splitter error of the SMZIC.

[0014] Preferably, for the triangular symmetric Mach-Zehnder interferometer structure loop SMZIC, the specific steps of the error improvement method are as follows:

[0015] (1.1) Set the auxiliary matrix V = U * , where U is the target matrix, * represents the complex conjugate transpose of the matrix, and W -1 = E. Set the phase shift of the phase shifter in the loop to 0, and set each basic unit M j,k to the cross state; among them, each basic unit M j,k is numbered according to its position on the diagonal in the structure and its arrangement order along the diagonal. j = 1, 2,..., N - 1 is the diagonal number, numbered from left to right; k = 1, 2,..., j is the arrangement order of the basic units along the diagonal direction; N is the order of the target matrix.

[0016] (1.2) Judge whether the element to be zeroed is the first element on the diagonal:

[0017] If it is the first element, calculate the phase shift of the phase shifter P j required for loop construction under ideal conditions and the parameters of the basic unit M j,k , and update the matrix Input the column vector on the left side of the loop, that is, the (j - k + 1)-th column of the W -1 matrix, and adjust the phase shift of P j ' and the parameters of M' j,k to make the output result of a specific port on the right side of the loop the same as the output result under ideal conditions;

[0018] (1.3) Judge whether the element to be zeroed is the first element on the diagonal:

[0019] If it is not the first element, calculate the basic unit M required for loop construction under ideal conditions j,k parameters, and update the matrix Introduce an external phase shifter P′ j,k , and input the column vector i.e., W -1 the (j - k + 1)-th column of the matrix, and adjust the phase shift of P′ j,k and the parameters of M′ j,k to make the output result of a specific port on the right side of the loop the same as the output result under ideal conditions;

[0020] (1.4) Repeat steps (1.2) and (1.3) successively until all the lower triangular elements of the auxiliary matrix V are set to zero, then each element of the upper triangular part of the auxiliary matrix V is also set to zero, obtaining the diagonal matrix D;

[0021] (1.5) Right multiply the auxiliary matrix V by the phase shifter matrix Q j to make the phases of the matrix elements of the diagonal matrix D equal, thus completing the construction of SMZIC and realizing the improvement of the manufacturing error of the 3dB beam splitter in the symmetric Mach-Zehnder interferometer structure loop SMZIC;

[0022] (1.6) Utilize the phase shifter position transformation characteristic to merge the added external phase shifter with the existing phase shifters to realize the simplification of the final structure.

[0023] Preferably, for the rectangular symmetric Mach-Zehnder interferometer structure loop SMZIC, the specific steps of the error improvement method are as follows:

[0024] (2.1) Set the auxiliary matrix V = U * , where U is the target matrix, * represents the complex conjugate transpose of the matrix, W -1 = E, Z -1 = E, set the phase shift of the phase shifters in the loop to 0, and set each basic unit M j,k to the cross state; among them, each basic unit M j,k is numbered according to its position on the diagonal in the structure and its arrangement order along the diagonal. j = 1, 2,..., N - 1 is the diagonal number, and the diagonals are numbered alternately from the left and right sides of the loop; k = 1, 2,..., j is the arrangement order of the basic units along the diagonal, and the arrangement orders of the basic units on the diagonals numbered from the left and right sides are opposite; N is the order of the target matrix;

[0025] (2.2) Determine whether the element to be set to zero is the first element on the diagonal:

[0026] If it is the first element, calculate the phase shifter P required for loop construction under ideal conditions jPhase shift and basic unit M j,k parameters;

[0027] When j is odd, update matrix Input the column vector on the left side of the loop That is, W -1 The (j - k + 1)-th column of the matrix, adjust P′ j phase shift and M′ j,k parameters to make the output result of a specific detector in the loop the same as the output result in the ideal case;

[0028] When j is even, update matrix Input the column vector on the right side of the loop That is, Z -1 The (N - j + k)-th column of the matrix, adjust P′ j phase shift and M′ j,k parameters to make the output result of a specific detector in the loop the same as the output result in the ideal case;

[0029] (2.3) Determine whether the element to be set to zero is the first element on the skew diagonal:

[0030] If it is not the first element, calculate the parameters of the basic unit M required for loop construction in the ideal case j,k parameters;

[0031] When j is odd, update matrix Introduce an external phase shifter P′ j,k , input the column vector on the left side of the loop That is, W -1 The (j - k + 1)-th column of the matrix, adjust P′ j,k phase shift and M′ j,k parameters to make the output result of a specific detector in the loop the same as the output result in the ideal case;

[0032] When j is even, update matrix Input the column vector on the right side of the loop That is, Z -1 The (N - j + k)-th column of the matrix, adjust P′ j,k phase shift and M′ j,k parameters to make the output result of a specific detector in the loop the same as the output result in the ideal case;

[0033] (2.4) Repeat steps (2.2) and (2.3) in sequence until all the lower triangular elements of the auxiliary matrix V are set to zero, then each element in the upper triangular of the auxiliary matrix V is also set to zero, obtaining the diagonal matrix D;

[0034] (2.5) Right multiply the auxiliary matrix V by the phase shifter matrix Q j, equalize the phases of the matrix elements of the diagonal matrix D, thereby completing the construction of the SMZIC and realizing the improvement of the manufacturing error of the 3dB beam splitter in the symmetric Mach-Zehnder interferometer structure loop SMZIC;

[0035] (2.6) Utilize the phase shifter position transformation characteristic to merge the added external phase shifter and the existing phase shifters, realizing the simplification of the final structure.

[0036] Preferably, use the error improvement method of the programmable photonic integrated circuit of the present invention to analyze the change of the loop fidelity before and after the error improvement with respect to the target matrix order, and determine whether the improvement of the fidelity reaches the required level.

[0037] Compared with the prior art, the present invention has the following obvious outstanding substantive features and remarkable advantages:

[0038] 1. The method of the present invention does not require adding an additional 1:1 tunable basic unit (TBU) in the loop, does not require measuring the manufacturing error of each 3dB beam splitter in the loop in advance, does not require adding a large number of internal power monitors equal to the number of TBUs in the loop, and is applicable to any matrix. Therefore, it has outstanding features such as simple structure, small insertion loss, excellent performance, and wide application range;

[0039] 2. Most importantly, the existing prior art all targets the traditional ASMZI structure loop, while the method of the present invention is for the 3dB error improvement of the current novel SMZI structure loop, and there are fundamental differences in structure; the structure of the present invention is a photonic integrated waveguide grid structure composed of a symmetric Mach-Zehnder interferometer (SMZI) with a phase shift adjustable function in the upper and lower arms as a tunable basic unit (TBU), and multiple such tunable basic units are spatially expanded in a certain manner; the method of the present invention has a significant improvement effect on the loop error, and the loop fidelity after the error improvement has a large increase compared with that before the improvement, approaching 100%, and does not show an obvious decrease with the increase of the target matrix order and the 3dB beam splitter error. Description of the Drawings

[0040] Figure 1 This is the entire process of the 3dB beam splitter error improvement compensation of the SMZIC of the present invention.

[0041] Figure 2 It includes Figures (a - e). Among them, Figures (a - d) are the flowcharts for successively improving the 3dB beam splitter error of the 4th-order triangular SMZIC using the method of the present invention; Figure (e) is the final triangular SMZIC structure after the error improvement and the phase shifter merger.

[0042] Figure 3Including FIGS. (a - e). Among them, FIGS. (a - d) are flowcharts for successively improving the 3dB beam splitter error of a 4 - order rectangular SMZIC using the method of the present invention; FIG. (e) is the final rectangular SMZIC structure after the error improvement and the phase shifter combination.

[0043] Figure 4 It is the comparison of the fidelity before and after the improvement of the 3dB beam splitter error compensation of the triangular SMZIC when the 3dB beam splitter errors are different.

[0044] Figure 5 It is the comparison of the fidelity before and after the improvement of the 3dB beam splitter error compensation of the rectangular SMZIC when the 3dB beam splitter errors are different. Detailed implementation manners

[0045] A method for improving the error of a programmable photonic integrated circuit according to the present invention starts from the perspective of constructing a symmetric Mach - Zehnder interferometer structure loop SMZIC, sets an auxiliary matrix as the target matrix; successively zeros each element of the upper triangle and the lower triangle of the target matrix to improve the 3dB beam splitter manufacturing error, and successively zeros the target matrix elements for structure construction; during the process of zeroing the target matrix elements for structure construction, specifically when zeroing an element, first calculate the relevant component parameters required for loop construction under ideal conditions and update the matrix; then input the corresponding column vector on the left or right side of the loop, and adjust the parameters of the phase shifter and the basic unit to make the output result of a specific port of the loop the same as the output result under ideal conditions; then repeat the process of zeroing the target matrix elements for structure construction until each element of the auxiliary matrix is also zeroed to obtain a diagonal matrix, and make the phases of the matrix elements of the diagonal matrix equal, so as to achieve the improvement and compensation of the 3dB beam splitter error of the SMZIC.

[0046] In the ideal case, each basic unit in the SMZIC is represented by M j,k The corresponding parameters are Σ j,k and Δ j,k where Σ j,k is the average value of the sum of the phase shifts of the upper and lower internal phase shifters on M j,k and Δ j,k is the average value of the difference in the phase shifts of the upper and lower internal phase shifters on M j,k The phase shifters are represented by P j and Q j The corresponding phase shifts are ξ j and ζ j .

[0047] When there is a 3dB beam splitter error, the basic unit structure in the loop is represented by M' j,k The corresponding parameters are Σ' j,k and Δ' j,k where Σ'j,k is M' j,k The average value of the phase shifts of the upper and lower internal phase shifters, Δ' j,k is M' j,k The average value of the difference in phase shifts between the upper and lower internal phase shifters; the phase shifters in the loop are represented by P j ' and Q' j and the corresponding phase shifts are ξ' j and ζ j '. α j,k and β j,k respectively represent the manufacturing errors of the front and rear 3dB beam splitters in the basic unit structure M' j,k in the middle.

[0048] 1. Implementation of the error improvement method for triangular SMZIC

[0049] Figure 1 This is the entire process for implementing the error improvement compensation of the 3dB beam splitter of SMZIC. According to this process, the error improvement method of the 3dB beam splitter will be described below with a 4-order triangular SMZIC as an example.

[0050] Assume that the target matrix U is a random complex unitary matrix, set the auxiliary matrix V = U*, * represents the complex conjugate transpose of the matrix, W -1 = E, set the phase shifts of the phase shifters in the actual loop to 0, and set the basic unit structure M j,k to the cross state. Among them, each basic unit M j,k is numbered according to its position on the diagonal in the structure and its arrangement order along this diagonal. j = 1, 2,..., N - 1 is the diagonal number, numbered from left to right; k = 1, 2,..., j is the arrangement order of the basic units along the diagonal direction; N is the order of the target matrix.

[0051] When setting the first target matrix element to zero, j = 1, k = 1, calculate the phase shift of the phase shifter P1 in the ideal case and the parameters Σ 1,1 and Δ 1,1 of the basic unit structure M 1,1 , and update the matrix W -1 to be

[0052]

[0053] At this time, j - k + 1 = 1, the column vector (T represents the transpose of the matrix).

[0054] Input on the left side of the loop in the ideal case Calculate the output of the light passing through the phase shifter P1 and the basic unit structure M 1,1 to be

[0055]

[0056] It can be seen that the output at the output port shown by the dotted line on the far right of the loop is 0, as Figure 2 (a) shows.

[0057] When there is a 3dB beam splitter error, the input column vector on the left side of the loop is The output of the light passing through the phase shifter P1' and the basic unit structure M' 1,1 is

[0058]

[0059] It can be seen that the lower output port i+1 of the basic unit structure M' 1,1 has an output of

[0060]

[0061] When Σ' 1,1 = Σ 1,1 , Equation (4) can be simplified to

[0062]

[0063] If the parameter Δ' 1,1 satisfies the relationship

[0064] [cos(α 1,1 + β 1,1 )cosΔ' 1,1 ) 2 + [sin(α 1,1 - β 1,1 )sinΔ' 1,1 ) 2 = cos 2 Δ 1,1 (6)

[0065] Then the following equation

[0066] [cos(α 1,1 - β 1,1 )sinΔ' 1,1 ) 2 + [sin(α 1,1 + β 1,1 )cosΔ' 1,1 ) 2 = sin 2 Δ 1,1 (7)

[0067] holds. At this time, Equation (5) can be simplified to

[0068]

[0069] where μ1,1 and ν 1,1 are the phase shifts of the complex numbers within the square brackets in the two terms on the right side of Equation (5), respectively, and are

[0070]

[0071] When Equation (6) satisfies the condition:

[0072]

[0073] the parameter Δ′ can be solved and obtained 1,1 The value is specifically:

[0074]

[0075] When the parameter ξ′1 = ξ1 - v 1,1 + μ 1,1 in Equation (8), Equation (8) is 0, that is, the output at the output port shown by the dashed line on the rightmost side of the loop is 0, which is consistent with the result of the ideal situation. Therefore, by inputting a column vector at the left port of the loop it is not necessary to measure the 3dB beam splitter error of the basic unit structure M′ in advance 1,1 Just observe the output result of the output port shown by the dashed line on the rightmost side of the loop, and by adjusting the phase shift ξ′1 of the phase shifter P1′ and the parameter Δ′ 1,1 of the basic unit structure M′ 1,1 to make the output of this specific output port 0, the improvement of the 3dB beam splitter error of this basic unit structure can be achieved.

[0076] When j = 2 and k = 1, it is similar to the case when j = 1 and k = 1 above. By inputting a column vector at the left port of the loop Just observe Figure 2 the output result of the output port shown by the dashed line on the rightmost side of the loop in (b), and by adjusting the phase shift ξ′2 of the phase shifter P2′ and the parameter Δ′ 2,1 of the basic unit structure M′ 2,1 to make the output of this specific output port 0, the improvement of the 3dB beam splitter error of this basic unit structure can be achieved. When j = 2 and k = 2, through a derivation similar to Equations (1)-(7), the output of the lower output port i + 1 of the basic unit structure M′ 2,2 can be calculated as

[0077]

[0078] From Equation (9), it can be seen that μ 2,2 and ν 2,2 are not equal. In order to make the output of the lower output port i + 1 of M′ 2,2 be 0, an external phase shifter P′ is introduced at the lower input port of this basic unit2,2 , whose phase shift ξ′ 2,2 = μ 2,2 - v 2,2 , so that the value of equation (12) becomes 0. Therefore, input a column vector at the left port of the loop Only need to observe Figure 2 the output results of the two output ports shown by the dotted line at the rightmost of the loop in (c). By adjusting the phase shift ξ′ of the newly added phase shifter P′ 2,2 and the parameter Δ′ of the basic unit structure M′ 2,2 to make the output of this specific output port be 0, the 3dB beam splitter error of this basic unit structure can be improved. And so on, the 3dB beam splitter errors of multiple basic unit structures on the subsequent skew diagonals can be improved. 2,2 2,2

[0079] When each element in the lower triangle of the target matrix V has been set to zero, due to the properties of the unitary matrix, each element in the upper triangle of the matrix V is also set to zero, and the matrix V becomes a diagonal matrix D, where the diagonal elements are complex numbers with unit norm, as shown in the following equation

[0080] VP1′M′ 1,1 P′2M′ 2,1 P′ 2,2 M′ 2,2 P3′M′ 3,1 P′ 3,2 M′ 3,2 … = D (13)

[0081] Finally, right multiply it by the phase shifter matrix Q′ j , j = 2, …, N, and the corresponding phase shift value ζ′ j satisfies

[0082] ζ′ j = arg(V 1,1 ) - arg(V j,j ) (14)

[0083] so that the phases of the diagonal elements in the diagonal matrix D are equal, and the diagonal matrix D′ is obtained. At this time, the matrix V is expanded to

[0084] VP1′M′ 1,1 P2′M′ 2,1 P′ 2,2 M′ 2,2 P3′M′ 3,1 P′ 3,2 M′ 3,2 …Q′2…Q′ N = D′ (15)

[0085] ​​Since the complex conjugate transpose of a unitary matrix is its inverse, the target matrix U can be expressed as

[0086] U = (D′) -1 Q′ N …Q′2…M′ 3,2 P′ 3,2 M′ 3,1 P3′M′ 2,2 P′ 2,2 M′ 2,1 P′2M′ 1,1 P1′ (16)

[0087] At this time, the SMZIC is constructed, and its structure is as Figure 2 (d) shown.

[0088] Utilizing the phase shifter position transformation characteristic, the combination of the added external phase shifters and the existing phase shifters can be achieved, and the final structure is as Figure 2 (e) shown. Compared with the ideal triangular SMZIC structure, this structure realizes the improved compensation of the 3dB beam splitter error of the triangular SMZIC without adding components, without changing the original optical loop depth, and without the need to measure in advance the manufacturing errors of each 3dB beam splitter in the loop.

[0089] 2. Implementation of the error improvement method for rectangular SMZIC

[0090] For each basic unit M of the rectangular SMZIC j,k It is still numbered according to its position on the diagonal in the structure and its arrangement order along the diagonal. j = 1, 2, …, N - 1 is the diagonal number; k = 1, 2, …, j is the arrangement order of the basic units along the diagonal; N is the order of the target matrix. Different from the triangular SMZIC, the rectangular SMZIC numbers the diagonals alternately from the left and right sides of the loop, and the arrangement order of the basic units on the diagonals numbered in the left and right directions is opposite.

[0091] For the rectangular SMZIC, a power detector D needs to be added to the right side of each phase shifter Q j , where j = 1, 2, …, N - 1. When there is a 3dB beam splitter error, during the process of successively setting the target matrix elements to zero, according to the parity of j, by inputting a specific column vector to the left or right side of the loop, the corresponding component phase shift parameters are adjusted so that the result output by the specific detector in the loop is the same as the output result in the ideal case, thereby realizing the improved compensation of the 3dB beam splitter error of the rectangular SMZIC. j

[0092] According to Figure 1 ​The entire process of improving and compensating the 3dB beam splitter error of the shown SMZIC is described below. Taking the 4th-order rectangular SMZIC as an example, the method for improving the 3dB beam splitter error is explained as follows.

[0093] Assume that the target matrix U is a random complex unitary matrix. Set the auxiliary matrix V = U* (where * represents the complex conjugate transpose of the matrix), and W -1 = E, and Z -1 = E. Set the phase shift of the phase shifter in the actual loop to 0, and the basic unit structure M j,k is set to the cross state.

[0094] When j is odd, the process of improving the 3dB beam splitter error is similar to that of improving the 3dB beam splitter error of the triangular SMZIC, which will not be elaborated here. When j is even and k = 1, calculate the phase shift of the phase shifter P j in the ideal case and the parameters Σ j,k and Δ j,k of the basic unit structure M j,k , and update the matrix

[0095] When the column vector (i.e., the (N - j + k)-th column of the Z -1 matrix) is input on the right side of the loop in the ideal case, the output of the upper output port of the basic unit structure M j,k is 0 at this time. Therefore, the output of the detector connected to the upper output port of this basic unit structure M j,k in the loop is still 0. When j = 2 and k = 1, this detector is represented by D1, as shown in Figure 3 (b).

[0096] When there is a 3dB beam splitter error, since the column vector is input from the right side of the loop, the transfer matrix of the basic unit structure M' j,k becomes

[0097]

[0098] It can be seen that the output of the upper output port i of the basic unit structure M' j,k is

[0099]

[0100] Through a derivation similar to that of equations (4)-(11), it can always be found that a set of values of ξ' j and Δ' j,k make equation (18) equal to 0, that is, the output of the upper output port i of M' j,k is 0, which is consistent with the result in the ideal case. Therefore, input a column vector at the right-side port of the loop No need to measure the basic unit structure M' in advance j,k To reduce the 3dB beam splitter error, we only need to observe the output of a specific detector in the loop and adjust the phase shifter P′ j Phase shift ξ′ j and the basic unit structure M′ j,k The parameter Δ′ j,k By making the output of the detector 0, the 3dB beam splitter error of the basic unit structure can be improved.

[0101] When j is an even number and k≠1, similar to the case of triangular SMZIC, it is necessary to j,k An external P′ is introduced at the lower input port of j,k The specific process will not be described in detail. When each element of the lower triangle of the target matrix V is set to zero, the phase shifter matrix Q′ is right-multiplied to it. j , j=1,…,N-1, see equations (14)-(16) in the previous section for details.

[0102] At this point, the rectangular SMZIC is completed, and its structure is as follows Figure 3 (d) As shown. The added external phase shifter is combined with the existing phase shifter, and the final structure is as follows Figure 3 Compared to the ideal rectangular SMZIC structure, this structure requires the addition of N-1 (N is the target matrix order) detectors to the original loop. This improves the compensation for the 3dB beam splitter error of the rectangular SMZIC without having to measure the manufacturing error of each 3dB beam splitter in the loop in advance.

[0103] The above solution is further described below with reference to specific implementation examples. The preferred embodiments of the present invention are described in detail as follows:

[0104] Embodiment 1:

[0105] In this embodiment, a preferred embodiment of the error improvement method for a SMZI structure programmable photonic integrated circuit is described in detail with reference to the accompanying drawings as follows: A triangular SMZIC is used as the target to improve the 3dB beam splitter error. The target matrix consists of 100 randomly generated complex unitary matrices, and the fidelity is calculated by taking the average of the fidelity of these 100 complex unitary matrices. For ease of analysis, it is assumed that in each basic unit structure: the manufacturing error of the previous 3dB beam splitter is equal, and α is used as the error. s Indicates that the manufacturing error of the latter 3dB beam splitter is equal to β s express.

[0106] When the 3dB beam splitter error of the SMZI in the loop is unknown, Figure 4 Given that α s =0.01,β s= 0.005; α s = 0.01, β s = 0.02 and α s = β s = 0.02, the variation of the loop fidelity with the target matrix order before and after improving the error using this error improvement method. From Figure 4 it can be seen that before the error improvement, when given α s and β s values, the loop fidelity decreases as the target matrix order increases; when the values of α s and β s increase, the loop fidelity decreases faster as the target matrix order increases. This error improvement method has a significant improvement effect on the 3dB beam splitter error of the triangular SMZIC. The loop fidelity after improving the error is greatly improved compared with that before the improvement, approaching 100%, and does not decrease significantly with the increase of the target matrix order and the values of α s and β s values.

[0107] Example Two:

[0108] This example is basically the same as Example One, with the special feature being:

[0109] In this example, a preferred embodiment of the error improvement method for the programmable photonic integrated circuit with an SMZI structure is described in detail with reference to the accompanying drawings: Taking the rectangular SMZIC as the object for improving the 3dB beam splitter error, the target matrix consists of 100 randomly generated complex unitary matrices, and the fidelity is calculated by taking the average of the fidelities of these 100 complex unitary matrices. For ease of analysis, it is assumed that in each basic unit structure: the manufacturing errors of the previous 3dB beam splitter are equal, represented by α s ; the manufacturing errors of the latter 3dB beam splitter are equal, represented by β s .

[0110] In the case where the 3dB beam splitter error of the SMZI in the loop is unknown, Figure 5 it is given that when α s = 0.01, β s = 0.005; α s = 0.01, β s = 0.02 and α s = β s = 0.02, the variation of the loop fidelity with the target matrix order before and after improving the error using this error improvement method. From Figure 5It can be seen that, similar to the conclusion of the triangular SMZIC, the above error improvement method also has a significant improvement effect on the 3dB beam splitter error of the rectangular SMZIC. The loop fidelity after error improvement has a substantial increase compared to that before improvement, approaching 100%, and does not show an obvious decrease with the increase of the target matrix order and the values of α s and β s .

[0111] The error improvement method for the programmable photonic integrated circuit in the above embodiments of the present invention. The programmable photonic integrated circuit structure is a photonic integrated waveguide grid structure formed by symmetric Mach-Zehnder interferometers (SMZIs) with phase-shift adjustable functions on the upper and lower arms as tunable basic units (TBUs), and multiple such tunable basic units are spatially expanded in a certain way. An error improvement method that does not require pre-measuring the manufacturing error of each 3dB beam splitter in the loop is proposed for this structure. For a triangular loop, by inputting a varying vector from the left side of the loop and adjusting the parameters of the basic unit to make the output result of a specific port on the rightmost side of the loop the same as the output result in the ideal case, the error improvement can be achieved without adding additional components to the entire loop; for a rectangular loop, a few internal power monitors need to be added to the loop. By inputting a varying vector from both the left and right ends of the loop and adjusting the parameters of the basic unit to make the output result of a specific internal power monitor in the loop the same as the output result in the ideal case. The method of the present invention has a significant improvement effect on the loop error. The loop fidelity after error improvement has a substantial increase compared to that before improvement, approaching 100%, and does not show an obvious decrease with the increase of the target matrix order and the 3dB beam splitter error.

[0112] The above has described the embodiments of the present invention in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments and can be varied in many ways according to the purpose of the invention of the present invention. Any changes, modifications, substitutions, combinations, or simplifications made based on the spirit and principle of the technical solution of the present invention shall be equivalent replacement methods. As long as they meet the invention purpose of the present invention and do not deviate from the technical principle and inventive concept of the present invention, they all fall within the protection scope of the present invention.

Claims

1. An error improvement method for a programmable photonic integrated circuit, characterized in that, From the perspective of constructing the symmetric Mach-Zehnder interferometer structure loop SMZIC, set the auxiliary matrix as the target matrix; improve the manufacturing error of the 3dB beam splitter by setting each element of the upper triangle and lower triangle of the target matrix to zero in turn, and construct the structure by setting the elements of the target matrix to zero in turn; during the process of constructing the structure by setting the elements of the target matrix to zero, specifically when setting the elements to zero, first calculate the relevant component parameters required for loop construction under ideal conditions and update the matrix; then input the corresponding column vector on the left or right side of the loop, and adjust the parameters of the phase shifter and basic unit to make the output result of a specific port of the loop the same as the output result under ideal conditions; then repeat the process of constructing the structure by setting the elements of the target matrix to zero until each element of the auxiliary matrix is also set to zero, obtaining a diagonal matrix, and making the phases of the matrix elements of the diagonal matrix equal, so as to realize the improvement and compensation of the 3dB beam splitter error of SMZIC.

2. The error improvement method of the programmable photonic integrated circuit according to claim 1, characterized in that, For the triangular symmetric Mach-Zehnder interferometer structure loop SMZIC, the specific steps of the error improvement method are as follows: (1.1) Set the auxiliary matrix V = U * , where U is the target matrix, * represents the complex conjugate transpose of the matrix, and W -1 = E. Set the phase shift of the phase shifter in the loop to 0, and set each basic unit M j,k to the cross state; among them, each basic unit M j,k is numbered according to its position on the skew diagonal in the structure and its arrangement order along the diagonal direction. j = 1, 2, …, N - 1 is the skew diagonal number, numbered from left to right; k = 1, 2, …, j is the arrangement order of the basic units along the skew diagonal direction; N is the order of the target matrix; (1.2) Judge whether the element to be set to zero is the first element on the skew diagonal: If it is the first element, calculate the phase shift of the phase shifter P required for loop construction under ideal conditions and the parameters of the basic unit M j and update the matrix j,k Input the column vector on the left side of the loop i.e., the (j - k + 1)-th column of the W -1 matrix, and adjust the phase shift of P j ′ and the parameters of M′ j,k to make the output result of a specific port on the right side of the loop the same as the output result under ideal conditions; (1.3) Judge whether the element to be set to zero is the first element on the skew diagonal: If it is not the first element, calculate the parameters of the basic unit M required for loop construction under ideal conditions and update the matrix j,k and update the matrix Introduce an external phase shifter P′ j,k and input the column vector i.e., W -1 the (j - k + 1)-th column of the matrix on the left side of the loop, and adjust the phase shift of P′ j,k and the parameters of M′ j,k to make the output result of a specific port on the right side of the loop the same as the output result under ideal conditions; (1.4) Repeat steps (1.2) and (1.3) in turn until all the lower triangular elements of the auxiliary matrix V are set to zero, then each element of the upper triangular part of the auxiliary matrix V is also set to zero, obtaining a diagonal matrix D; (1.5) Right-multiply the auxiliary matrix V by the phase shifter matrix Q j , so that the phases of the matrix elements of the diagonal matrix D are equal, thereby completing the construction of the SMZIC and realizing the improvement of the manufacturing error of the 3dB beam splitter in the symmetric Mach-Zehnder interferometer structure loop SMZIC; (1.6) Utilize the position transformation characteristic of the phase shifter to merge the added external phase shifter and the existing phase shifters to realize the simplification of the final structure.

3. The error improvement method for the programmable photonic integrated circuit according to claim 1, characterized in that For the rectangular symmetric Mach-Zehnder interferometer structure loop SMZIC, the specific steps of the error improvement method are as follows: (2.1) Set the auxiliary matrix V = U * , where U is the target matrix, * represents the complex conjugate transpose of the matrix, and W -1 = E, Z -1 = E. Set the phase shift of the phase shifter in the loop to 0, and set each basic unit M j,k to the cross state; among them, each basic unit M j,k is numbered according to its position on the diagonal in the structure and its arrangement order along the diagonal direction. j = 1, 2, …, N - 1 is the diagonal number, and the diagonals are numbered alternately from the left and right sides of the loop; k = 1, 2, …, j is the arrangement order of the basic units along the diagonal direction, and the arrangement orders of the basic units on the diagonals numbered from the left and right sides are opposite; N is the order of the target matrix. (2.2) Judge whether the element to be set to zero is the first element on the skew diagonal: If it is the first element, calculate the phase shift of the phase shifter P required for loop construction under ideal conditions and the parameters of the basic unit M j ; j,k ​ When j is odd, update the matrix Input the column vector on the left side of the loop That is, W -1 The (j - k + 1)-th column of the matrix, adjust the phase shift of P′ j and the parameters of M′ j,k to make the output result of a specific detector in the loop the same as the output result in the ideal case; When j is even, update the matrix Input the column vector on the right side of the loop That is, Z -1 The (N - j + k)-th column of the matrix, adjust P j The phase shift of' and M j ' ,k The parameters of, so that the output result of a specific detector in the loop is the same as the output result in the ideal case; (2.3) Judge whether the element to be set to zero is the first element on the skew diagonal: If it is not the first element, calculate the parameters of the basic unit M required for loop construction under ideal conditions j,k ; When j is odd, update the matrix Introduce an external phase shifter P′ j,k , input a column vector on the left side of the loop That is, W -1 The (j - k + 1)-th column of the matrix, adjust the phase shift of P′ j,k and the parameters of M′ j,k to make the output result of a specific detector in the loop the same as the output result in the ideal case; When j is even, update the matrix Input the column vector on the right side of the loop That is, Z -1 The (N - j + k)-th column of the matrix, adjust P′ j,k The phase shift of and M′ j,k The parameters of, so that the output result of a specific detector in the loop is the same as the output result in the ideal case; (2.4) Repeat steps (2.2) and (2.3) in turn until all the lower triangular elements of the auxiliary matrix V are set to zero, then each element of the upper triangular part of the auxiliary matrix V is also set to zero, obtaining a diagonal matrix D; (2.5) Right-multiply the auxiliary matrix V by the phase shifter matrix Q j , so that the phases of the matrix elements of the diagonal matrix D are equal, thus completing the construction of the SMZIC and realizing the improvement of the manufacturing error of the 3dB beam splitter in the symmetric Mach-Zehnder interferometer structure loop SMZIC; (2.6) Utilize the position transformation characteristic of the phase shifter to merge the added external phase shifter and the existing phase shifters to realize the simplification of the final structure.

4. The error improvement method of the programmable photonic integrated circuit according to claim 2 or 3, characterized in that, Analyze the change of the loop fidelity with the order of the target matrix before and after improving the error using the error improvement method of the programmable photonic integrated circuit, and judge whether the improvement of the fidelity reaches the required level.

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