Method for realizing Haar unitary positive randomness on a three-dimensional photonic chip based on classical random numbers

Abstract

A method for realizing Haar unitary positive randomness on a three-dimensional photonic chip based on classical random numbers. Waveguides are fabricated using different femtosecond laser direct writing speeds, such that the diagonal of the Hamiltonian of the obtained waveguides contains a Δβ term. By injecting classical light into the fabricated waveguides, quantum random walks of photons between the waveguides can be obtained, and the evolution result satisfies the random unitary positive operation of the Haar measure. The present invention can achieve true randomness and is simpler, and can be applied to boson sampling, quantum cryptography, quantum process tomography, entanglement generation, fidelity estimation, etc.

Description

Technical Field

[0001] The present invention relates to a technology in the field of three-dimensional photonic chips, specifically a method for realizing Haar unitary positive randomness on a three-dimensional photonic chip based on classical random numbers. Background Art

[0002] Random operations of quantum systems play an important role in quantum information processing. Especially in recent years, various studies on boson sampling have demonstrated the superiority of quantum computing, and the Haar random unitary matrices required by these studies have attracted more and more attention. The Haar measure is not only a theoretical tool for studying randomness now, but also a practical module for constructing quantum protocols or algorithms, and is widely used in boson sampling, quantum cryptography, quantum process tomography, entanglement generation, fidelity estimation, etc. Currently, there are a series of research schemes, which propose experimental schemes for realizing random or pseudo-random quantum operations. So far, these experimental schemes either use a large number of quantum gates or use beam splitters and interferometers, and their implementation is quite complex through the Reck / Clements decomposition method. Summary of the Invention

[0003] Aiming at the above deficiencies of the existing technology, the present invention proposes a method for realizing Haar unitary positive randomness on a three-dimensional photonic chip based on classical random numbers. Classical randomness is introduced into the Hamiltonian through classical random numbers, and then a three-dimensional waveguide array is constructed. Photons are injected into the array, and the evolution result can obtain randomness that satisfies the Haar measure. Compared with the previous methods, the present invention can achieve true randomness and is simpler, and can be applied in boson sampling, quantum cryptography, quantum process tomography, entanglement generation, fidelity estimation, etc.

[0004] The present invention is realized through the following technical solutions:

[0005] The present invention relates to a method for realizing Haar unitary positive randomness on a three-dimensional photonic chip based on classical random numbers. Waveguides are prepared by using different femtosecond laser direct writing speeds, so that the diagonal of the Hamiltonian of the obtained waveguides contains the Δβ term. By injecting classical light into the prepared waveguides, quantum random walks of photons between the waveguides can be obtained, and the evolution result is a random unitary positive operation that satisfies the Haar measure.

[0006] The femtosecond laser direct writing mentioned above means: focusing a femtosecond-level laser on the surface or inside of the chip, and forming a waveguide by changing the optical properties of this point through the laser energy. Specifically: creating a process file for femtosecond laser direct writing according to a randomly generated matrix group, and burning the chip through a laser direct writing device to obtain the corresponding waveguide.

[0007] The material of the chip mentioned above is but not limited to borosilicate glass.

[0008] The process document mentioned above is preferably a fab file with specific waveguide parameters generated by SCA software, but not limited to this.

[0009] The structure of the waveguide mentioned above is a one-dimensional or two-dimensional array, such as a square array, and preferably a two-dimensional array.

[0010] The randomly generated matrix group mentioned above refers to: generating a group of random numbers using a random number generator to introduce classical randomness into the Hamiltonian of the quantum system. That is, after introducing the △β term into the diagonal elements of the Hamiltonian matrix, the △β term is converted into the change in the moving speed of the laser through a conversion relationship.

[0011] The random number generator mentioned above includes but is not limited to MATLAB, Excel, etc.

[0012] The conversion mentioned above refers to: based on the fact that △β (unit: mm -1 ) and △v (unit: mm / s) are approximately linearly related, then

[0013] △β = 0.02△v, where: △β > 0, and △v refers to the change speed of the laser compared to the basic moving speed during the direct writing process of the waveguide.

[0014] For the quantum random walk mentioned above, by injecting a laser with a wavelength of 810 nm into the prepared waveguide, photons will perform quantum random walk evolution therein. Using a beam analyzer to arrange the intensity of each output point light, a light intensity distribution matrix is obtained. Reading and / or comparing operations are performed on the matrix to obtain a random unitary positive matrix that meets the Haar measure |E i [U i ρU + i -1 / N| d <ε, where: E i [...] represents taking the average of the numbers in the brackets. represents the operation on the quantum state, N is the number of modes, that is, the number of waveguides, and |...| d represents taking the 2-norm of the matrix in the brackets, and ε is an arbitrary infinitesimal quantity.

[0015] For the laser injection mentioned above, it is preferred to polish the laser injection surface and the output surface of the prepared waveguide first.

[0016] For the light intensity distribution matrix mentioned above, by reading the intensity of each light spot and normalizing it, the percentage of each light spot in the total light intensity is obtained, that is, the probability distribution of photons in each mode; the same operation is performed on multiple groups of data to obtain a series of probability distributions, and the probability of the points with the same coordinates is averaged to obtain the overall probability distribution.

[0017] The read and / or comparison operation mentioned above refers to: reading matrix elements and / or calculating the norm by subtracting the difference between the whole matrix and the standard average distribution. Description of the Drawings

[0018] Figure 1 a is a theoretical schematic diagram of Haar randomness;

[0019] Figure 1 b is a schematic diagram of a waveguide array for realizing Haar randomness;

[0020] Figure 1 c is a real - shot cross - sectional view of waveguides in another waveguide array, where each bright spot is a waveguide;

[0021] Figure 2 Real - shot pictures of some experimental devices, Figure 2 a are two multi - dimensional adjustable mirrors, Figure 2 b is a three - dimensional precision translation stage and a convex lens, Figure 2 c is a schematic diagram of the optical path.

[0022] Figure 3 Schematic diagrams of the light spots obtained at different evolution lengths (right) when realizing Haar randomness and the light intensity read by this method (left);

[0023] Figure 4 Schematic diagram of the process of processing experimental data once in the embodiment;

[0024] Figure 5 Schematic diagram of the theoretical curve and experimental values in the embodiment;

[0025] Figure 6 a is a schematic diagram of the one - dimensional scheme in the embodiment;

[0026] Figure 6 b is a schematic diagram of the two - dimensional scheme in the embodiment;

[0027] Figure 7 Schematic diagram of the evolution time in the embodiment. Detailed Implementation Manner

[0028] Embodiment 1

[0029] As Figure 1 shown, this embodiment relates to a method for realizing Haar unitary randomness on a three - dimensional photonic chip based on classical random numbers. Based on classical random numbers, quantum random walks of photons are realized in a 5×5 optical waveguide array to obtain Haar unitary randomness, and its evolution lengths are 1 cm, 2 cm, 3 cm, 4 cm, 5 cm, 6 cm, 7 cm, and 8 cm respectively, including the following steps:

[0030] Step 1) Use a classical random number generator to generate random numbers for introducing classical randomness into the Hamiltonian of the quantum system. Since each evolution length is 2 mm, 40 groups of random numbers are prepared in advance, with 25 numbers in each group. The first 5, first 10... first 40 groups are used successively according to the increasing length.

[0031] Step 2) Implement the waveguide structure in the chip using femtosecond laser direct writing technology. The formed two-dimensional waveguide structure is as shown in Figure 1 b, and the actual photo of the waveguide is as shown in Figure 1 c, specifically including:

[0032] 2.1) Determine the direct writing speed of each segment according to the random numbers and create a program required for femtosecond laser direct writing. In this embodiment, the conversion formula is △β = 0.02△v, and the maximum value of △β can vary arbitrarily from 0.1 mm -1 to 0.8 mm -1 and is generally selected as 0.4 mm -1 .

[0033] Table 1

[0034]

[0035]

[0036]

[0037] Table 1 shows the direct writing speeds used in this embodiment. There are 25 columns, and the 40 numbers in each column represent the direct writing speeds (laser moving speeds) of each small segment from 1 to 8 cm in this group of embodiments.

[0038] 2.2) Write the waveguide in the program into the photonic chip using femtosecond laser direct writing technology.

[0039] Step 3) Measure the prepared photonic chip. The specific steps include:

[0040] 3.1) Polish the end faces for laser injection and output.

[0041] 3.2) Place the photonic chip in the optical path composed of a three-dimensional precision translation stage, multi-dimensional adjustable mirrors, and a convex lens, as shown in Figure 2 below. Generate laser with a wavelength of 810 nm from laser 1, split it into H light and V light by 2, focus the H light and inject it into the waveguide structure 6 (the waveguide structure 6 is located on the three-dimensional precision translation stage 7) through the multi-dimensional adjustable mirrors 3 and 4 and the convex lens 5, obtain a light spot by focusing the outgoing light with the convex lens 8, and observe its output result using a beam analyzer 9 (the instrument of 9 may be different in different embodiments), as shown in Figure 3 shown, which is the actual photo light spot of the waveguide structure obtained by a group of random numbers.

[0042] 3.3) Read the intensity of each light spot (manually select the center and radius, both in pixels, and accumulate the light spots of each pixel using software), obtain the light intensities of 25 light spots, and perform normalization to obtain the percentage of each light spot in the total light intensity, that is, the probability distribution of photons in each mode. Table 2 shows Figure 4 the reading results of

[0043] Table 2

[0044] 0.057851 0.022992 0.035131 0.034493 0.03819 0.020045 0.055626 0.011995 0.026563 0.127516 0.008902 0.112173 0.066848 0.052923 0.029726 0.018667 0.006798 0.004747 0.08982 0.077402 0.003105 0.001624 0.031193 0.015685 0.049986

[0045] 3.4) Perform the same operations on multiple groups of data to obtain a series of probability distributions, obtain Table 3, and take the average of the probabilities of the corresponding modes (that is, the points at the same coordinates in different experiments) to obtain the overall probability distribution, as shown in Table 4.

[0046] Table 3

[0047] 0.057851 0.022992 0.035131 0.034493 0.03819 0.003831 0.002456 0.040119 0.064667 0.023815 0.020045 0.055626 0.011995 0.026563 0.127516 0.063221 0.060396 0.113841 0.01443 0.008224 0.008902 0.112173 0.066848 0.052923 0.029726 0.011478 0.120429 0.079584 0.021669 0.017525 0.018667 0.006798 0.004747 0.08982 0.077402 0.009642 0.090239 0.032112 0.008689 0.096643 0.003105 0.001624 0.031193 0.015685 0.049986 0.012601 0.004329 0.046142 0.039142 0.014775 Data Group A Data Group B 0.007302 0.113077 0.050312 0.03858 0.020818 0.048562 0.03389 0.014435 0.23646 0.030694 0.059229 0.059986 0.01105 0.074302 0.008354 0.012751 0.024394 0.078373 0.009542 0.011454 0.021638 0.076372 0.072555 0.007846 0.009738 0.033115 0.037169 0.013277 0.052312 0.059501 0.009265 0.078918 0.008822 0.081699 0.01671 0.025322 0.064448 0.030565 0.038295 0.01543 0.027241 0.025199 0.078347 0.023583 0.019055 0.020225 0.029177 0.019597 0.032528 0.028483 Data Group C Data Group D 0.00871 0.008513 0.06003 0.020082 0.044728 0.07659 0.117461 0.030438 0.058552 0.113888 0.028221 0.008666 0.073485 0.024626 0.062567 0.031789 0.006227 0.011487 0.005176 0.04605 0.009053 0.013007 0.039732 0.039651 0.061268 Data Group E

[0048] Table 4

[0049] 0.025251 0.036185 0.040005 0.078856 0.031649 0.046367 0.063573 0.04914 0.036678 0.053887 0.020671 0.070962 0.06115 0.031875 0.035812 0.018937 0.049326 0.017547 0.044736 0.050447 0.014445 0.014668 0.043002 0.030118 0.034714

[0050] Based on the Haar random theory, each number in this probability distribution should approach 0.04 infinitely. To prove this, in this embodiment, each number in the overall probability distribution is subtracted by 0.04 to obtain the difference distribution from the theory, that is, Table 5; further, the norm is used to describe the degree of difference. Calculate the norm for this distribution to obtain the output result, square each number and then sum them up. The result obtained in Table 5 is 0.052. Comparing the output result with the theoretical simulation result can prove that the experiment in this embodiment satisfies the Haar randomness. As Figure 5 shown, the smaller the norm, the more in line with the Haar randomness. Ideally, the norm should approach zero. As the evolution length increases, the norm tends to zero and fits well with the theoretical curve.

[0051] Table 5

[0052] -0.01475 -0.00381 5.46E-06 0.038856 -0.00835 0.006367 0.023573 0.00914 -0.00332 0.013887 -0.01933 0.030962 0.02115 -0.00812 -0.00419 -0.02106 0.009326 -0.02245 0.004736 0.010447 -0.02555 -0.02533 0.003002 .0.00988 -0.00529

[0053] Example 2

[0054] Step 4) Construct a one-dimensional waveguide array with the same parameters, as Figure 6 shown in a, and repeat Step 2) and Step 3).

[0055] Compare the structure obtained in Step 4) with the results obtained in the previous Step 2) and Step 3), which proves the superiority of the two-dimensional structure, as Figure 6As shown in Fig. b, under the same conditions, the norm of the two-dimensional waveguide array is smaller than that of the one-dimensional waveguide array (for the one-dimensional and two-dimensional comparison with different △β, numerical simulations in this embodiment verify the theory of this embodiment).

[0056] In this embodiment, through numerical simulation, it is proved that the longer the evolution time (proportional to the evolution length), as Figure 7 shown, the more evolution groups ( Figure 7 ), and the larger the maximum value of △β ( Figure 7 ), the more the norm tends to zero. Therefore, the parameters involved in this method can be flexibly adjusted according to requirements such as precision and equipment.

[0057] In practical applications, several groups of such photon probability distributions are obtained by the above method in this embodiment, and various desired random unitary positive matrices can be obtained by this embodiment through various means.

[0058] In summary, this method can realize a random unitary positive matrix that truly satisfies the Haar measure.

[0059] Those skilled in the art can make local adjustments to the above specific implementation in different ways without departing from the principles and purposes of the present invention. The protection scope of the present invention is subject to the claims and is not limited by the above specific implementation, and all implementation solutions within its scope are subject to the present invention.

Claims

1. A method for realizing Haar unitary positive randomness on a three-dimensional photonic chip based on classical random numbers, characterized in that, waveguides are fabricated using different femtosecond laser direct writing speeds, such that the Hamiltonian of the obtained waveguides contains a Δβ term on the diagonal. By injecting classical light into the fabricated waveguides, quantum random walks of photons between the waveguides can be obtained, and the evolution result thereof satisfies the random unitary positive operation of the Haar measure; the femtosecond laser direct writing mentioned above refers to: focusing a femtosecond-level laser on the surface or inside of the chip, and forming waveguides by changing the optical properties of that point through the laser energy. Specifically: creating a process file for femtosecond laser direct writing according to a randomly generated matrix group, and burning the chip through a laser direct writing device to obtain corresponding waveguides; the randomly generated matrix group mentioned above refers to: generating a group of random numbers using a random number generator for introducing classical randomness into the Hamiltonian of the quantum system, that is, after introducing a Δβ term into the diagonal elements of the Hamiltonian matrix, converting the Δβ term into a change in the moving speed of the laser through a conversion relationship; The conversion mentioned above means that: △β = 0.02△v, where: △β > 0, and △v refers to the change rate of the laser relative to the basic moving speed during the waveguide direct writing process, with the unit of △β being mm -1 , and the unit of △v being mm / s; The described quantum random walk means that after polishing the laser injection surface and the output surface of the prepared waveguide, a laser with a wavelength of 810 nm is injected into the prepared waveguide, and photons will perform quantum random walk evolution therein. The beam analyzer is used to arrange the light intensity of each output point to obtain the light intensity distribution matrix, and read and / or compare operations are performed on the matrix to obtain a random unitary positive matrix that conforms to the Haar measure |E i [U i ρU + i -1 / N| d <ε, where: E i […] represents taking the average of the numbers in the brackets, represents the operation on the quantum state, N is the number of modes, that is, the number of waveguides, |…| d represents taking the 2-norm of the matrix in the brackets, and ε is an arbitrary infinitesimal quantity; the light intensity distribution matrix is obtained in the following manner: by reading the intensity of each light spot, and obtaining the percentage of each light spot in the total light intensity after normalization, that is, the probability distribution of photons in each mode; performing the same operation on multiple groups of data to obtain a series of probability distributions, and taking the average of the probabilities of points with the same coordinates to obtain the overall probability distribution; the reading and / or comparison operation mentioned above refers to: reading matrix elements and / or calculating the norm by subtracting the difference between the overall matrix and the standard average distribution.

2. The method for realizing Haar unitary positive randomness on a three-dimensional photonic chip based on classical random numbers according to claim 1, characterized in that, the structure of the waveguides is a one-dimensional or two-dimensional array.

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