Gaussian boson sampling system and method

Abstract

The present disclosure relates to a system and method for performing Gaussian boson sampling by time-multiple correlation of squeezed vacuum states for quantum information experiments. One embodiment relates to a method for performing Gaussian boson sampling, comprising the steps of generating a set of pulse pairs of squeezed vacuum states, performing time-multiple correlation of a plurality of such pairs of squeezed vacuum states, measuring states from the generated pairs of squeezed vacuum states by homodyne detection, feeding forward the homodyne results of the measured states to a displacement unit, performing a displacement operation on remaining states from the generated pairs of squeezed vacuum states, and counting the states output from the displacement unit.

Description

[Technical Field]

[0001] The present disclosure relates to systems and methods for Gaussian boson sampling with time-multiple correlation of squeezed vacuum states for quantum information experiments. [Background technology]

[0002] Boson sampling is a method in photonics that is used, among other things, to demonstrate quantum supremacy. It consists of N single photons incident on an M-mode interferometer consisting of a beam splitter, a phase shifter, and a photon detector that measures the output. Calculating the probability of detecting a photon at each photon detector is a classically intractable problem, with computational complexity that grows exponentially with the number of detected photons. When the number of photons is sufficiently large, classical computers cannot predict the outcome of a boson sampling experiment.

[0003] However, due to imperfections such as losses, photon distinguishability, dark counts, and phase fluctuations, boson sampling experiments can only approximate to a certain extent the theoretical model that defines the experiment. Because this sampling approximation is also a classical challenge, boson sampling experiments can still outperform classical computer simulations in the presence of feasible experimental noise sources. In other words, the task of a boson sampling experiment is to create a sample distribution that is as similar as possible to a theoretical interferometer defined by N and M.

[0004] Photon loss and experimental error increase with the size of the boson sampling interferometer until the problem can be simulated classically. Therefore, the limiting factors of boson sampling experiments are usually the finite efficiency of the single-photon source and the requirement to synchronize the single-photon source. Therefore, it is necessary to design an experimental setup that is small enough to avoid unwanted noise generation and photon loss, yet complex enough to achieve quantum supremacy.

[0005] Gaussian boson sampling is an implementation of boson sampling that has recently gained interest in the field of photonics, particularly in demonstrating quantum supremacy experiments. While boson sampling experiments require the use of single photons, Gaussian boson sampling uses a squeezed vacuum for the input state. This means that the Gaussianity of the input state causes the distribution function of the state to follow Gaussian statistics.

[0006] For these reasons, improvements and simplifications to the experimental setup of Gaussian boson sampling experiments will benefit the quality of the output produced and aid in demonstrating the concept of quantum supremacy using this platform. Summary of the Invention

[0007] In view of the above prior art, the objective of this invention is to demonstrate a novel approach to boson sampling for quantum supremacy using an optical platform. Non-classical light sources, such as two-mode squeezed states, are proposed for use in time-multiplexed boson sampling with homodyne detection due to their ability to be generated on demand rather than as single-photon states.

[0008] Accordingly, the present disclosure relates to a system for performing Gaussian boson sampling, the system including an optical input generator configured to generate a squeezed vacuum state. The system preferably includes a time multiplexing unit configured to receive from the optical input generator and transmit at least a first portion of the generated squeezed vacuum state through a first optical line, receive from the optical input generator and transmit at least a second portion of the generated squeezed vacuum state through a second optical line, correlate the first portion of the squeezed vacuum state from the first optical line with the second portion of the squeezed vacuum state from the second optical line using a plurality of beam splitters, and delay the state of the second optical line using a number of delay lines located between the plurality of beam splitters. Thus, the first optical line, the second optical line, the plurality of beam splitters, and / or the number of delay lines are typically part of the time multiplexing unit.

[0009] The system may also include a measurement unit that utilizes a combination of homodyne detection, displacement manipulation, and photon counting. In one embodiment, the measurement unit is configured to measure a characteristic of an optical input at the end of one of the first or second optical lines, preferably by a homodyne detector. At the other end of the first or second optical line, the optical input can be delayed so that an output signal based on the measured characteristic can be fed forward and provided to the optical displacement operator unit along with the delayed optical input. The optical input can be delayed by a delay line, particularly a "long" delay line that is long enough (in distance and / or time) to "wait" for the measured characteristic. Here, the delay line(s) of the measurement unit are referred to as the "last delay line." Therefore, the optical displacement operator unit is preferably located after the last (long) delay line. The displacement manipulation can then be provided by the optical displacement operator, and the optical input can be counted after the optical displacement operator, preferably by a photon counter.

[0010] In one embodiment, the measurement unit is configured such that homodyne detection is provided only in one of the first optical line or the second optical line, and photon counting is provided only in the other of the first optical line or the second optical line. That is, the measurement unit is configured to delay the state of the second optical line using a last (long) delay line located after the previous beam splitter (of the time multiplexing unit), measure a property of the state using a homodyne detector at the end of the first optical line, and based on the measured property, feed an output signal forward to an optical displacement operator unit located after the last delay line of the second optical line, apply a displacement operation to the state of the second optical line, and count photons at the end of the second optical line. An example of this setup is shown in Figure 1A.

[0011] However, more flexibility is provided if the selection of which squeezed states are measured by homodyne detection and which by photon counting is not determined by the optical line. This can be provided, for example, if the measurement unit is configured to switch between homodyne detection and photon counting for each optical input of both the first and second optical lines. For example, the measurement unit may include a switch, preferably a high-speed switch, on each optical line to switch between homodyne detection and photon counting on each optical line. In this more flexible approach, a final delay line and optical displacement operator unit may be placed before each of the photon counters, and the output signals of both homodyne detectors may be fed forward to the corresponding displacement operator unit. An example of this more flexible setup is shown in Figure 1B.

[0012] The approach disclosed herein enables a reduction in the number of optical components required to achieve quantum supremacy through time-multiplexed Gaussian boson sampling experiments. This reduction in components reduces state loss, the computational requirements to operate at speeds fast enough for optical devices, and unwanted noise generation in optical systems, which are typically limiting factors when testing quantum supremacy through photonic platforms.

[0013] It should be noted that the final delay line(s), homodyne detector(s), optical displacement operator(s) and / or photon counter(s) are typically part of the measurement unit.

[0014] The present disclosure further relates to a method for performing Gaussian boson sampling, the method comprising: a) generating a set of pulse pairs in a squeezed vacuum state; b) performing time-multiple correlations of a plurality of such pairs of squeezed vacuum states; c) measuring a state from the pair of generated squeezed vacuum states by homodyne detection; d) feeding forward the homodyne results of the measured state to the displacement unit; e) performing a displacement operation on the remaining states from the pair of squeezed vacuum states generated; f) counting the states output from the displacement units.

[0015] This can be done, for example, using the systems disclosed herein.

[0016] The present disclosure further relates to a measurement unit for receiving a squeezed vacuum as disclosed herein.

[0017] The invention will now be described in more detail with reference to the accompanying drawings. [Brief explanation of the drawings]

[0018] [Figure 1] A–B show schematic diagrams of the optical setup for homodyne-assisted time-multiplexed Gaussian boson sampling. [Figure 2] We show a schematic of the induced coupling of squeezed vacuum states in the proposed optical setup. [Figure 3] 1A and 1B show the detection principle of FIGS. [Figure 4] A shows a simulation of the Kolmogorov-Smirnov statistics for a setup containing two delay lines with lengths L1 = 1 and L2 = 8. B shows a simulation of the Kolmogorov-Smirnov statistics for a setup containing three delay lines with lengths L1 = 1, L2 = 8, and L3 = 4. [Figure 5] 1 shows the histogram distribution of elements from a simulation of the unitary matrix obtained in terms of amplitude. [Figure 6] 1 shows a histogram distribution of elements from a simulation of the unitary matrix obtained for the phase. [Figure 7] The distribution of amplitude components of the induced interferometer compared to an ideal interferometer chosen from Haar measurements is shown. Results represent the average of seven experiments. [Figure 8] The distribution of the phase elements of the induced interferometer compared to an ideal interferometer chosen from Haar measurements is shown. The results show the average of seven experiments. [Figure 9] Distances of ensembles of states created by linear measurements (Figure 1A) and by the flexible approach (Figure 1B) from a reference ensemble of states are shown. [Figure 10A] The scheme of the "linear measurement" from FIG. 1A and the flexible approach from FIG. 1B are shown. [Figure 10B] We present experimental results in the form of unitary matrices that lead to induced states. [Figure 11] A–D show the six-mode graph states generated by the linear measurement scheme, along with the interferometer that induces them and the amplitude and phase elements of the unitary matrix. DETAILED DESCRIPTION OF THE INVENTION

[0019] Boson sampling was initially proposed as a simple experimental approach to demonstrating quantum supremacy, but building a sufficiently large interferometer with many nonclassical optical input sources and detectors is relatively difficult. Therefore, there is interest in developing experimental improvements that reduce the physical resources involved in such a setup and relax the tight requirements for achieving quantum supremacy via boson sampling. Such a setup can be implemented by Gaussian cluster state generation. By utilizing the concept of time-multiple correlations, several entangled Gaussian states are generated using a fixed number of beam splitters and optical input generators. In principle, two-dimensional Gaussian cluster states containing optical squeezed modes can be used to implement any Gaussian operation, and therefore any linear optical network can be simulated with Gaussian cluster states.

[0020] 1A and 1B show examples of setups 100, 100′ for homodyne-assisted boson sampling. A pair of single squeezed states 101 and 102 is created by one or more optical input generators. The pair is separated from the next pair by a period. Typically, the shorter the period, the higher the computational power of the presented optical setup. The limitation on the duration of the generation period may be a limitation on the computational processing speed of the generated data. One squeezed state of the generated squeezed state pair is injected into a first optical beam 103, and the second squeezed state is injected into a second optical beam 104. Preferably, the optical beams carrying the squeezed states are typically constituted by optical fibers, e.g., generalized single-mode optical fibers (SSMFs), but they can also be constituted by free air or photonic waveguides.

[0021] A first 50:50 beam splitter device 105 is positioned between the first and second optical lines to correlate the squeezed states arriving simultaneously from the optical input generator. The first optical line after the beam splitter carries the correlated squeezed states emerging from one part of the beam splitter, while the second optical line includes a delay line 106. The delay line is designed to induce a time delay L between the correlated squeezed states emerging from the other part of the beam splitter, the length of which is equal to the generation period of the pair of squeezed modes. A second 50:50 beam splitter 107 is then positioned between the first and second optical lines to correlate the squeezed states arriving simultaneously from the first beam splitter 105 and the delay line 106 located in the second optical line.

[0022] The structure formed by the beam splitter 108, the first optical line 103, the second optical line 104, and the delay line 109 of the second optical line 104 is defined as a structural unit and can be repeated continuously. Because each additional structural unit includes a longer delay line than the previous one, the squeezed state of the second optical line 104 is delayed by a greater number of period units L in all structural units compared to the squeezed state generated simultaneously traveling along the first optical line 103. This procedure of correlating and mixing squeezed states based on delay lines and a 50:50 beam splitter is defined as time multiplexing. This operation generates highly correlated multimode Gaussian states, which allows for the simulation of a universal Gaussian network. Generally, time multiplexing requires fewer optical components to correlate photons than the widely used spatial multiplexing.

[0023] In a preferred embodiment, the homodyne-assisted boson sampling measurement unit is located after a series of structural units, including a 50:50 beam splitter and delay line, responsible for time-multiplexing the squeezed modes. Figures 1A and 1B show two different examples of homodyne-assisted boson sampling measurement units. In the setup 100 of Figure 1A, the final beam splitter 110 sends the squeezed states to the first optical line 103, and the homodyne detector 111 measures them using a variable orthogonal basis set for each squeezed mode. These orthogonal base sets can be randomly selected to demonstrate quantum supremacy. Alternatively, they can be programmed to a fixed pattern, allowing for the implementation of any desired linear optical network. The final beam splitter 110 sends the squeezed states to the second optical line 104, where they are delayed, i.e., temporarily stored, in the final (long) delay line 112. The homodyne measurement of the squeezed state of the first optical beam 103 transforms the correlation of the squeezed state of the second optical beam 104 in a manner determined by the correlations induced by the optical input state generators 101-102 and the series of structural units 105-110, as well as the orthogonal basis setting of the homodyne detector 111. Due to the non-zero mean vector resulting from the homodyne measurement of the squeezed mode, a displacement operation must be performed on the squeezed state of the second optical beam 104. Therefore, the final delay line 112, which stores / delays the squeezed state, must be long enough to allow the homodyne detector to transmit its measurement (via optical beam 114 and digital signal processor (DSP) 117) to the displacement unit 113 located on the second optical beam 104. The final photon counter 115 is located at the end of the second optical beam 104, i.e., after the displacement unit 113. The DSP is preferably configured to process the homodyne measurement results and calculate the required displacement to be fed forward before the photon counter.

[0024] Increased flexibility can be provided by the setup 100' of FIG. 1B. In FIG. 1B, the homodyne-assisted measurement unit from FIG. 1A is duplicated like the measurement unit from FIG. 1A and is available for both the first optical beam 103 and the second optical beam 104. By providing a 1×2 switch 116 at each output of the preceding beam splitter 110, it is possible to select which of the first optical beam 103 and the second optical beam 104 is measured by homodyne detection and which by photon counting. Thus, at each of the two outputs from the preceding beam splitter 110, a measurement unit is provided, each including a homodyne detector 111 and a delay 112+displacement 113+photon counter unit 115, which can be correspondingly selected by the two 1×2 switches 116. The measured output from the homodyne detector 111 of FIG. 1B can be fed forward 114 to a corresponding displacement unit 113 via a digital signal processor (DSP) 117 .

[0025] The delay line(s) of the measurement unit, referred to herein as the "last" delay line, are typically used to "park" light in one of the optical lines while the other line is being measured. That is, the light is temporarily stored while the other lines are being measured, but in reality, the light is only delayed in the last delay line. In that regard, it is preferable that the last delay line(s) of the measurement unit be at least longer than the longest delay line of the interferometer, i.e., structural unit. While not necessarily much longer, in practice, it is preferable to make the last delay line several times (e.g., 1, 2, 3, or 4 times) longer than the longest delay line of the structural unit, i.e., interferometer, although this is not a requirement. Thus, once the length of the first delay line 106 of the first structural unit is selected, the remaining delay lines, e.g., the delay line 109 immediately preceding the measurement unit and the last delay line 112, can be selected therefrom.

[0026] It should be noted that when using the term "length" with respect to a delay line, it can refer to both the physical length and the time length. For example, when using optical fiber as a delay line, the length of the optical fiber corresponds to the duration of the delay. That is, the length of such an optical fiber-based delay line can be the physical length and / or the duration of the delay.

[0027] In alternative embodiments, the beam splitter may be set in any configuration different from balanced 50:50, which may allow for a larger parameter space in the results obtained.

[0028] Figure 2 shows a schematic diagram of the couplings generated in squeezed states 200 in the homodyne-assisted boson sampling setup described above. Solid circles, such as 211, represent squeezed states, and open circles, such as 241, represent vacuum states. At 210, squeezed states 211 and 213 and the remaining solid circles in the top row are transported through the first optical line. Squeezed states 212 and 214 and the remaining solid circles in the bottom row are transported through the second optical line. At 220, the squeezed states are sent through the first beam splitter. This generates a coupling between squeezed states that simultaneously enter the beam splitter, defined by the solid black line 222 between squeezed states 221 and 223.

[0029] After the first beam splitter, at 230, a first delay line of length L1=1 is introduced into the second optical line, causing these states 232 to be time delayed by one period compared to the correlated squeezed states from the first optical line 231. The squeezed states enter the second beam splitter at 240 and couple to states entering the beam splitter at the same time. Squeezed state 243, previously coupled to squeezed state 245 by coupling 222 / 244, is now coupled to vacuum state 241 by coupling 242. At 250, L2A second delay line with a defined length L = 2 further delays the squeezed state of the second optical line. Such a delay line with length L = 2 is used as an example setup for a Gaussian boson sampling experiment and may have different lengths in different setup configurations. Upon entering the beam splitter just before 260, squeezed state 263, previously coupled to squeezed state 265 by coupling 222 / 244 / 267 and to vacuum state 264 by coupling 242 / 266, is now coupled to vacuum state 261 by coupling 262. The optical setup including two delay lines shown in FIG. 2 is an example of the time-multiplexed Gaussian boson sampling disclosed herein. Similar setups with slight modifications may be generated with a different number of components.

[0030] At 270, homodyne detection is performed on the squeezed states from one of the first or second optical lines. The measurements are then fed forward to a displacement unit that performs a displacement operation on the squeezed states from the other of the first or second delay line, with each dotted line indicating the resulting correlation between the squeezed states in the other of the first or second delay line.

[0031] The approach presented in Figures 1 and 2 involves fewer homodyne measurements than are necessary to simulate a universal Gaussian network. This helps keep the required squeezing level reasonable and makes experimental realization practical. However, time-multiplexed Gaussian boson sampling allows for more complex implementations, so it is not limited to the combinations disclosed herein. The setup shown in Figures 1A and 1B is highly experimentally friendly. In principle, the number of optical lines is not limited to two, and the number of setup units, including delay lines and beam splitters, is not limited to two. However, compared to other optical setups, the ultimate limit to the scalability of the system disclosed herein is determined by photon losses along the optical lines, errors in the homodyne measurements, errors in the displacement manipulation, and errors in photon counting.

[0032] One possible alternative embodiment, capable of implementing a Gaussian network over a broader range, is shown in FIG. 3B and can be implemented using the setup of FIG. 1B. Meanwhile, FIG. 3A illustrates an approach in which one optical line is fixed by homodyne detection and the other optical line is photon-counted, i.e., a kind of "linear measurement." The graph in FIG. 3A shows the correlation obtained with a single structural unit, corresponding to the state obtained after 240 in FIG. 2, but can be generalized to any number of structural units. The dots with arrows and meters in FIG. 2 indicate the squeezed state of the first optical line measured by homodyne detection, and the circled dots indicate the squeezed state of the second optical line measured by photon counters.

[0033] FIG. 3B illustrates the measurement procedure illustrated in FIG. 1B, where the selection of which squeezed states are measured by homodyne detection and which by photon counting is not determined by the optical line. In this particular example of FIG. 3B, five squeezed states are measured by homodyne detection and three squeezed states are measured by photon counting. To implement such variable measurement selection, as shown in FIG. 1B, both optical lines can be equipped with an optical one-to-two switch, for example, after the beam splitter 110. As can be seen in FIGS. 1B and 3B, successive output modes alternate between two spatial modes and can be separated by two temporal modes. Thus, more than half of the modes can be measured by homodyne detection, and the output modes circled in FIG. 2, where photon counting is performed, are separated by a "jump."

[0034] Gaussian boson sampling has proven useful in experiments with applications in fields such as graph theory and in simulating molecular vibrational spectra.

[0035] Alternative setups to perform time-multiplexed Gaussian boson sampling with homodyne detection may be possible, potentially resulting in a simplification of the setup. [Example]

[0036] Figure 4A shows a simulation of the Kolmogorov-Smirnov statistical test showing the distance from a Gaussian unitary Haar random matrix implemented for the homodyne-assisted Gaussian boson sampler disclosed herein. In the simulation, the optical setup includes two setup units (described in Figure 2) with L varying from [1, 20], both in units of the squeezed state generation period. The x-axis corresponds to the delay length of delay line L2, and the y-axis corresponds to delay line L1. Based on the presented simulation, the optimal values ​​for L1 and L2 are [L1, L2] = [1, 8], which corresponds to the minimum value of the Kolmogorov-Smirnov statistical test.

[0037] Figure 4B shows a simulation of the Kolmogorov-Smirnov statistical test showing a further plot of the distance of the implemented Gaussian unitary from a Haar random matrix for the homodyne-assisted Gaussian boson sampler disclosed herein. In the simulation, the optical setup includes three structural units (as described in Figure 2) and has a length L1 = 1, with a fixed first delay line of lengths L2 and L3 varying from [1, 20], all in units of squeezed-state generation periods. The x-axis corresponds to the delay length of delay line L3, and the y-axis corresponds to delay line L2. Based on the presented simulations, the optimal values ​​for L2 and L3 are [L2, L3] = [2, 4], which corresponds to the minimum value of the Kolmogorov-Smirnov statistical test. This distance is slightly smaller than the simulation of FIG. 4A using two delay lines. Therefore, based on the simulations presented in FIGS. 4A and 4B, the addition of a third setup unit and delay line improves the results obtained by the Gaussian boson sampler disclosed herein compared to the example including two setup units and two delay lines.

[0038] The simulations shown in Figures 4A and 4B included a setup that generated 100 input modes and 5 dB squeezing of the states. In each simulation, the homodyne measurement criteria were randomly selected. The simulations were repeated 100 times. Figures 4A-4B show the minimum achieved KS statistics for each delay path configuration.

[0039] 5-6 show histograms of the amplitude and phase probability densities of the unitary matrix, respectively, obtained for the setup simulated for FIG. 4B. In plot 500, x-axis 501 corresponds to the amplitude of each element in the matrix, and y-axis 502 corresponds to the probability density. Curve 503 superimposed on the histogram represents the expected amplitude distribution of the Haar random matrix, providing a highly accurate fit to the data. In plot 600 of FIG. 6, x-axis 601 corresponds to the phase of each element in the matrix, and y-axis 602 corresponds to the probability density. Curve 603 superimposed on the histogram represents the expected phase distribution of the Haar random matrix, providing a highly accurate fit to the data.

[0040] The representational power of a measurement procedure that generates pure Gaussian states can be defined as its ability to not only represent a reference ensemble of Gaussian random matrices, but also to generate an ensemble of such states. The closeness of the representations is measured in terms of a distance based on the Hausdorff distance, well known in set theory. A shorter distance is evidence that most states in the reference ensemble are exactly represented by the induced ensemble, and vice versa.

[0041] Figures 7-8 show experimental distributions of amplitude and phase components of the induced interferometer compared to an ideal interferometer selected from Haar measurements. In the absence of switching, linear measurements are used to induce a 400-mode Haar random interferometer. Results are the average of seven experiments performed, creating histograms with thin bars due to the large number of experimental samples created. Figures 7-8 therefore provide experimental demonstrations of the principles disclosed herein and complement the demonstrations from simulations in Figures 5-6.

[0042] Figure 9 shows the distances for the ensemble created by the "linear measurement" shown in Figures 1A and 3A, marked as 900 in Figure 9, and the flexible approach shown in Figures 1B and 3B, marked as 901 in Figure 9, both from the reference ensemble. It can be seen that the flexible approach 901 gives smaller distances across all squeezing levels, r, and interferometer sizes, N. The optimal procedure for the 1D cluster case is the flexible approach from Figure 1B, where the correlation matrix has four entries, the maximum amount of entries it can have for a 1D cluster. For the N-mode unitary case, 3N-2 output modes are measured. The parameter space is clearly larger here, which should also give more control over the neighbors generated.

[0043] Figure 10A shows a "linear measurement" scheme and a more flexible approach for generating 2D clusters. Reference numeral 1000 in Figure 10A marks a linear measurement scheme (Figure 1A) that generates a bimodal state in which a yellow mode is measured (to the right) and a red mode is used as the output mode (to the left). Similarly, reference numeral 1001 marks a flexible measurement approach (Figure 1B) that generates a bimodal state in which four modes of green 1002 are measured and two modes of blue 1003 are used as the output mode.

[0044] Figure 10B shows the 2 × 2 unitary matrix generated in the process of inducing states using the aforementioned scheme. The blue dots are organized into a circle with a unit radius on the diagonal and a unit radius near zero off the diagonal, indicating that these "blue unitary matrix entries," which represent linear measurements, can only be rotated. Meanwhile, the red dots are well-distributed throughout the unit circle, demonstrating the ability of the flexible approach (Figure 1B) to also generate mode mixing and induce correlations between modes. This is seen against the background of the green Haar random unitary matrix entries. Clearly, measurements using the flexible approach (Figure 1B) closely approximate the distribution of the Haar random unitary matrix.

[0045] Figures 11A-11D show an example of an experimental implementation of the approach disclosed herein by generating a six-mode state from a linear measurement scheme (Figure 1A) for a 2D cluster state. Figure 11D shows a graph corresponding to such a state. Figure 11C shows an interferometer that induces this state. Figure 11B shows the phase element of the unitary induction. Figure 11A shows the amplitude element of the measurement induction unitary.

[0046] Overall, the examples show that measurement-guided interferometers can be guided in a scalable and accurate manner compared to those of an ensemble of Haar random matrices.

[0047] item 1. A system for performing Gaussian boson sampling, comprising: a) an optical input generator; b) receiving from the optical input generator and transmitting at least a first portion of the generated optical input through a first optical line; receiving from the optical input generator and transmitting at least a second portion of the generated optical input through a second optical line; using a plurality of beam splitters to correlate the first portion of the light input from the first optical line with the second portion of the light input from the second optical line; a time multiplexing unit configured to delay the optical input of the second optical line using a number of delay lines located between the plurality of beam splitters; measuring a characteristic of the optical input using a homodyne detector at the end of the first optical line; delaying the optical input of the second optical beam using a (long) delay line located after the immediately preceding beam splitter; feeding forward an output signal based on the measured characteristic to an optical displacement operator unit located after the (long) delay line of the second optical line; applying a displacement operation to the light input of the second optical beam; a measurement unit configured to count the light input at an end of the second optical line.

[0048] 2. The system of item 1, wherein the optical input generator comprises at least one squeezed vacuum state generator.

[0049] 3. The system of any preceding item, wherein the squeezed vacuum states generated by the at least one optical input generator are configured to be separated by a first period of time.

[0050] 4. The system of any of the preceding items, wherein the beam splitter is configured in a 50:50 balanced configuration.

[0051] 5. A system according to any preceding item, wherein each of the delay lines of the second optical line is configured to delay each squeezed vacuum state by a predetermined number of the first periods.

[0052] 6. A system according to any of the preceding items, wherein the (long) delay line of the second optical line is configured to store / delay the squeezed vacuum state for a second predetermined period of time that is longer than the first predetermined period of time.

[0053] 7. A system according to any preceding item, wherein the homodyne detector is configured to have processing time for measuring the correlated squeezed vacuum state from the first optical line and for feeding forward a signal to the displacement unit.

[0054] 8. A system according to any preceding item, wherein the measured property of the homodyne detector of the first optical line is a property of the correlated squeezed vacuum state, such as the quadrature amplitude of the electric field.

[0055] 9. A system according to any of the preceding items, wherein the (long) delay line of the measurement unit is configured to delay the correlated squeezed vacuum state by a time corresponding to the processing time of the homodyne detector.

[0056] 10. The system of any preceding item, wherein the displacement operator is configured to perform a displacement operation on the correlated squeezed vacuum state of the second optical beam.

[0057] 11. A system according to any preceding item, configured to perform the displacement operation on the position-momentum phase of the squeezed vacuum state of the second optical beam based on the measured characteristics by the homodyne detector of the squeezed vacuum state in the first optical beam.

[0058] 12. The system of any preceding item, wherein the configuration of the displacement operator is configured to change every first time period for each squeezed vacuum state.

[0059] 13. The detector that counts the squeezed vacuum states of the second optical beam is a single photon counter or a photon number resolving detector; and / or 10. The system of any of the preceding items, wherein the first optical line and delay line and the second optical line and delay line comprise a medium such as (low loss) optical fiber and / or free air.

[0060] 14. A method for performing Gaussian boson sampling, comprising: a) generating a set of pulse pairs in a squeezed vacuum state; b) performing time-multiple correlations of a plurality of such pairs of squeezed vacuum states; c) measuring a state from said pair of generated squeezed vacuum states by homodyne detection; d) feeding forward the homodyne result of the measured state to a displacement unit; e) performing a displacement operation on the remaining states from the pair of squeezed vacuum states created; f) counting the states output from the displacement unit.

[0061] 15. The method according to item 14, which is carried out using the system according to any one of items 1 to 13.

Claims

1. 1. A system for performing Gaussian boson sampling, comprising: an optical input generator; transmitting at least a first portion of the generated optical input received from the optical input generator through a first optical line; receiving from the optical input generator and transmitting at least a second portion of the generated optical input through a second optical line; correlating the first portion of the light input from the first optical line with the second portion of the light input from the second optical line using a plurality of beam splitters; delaying the optical input of the second optical beam using a number of delay lines located between the plurality of beam splitters; a time multiplexing unit configured to: measuring a characteristic of the optical input at an end of one of the first optical line or the second optical line with a homodyne detector; delaying the optical input on the other of the first optical line or the second optical line by a final delay line; feeding forward an output signal based on the measured characteristic to an optical displacement operator unit located after the last delay line; applying a displacement operation by said optical displacement operator; counting the light input after the light displacement operator, preferably by a photon counter; a measurement unit configured to: The system comprising:

2. The system of claim 1 , wherein the measurement unit is configured to switch between homodyne detection and photon counting for each optical input of both the first optical beam and the second optical beam.

3. 10. A system according to any preceding claim, wherein the measurement unit comprises a switch on each optical line for switching between homodyne detection and photon counting on each optical line.

4. The system of any one of claims 2 to 3, wherein a final delay line and an optical displacement operator unit are arranged before each of the photon counters, and output signals of both of the homodyne detectors can be fed forward to corresponding displacement operator units.

5. 10. A system according to any preceding claim, wherein the optical input generator comprises at least one squeezed vacuum generator.

6. 10. A system according to any preceding claim, configured such that the squeezed vacuum states generated by the at least one optical input generator are separated by a first period of time.

7. 10. A system according to any preceding claim, wherein the beam splitter is arranged in a 50:50 balanced configuration.

8. 10. A system according to any preceding claim, wherein each of the delay lines of the second optical line is configured to delay each squeezed vacuum state by a predetermined number of the first periods.

9. 10. A system according to any preceding claim, wherein the final delay line is configured to store the squeezed vacuum state for a second predetermined period of time that is longer than the first predetermined period of time.

10. 10. A system according to any preceding claim, wherein the homodyne detector is configured to have processing time for measuring the correlated squeezed vacuum state and for feeding forward a signal to the displacement unit.

11. 10. A system according to any preceding claim, wherein the measured property of the homodyne detector is a property of the correlated squeezed vacuum state, such as the quadrature amplitude of the electric field.

12. 10. A system according to any preceding claim, comprising a digital signal processor configured to process the measured property and calculate the displacement for feedforward purposes.

13. 10. A system according to any preceding claim, wherein the final delay line is configured to delay the correlated squeezed vacuum state by a time corresponding to the processing time of the homodyne detector.

14. 10. A system according to any preceding claim, wherein the displacement operator is configured to perform a displacement operation on the correlated squeezed vacuum states.

15. 10. The system of claim 9, configured to perform the displacement manipulation on a position-momentum phase of the squeezed vacuum state of the first optical beam or the second optical beam based on the measured property by the homodyne detector of the squeezed vacuum state in the first optical beam or the second optical beam.

16. 10. A system according to any preceding claim, wherein the configuration of the displacement operator is configured to change every first time period for each squeezed vacuum state.

17. 10. A system according to any preceding claim, wherein the detector for counting the squeezed vacuum states in the second optical beam is a single photon counter or a photon number resolving detector.

18. 10. A system according to any preceding claim, wherein the first and second optical lines and the delay line comprise a medium such as a transmission medium such as an optical fiber and / or free air.

19. 1. A method for performing Gaussian boson sampling, comprising: generating a set of squeezed vacuum state pulse pairs; performing a time-multiple correlation of a plurality of such pairs of squeezed vacuum states; measuring a state from said pair of generated squeezed vacuum states by homodyne detection; feeding forward the homodyne result of the measured state to a displacement unit; performing a displacement operation (by a displacement unit) on the remaining state from the pair of squeezed vacuum states created; counting the states output from the displacement unit; The method comprising:

20. 20. The method of claim 19 for conducting a quantum information experiment.

21. A method according to any of the preceding claims 19-20, carried out using a system according to any of claims 1-18.

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