A time-domain gaussian boson sampling system and method

Abstract

The application belongs to the technical field of quantum computing, and particularly relates to a time-domain Gaussian Bose sampling system and method. The system comprises: a quantum light source module for generating a pulse single-mode compressed state; a quantum interference module for realizing coherent coupling and unitary matrix evolution in the time mode dimension; a photon number detection and counting module for acquiring multi-photon coincidence counting sampling data within a preset time window; a measurement and control and data processing module for encoding graph data, controlling a modulator, stabilizing a phase of a loop, pre-processing and post-processing sampling data, and outputting a task result. The system integrates quantum light sources, interference, detection and counting, and measurement and control processing modules, realizes quantum acceleration solution of graph theory problems through a time-domain multiplexing architecture and quantum-classical hybrid computing.

Description

Technical Field

[0001] This invention belongs to the field of quantum computing technology, specifically relating to a time-domain Gaussian boson sampling system and method. Background Technology

[0002] In the field of quantum computing, Gaussian boson sampling (GBS) is an important scheme for demonstrating quantum advantage and has potential applications in solving graph theory problems such as dense subgraph mining. However, existing GBS systems suffer from the following technical bottlenecks: First, the quantum light source and interference modulation often use heterogeneous materials, leading to high losses and low integration; second, large-scale spatial interference networks are bulky and difficult to align; third, the dead time of a single detector limits the counting efficiency of dense time modes, affecting the statistical reliability of multiphoton interference; and fourth, there is a lack of a comprehensive collaborative mechanism from graph data encoding to quantum sampling to result output, making it difficult to efficiently solve complex combinatorial optimization tasks. Furthermore, while time-domain GBS reduces hardware complexity through time multiplexing, it still needs to address issues such as compressed state spectral purity, loop phase stability, and detector noise suppression to achieve high-fidelity quantum sampling and practical task solving. Therefore, there is an urgent need for a time-domain Gaussian boson sampling system and method with high integration, good stability, and efficient solution of graph theory problems. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a time-domain Gaussian boson sampling system and method. It integrates a quantum light source, interferometry, detection counting, and measurement and control processing modules, and achieves quantum-accelerated solutions to graph theory problems (such as dense subgraphs) through a time-domain multiplexing architecture and quantum-classical hybrid computation.

[0004] This invention provides a time-domain Gaussian boson sampling system, comprising: A quantum light source module for generating pulsed single-mode compressed states includes a nonlinear waveguide quantum light source based on lithium niobate, a pump filter unit, and a bandpass filter or wavelength division filter unit. The bandpass filter or wavelength division filter unit is used to select a target frequency band or target frequency channel and suppress non-target spectral modes. The quantum interference module, used to achieve coherent coupling and unitary matrix evolution in the time mode dimension, includes a 2×2 lithium niobate intensity modulator and a closed loop composed of optical fibers and devices. The closed loop connects one output and one input of the 2×2 lithium niobate intensity modulator to form a cyclic time-delay interference structure. A piezoelectric ceramic phase shifter and a 1×1 lithium niobate phase modulator are arranged in series in the closed loop to achieve stable phase and programmable phase modulation, so that the input single-mode compressed state forms multiple interfering time mode outputs after multiple cycles. The photon number detection and counting module is used to acquire multi-photon coincidence count sampling data within a preset time window. It includes an optical fiber splitter and N single-photon detectors. The optical fiber splitter splits the output light into 1×N beams to be input into the N single-photon detectors in parallel. The time-correlated single-photon counting device performs time marking and coincidence count statistics on the detection events. The measurement, control, and data processing module is used to encode the graph data, control the modulator, stabilize the loop, preprocess and postprocess the sampled data, and output the task results. The measurement, control, and data processing module maps the target problem to the setting of the compression degree of the quantum light source module and the modulation parameters of the quantum interference module, and outputs the task results based on coincidence counting sampling. Furthermore, the center wavelength and bandwidth of the bandpass filter or wavelength division filter unit are set according to at least one of the spectrum of the pulse pump light, the phase matching bandwidth of the nonlinear waveguide quantum light source, the time mode interval, the modulator operating passband, and the detector response range, so as to improve the spectral purity, time mode matching degree, and multiphoton interference visibility of the output compressed state.

[0005] Furthermore, the first input terminal of the 2×2 lithium niobate intensity modulator is connected to the pulsed single-mode compressed state output by the quantum light source module, the second input terminal is connected to the light field returned by the closed loop, the first output terminal is connected to the detection link, and the second output terminal is connected to the closed loop; the coupling ratio of the 2×2 lithium niobate intensity modulator is controlled at high speed by an external radio frequency signal to achieve programmable coupling between the input light field and the loop light field at each time step.

[0006] Furthermore, the closed loop includes an adjustable fiber delay line, which is used to set the time pattern interval. Δt This makes the pulse period of the pulse pump light... T rep and Δt satisfy T rep = Δt or T rep =n· Δt The synchronization constraint relationship ensures that different pulse time modes can be distinguished and interfere with each other within a preset time window.

[0007] Furthermore, it also includes a phase stabilization system, which splits the auxiliary light output from the loop through a wavelength division multiplexing module and sends it to a photodetector. The electrical signal is input to a lock-in amplifier, which then performs feedback control on the piezoelectric ceramic phase shifter to compensate for the slow-drift phase of the loop and stabilize the interference conditions.

[0008] Furthermore, the phase-stabilized system employs classical continuous light with reverse input for loop phase stabilization: the wavelength of the continuous laser is different from the output band of the single-mode compressed state and falls into the independent channel of the wavelength division multiplexing module, and its input direction is opposite to the propagation direction of the quantum light, so as to reduce crosstalk to quantum sampling and improve the stability signal-to-noise ratio.

[0009] Furthermore, the photon number detection and counting module achieves 1×N beam splitting and parallel detection by multiple detectors through an optical fiber splitter, so that when any single photon detector records a photon event, the event is mapped to photon detection in the corresponding time mode, thereby realizing multi-photon number pseudo-resolution detection and effective coincidence counting in dense time mode under the single detector recovery time limit.

[0010] Furthermore, the measurement and control and data processing module obtains the adjacency matrix A of the graph in the dense subgraph task, performs Takagi-Autonne decomposition on A to obtain the parameter set required for graph encoding, and encodes the parameter set into the compression degree of the quantum light source module and the electro-optic modulation parameters of the quantum interference module; wherein, the number of vertices of the graph is equal to the number of time modes, and the number of detected photons is equal to the number of vertices of the output dense subgraph seed graph.

[0011] Furthermore, after performing statistical analysis on the coincidence count sampling data to obtain a seed graph, the measurement and control and data processing module further expands the seed graph on the original graph through classical random search or heuristic optimization, and improves the density index by iteratively adding and deleting vertices, thereby obtaining the final dense subgraph.

[0012] The present invention also provides a time-domain Gaussian boson sampling method, using the above-described time-domain Gaussian boson sampling system, characterized by comprising the following steps: S1, Generate or read the graph adjacency matrix A for the target problem, and perform Takagi-Autonne decomposition on the adjacency matrix A to obtain the parameter set required for graph encoding; S2, map the parameter set to the compression degree of the quantum light source module and the modulation parameters of the quantum interference module, so that the time pattern evolution is equivalent to the target unitary matrix or its corresponding Gaussian transformation; S3, within a preset time window, multiphoton coincidence counting sampling data is collected by the photon number detection and counting module; S4. Perform preprocessing, coincidence counting, and post-processing analysis on the sampled data, and output the sampled distribution and its corresponding task results.

[0013] The beneficial effects of this invention are as follows: First, by using lithium niobate as a unified material platform, high-quality quantum light source generation and high-speed electro-optic modulation control are tightly integrated, avoiding the high loss and low integration problems caused by the splicing of heterogeneous materials. Second, by utilizing a closed-loop time multiplexing architecture, a large-scale spatial interference network is transformed into multiple cycles of a single fiber loop, greatly reducing hardware size and alignment difficulty. Third, by adopting a 1×N beam splitting and multi-detector parallel acquisition strategy, the bottleneck of single detector dead time counting of dense time patterns is effectively overcome, ensuring the reliability of multi-photon interference statistics. Finally, the hardware and software collaborative data processing link opens up the entire process from graph data encoding to quantum sampling to result output, enabling the device not only to verify quantum superiority but also to be practically used for solving complex combinatorial optimization tasks such as dense subgraphs. In one embodiment, the center wavelength and bandwidth of the bandpass filter or wavelength division filter unit are set according to at least one of the spectrum of the pulse pump light, the phase matching bandwidth of the nonlinear waveguide quantum light source, the time mode interval, the modulator operating passband, and the detector response range, in order to improve the spectral purity, time mode matching degree, and multiphoton interference visibility of the output compressed state. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the structure of the present invention; Figure 2 This is a schematic diagram of the quantum light source module; Figure 3 This is a schematic diagram of the quantum interference module. Figure 4 This is a schematic diagram of the photon number detection and counting module. Figure 5 This is a structural diagram of the measurement, control, and data processing module; Figure 6 This is a schematic diagram of the structure of a stable phase system; Figure 7 This is a flowchart illustrating the time stamping and coincidence counting process in TCSPC technology. Figure 8 This is a schematic diagram illustrating the process of decomposing the adjacency matrix A into Takagi-Autonne and mapping device parameters. Figure 9 A schematic diagram of the post-processing workflow for dense subgraphs (seed graph extraction and random search expansion). Figure 10 A schematic diagram of the system initialization and timing synchronization calibration process; Figure 11 A comparison diagram of the experimental two-photon probability distribution and the theoretical two-photon mode probability distribution; Figure 12 The image shows the TVD results obtained from the equivalent transmittance parameter scan. Figure 13 A visual structural diagram of a 20-node undirected weighted graph; Figure 14 A visual structural diagram of a four-vertex subgraph; Figure 15 A visual structural diagram of the densest subgraph of eight nodes; Figure 16 A visual structural diagram of a nine-node subgraph; Figure 17 A visual structural diagram of the densest subgraph with ten nodes.

[0015] In the diagram, 1-Quantum light source module; 11-Nonlinear waveguide quantum light source; 12-Pump filter unit; 13-Bandpass filter or wavelength division filter unit; 14-Pulsed laser; 15-Short-pass filter; 16-Tuned filter; 17-99:1 fiber beam splitter; 2-Quantum interference module; 21-2×2 lithium niobate intensity modulator; 22-Closed loop; 221-Tuned fiber delay line; 23-Piezoelectric ceramic phase shifter; 24-1×1 lithium niobate phase modulator; 3-Photon number detection and counting module; 31-Fiber optic splitter; 32-Single photon detector; 33-Time-correlated single photon counting device; 34-Polarization controller; 4-Measurement and control and data processing module; 41-Classical computer; 5-Phase stabilization system; 51-Wavelength division multiplexing module; 52-Photodetector; 53-Lock-in amplifier; 54-Continuous laser. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0017] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0018] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0019] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two elements or the interaction between two elements, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0020] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0021] like Figures 1-17 As shown, the present invention provides a time-domain Gaussian boson sampling system, comprising: The quantum light source module 1, used to generate pulsed single-mode compressed states, includes a nonlinear waveguide quantum light source 11 based on lithium niobate material, a pump filtering unit 12, and a bandpass filter or wavelength division filter unit 13. The bandpass filter or wavelength division filter unit 13 is used to select the target frequency band or target frequency channel and suppress non-target spectral modes. In actual operation, an external pulsed laser injects pump light into the nonlinear waveguide quantum light source 11, generating an output containing a compressed optical field. Subsequently, this optical field passes through the pump filtering unit 12 to filter out residual pump light, and then through the bandpass filter or wavelength division filter unit 13 to select pure single-mode compressed state pulses that meet the requirements of subsequent interference.

[0022] Quantum interference module 2, used to achieve coherent coupling and unitary matrix evolution in the time mode dimension, includes a 2×2 lithium niobate intensity modulator 21 and a closed loop 22 composed of optical fibers and devices. The closed loop 22 connects one output and one input of the 2×2 lithium niobate intensity modulator 21 to form a cyclic time-delay interference structure. A piezoelectric ceramic phase shifter 23 and a 1×1 lithium niobate phase modulator 24 are serially arranged in the closed loop 22 to achieve stable phase and programmable phase modulation, so that the input single-mode compressed state forms multiple interfering time mode outputs after multiple cycles. The compressed state pulse from the light source module enters from the first input of the 2×2 lithium niobate intensity modulator 21. The modulator determines whether the pulse is split into the closed loop 22 or directly output according to the external driving signal. The pulse entering the closed loop 22 undergoes a delay in the optical fiber, is mechanically tuned by the piezoelectric ceramic phase shifter 23 to eliminate the influence of ambient temperature drift, and is electro-optically phase-modulated by the 1×1 lithium niobate phase modulator 24 to inject the target phase. After the delay and phase modulation, the pulse returns to the second input of the 2×2 lithium niobate intensity modulator 21 and couples with the newly injected pulse. This cycle repeats, eventually forming a series of time pattern sequences with specific interference relationships at the output.

[0023] The photon count detection and counting module 3, used to acquire multiphoton coincidence count sampling data within a preset time window, includes an optical fiber splitter 31 and N single-photon detectors 32. The optical fiber splitter 31 splits the output light into 1×N beams to be input in parallel to the N single-photon detectors 32, and the time-correlated single-photon counting device 33 timestamps and counts the coincidence counts of the detection events. The time-mode optical signal after interference first enters the optical fiber splitter 31 and is proportionally divided into N independent optical signals. These N signals are simultaneously input to the N single-photon detectors 32 in operation for parallel detection. When any detector responds and generates an electrical pulse, the time-correlated single-photon counting device 33 immediately records the precise timestamp of the event and jointly correlates the response events of multiple detection channels within the preset time window to calculate the multiphoton coincidence count result.

[0024] The measurement, control, and data processing module 4 is used to encode graph data, control the modulator, stabilize the loop, preprocess and postprocess the sampled data, and output the task results. The module maps the target problem to the setting of the compression degree of the quantum light source module 1 and the modulation parameters of the quantum interference module 2, and outputs the task results based on coincidence counting sampling. The classical computer 41 first receives the graph theory problem data to be solved, converts it into the pump power configuration parameters of the light source and the driving waveform sequence of the 2×2 lithium niobate intensity modulator 21 and the 1×1 lithium niobate phase modulator 24, and sends them down for execution. Simultaneously, the computer reads the feedback signal of the lock-in amplifier in real time to adjust the piezoelectric ceramic phase shifter 23 to ensure loop phase locking. During the sampling phase, the computer receives the timestamp data uploaded by the time-correlated single-photon counting device 33, performs dark counting elimination and channel alignment, then statistically analyzes the photon distribution under each time mode, and finally inversely derives and outputs candidate solutions to the graph theory problem based on the distribution characteristics.

[0025] This invention achieves the following technical effects through the aforementioned system: First, by using lithium niobate as a unified material platform, it tightly integrates high-quality quantum light source generation with high-speed electro-optic modulation control, avoiding the high loss and low integration problems caused by the splicing of heterogeneous materials; second, by utilizing a closed-loop time-multiplexing architecture, it transforms a large-scale spatial interference network into multiple cycles of a single fiber loop, greatly reducing hardware size and alignment difficulty; third, by adopting a 1×N beam splitting and multi-detector parallel acquisition strategy, it effectively overcomes the counting bottleneck of single detector dead time for dense time modes, ensuring the reliability of multi-photon interference statistics; finally, the hardware-software collaborative data processing link connects the entire process from graph data encoding to quantum sampling and result output, enabling the device not only to verify quantum superiority but also to be practically used for solving complex combinatorial optimization tasks such as dense subgraphs. In one embodiment, the center wavelength and bandwidth of the bandpass filter or wavelength division filter unit 13 are set according to at least one of the spectrum of the pulse pump light, the phase matching bandwidth of the nonlinear waveguide quantum light source 11, the time mode interval, the modulator operating passband, and the detector response range, in order to improve the spectral purity, time mode matching degree, and multiphoton interference visibility of the output compressed state.

[0026] During the actual system calibration phase, the measurement, control, and data processing module 4 first acquires and evaluates the real-time spectral characteristics of the pump laser and the output characteristics of the nonlinear waveguide quantum light source 11. Subsequently, based on the preset time mode interval and the operating passband of the subsequent 2×2 lithium niobate intensity modulator 21, the center wavelength position and bandwidth of the bandpass filter or wavelength division multiplexing filter unit 13 are dynamically adjusted. This adjustment process ensures that only the spectral components that best match the system timing and hardware response can pass through, completely isolating sidelobes, stray spontaneous emissions, and non-target frequency channels from the interferometric network.

[0027] This invention, through the aforementioned parameter linkage setting mechanism, effectively eliminates the multispectral mode noise accompanying the generation of the compressed state light source, fundamentally avoiding crosstalk and interference ambiguity caused by different spectral modes cycling in the closed loop 22. This high-purity single-mode output not only significantly improves the visibility of multiphoton interference but also enhances the capture efficiency of the subsequent single-photon detector 32 for effective photon events, thereby providing a quantum input state with high fidelity and high consistency for Gaussian boson sampling.

[0028] In one specific embodiment, the single-photon detector 32 is a superconducting nanowire single-photon detector. In actual system deployment, this detector is encapsulated inside a liquid helium-free closed-loop refrigerator, maintained in an extremely low temperature environment of approximately 2.2 Kelvin, and is provided with a constant DC bias current by the measurement and control and data processing module 4, allowing it to operate at an avalanche triggering critical point just below the nanowire's critical current, thus possessing extremely high response sensitivity to weak single-mode squeezed photons. When the photon distributed by the fiber optic splitter 31 arrives at the single-photon detector 32, the superconducting nanowire instantly absorbs the photon energy and undergoes local quenching, generating an electrical pulse signal with an extremely fast rise time. This signal is transmitted through a high-frequency coaxial cable from the refrigerator to the time-correlated single-photon counting device 33. Simultaneously, the system's built-in dead-time feedback circuit briefly blocks the bias current of this channel to prevent afterpulse crosstalk, ensuring that photon events in each time mode are recorded independently and accurately.

[0029] This invention fully leverages the high detection efficiency, extremely low dark count rate, and picosecond-level time jitter of a single-photon detector 32 as the core detection device. This hardware choice perfectly matches the high-resolution requirements of time-domain Gaussian boson sampling for dense time modes, effectively suppresses the masking of higher-order quantum interference features by environmental background noise, and ensures the accuracy of the signal-to-noise ratio and time assignment of multiphoton coincidence counting. This provides high-purity raw data support for the accurate solution of subsequent graph theory problems.

[0030] In one specific embodiment, the quantum light source module 1 includes a pulsed laser 14, a short-pass filter 15, a nonlinear waveguide quantum light source 11, a pump filter unit 12, a bandpass filter or wavelength division filter unit 13 arranged in sequence, and finally outputs a pulsed single-mode compressed state.

[0031] Among them, the nonlinear waveguide quantum light source 11 is a periodically polarized lithium niobate waveguide.

[0032] In actual operation, the pulsed laser 14 first outputs pump light with a specific wavelength and pulse period. This pump light then enters a short-pass filter 15 to filter out short-wavelength stray radiation generated by the light source itself, thereby improving the spectral quality of the pump light. Subsequently, the high-purity pump light is coupled into a periodically polarized lithium niobate waveguide, which serves as a nonlinear waveguide quantum light source 11, and a compressed optical field is generated using the second-order nonlinear effect of the lithium niobate material. This compressed optical field then enters the pump filtering unit 12 to completely strip away any remaining strong pump light. Finally, the compressed optical field, containing only the signal light, passes through a bandpass filter or wavelength division multiplexing filter unit 13 to precisely select the target frequency channel that meets the requirements of the subsequent time mode interval and interferometric network, ultimately outputting a pulsed single-mode compressed state with high spectral purity and high interferometric visibility.

[0033] In one specific embodiment, an adjustable filter 16 and a 99:1 fiber optic beam splitter 17 are also provided between the quantum light source module 1 and the 2×2 lithium niobate intensity modulator 21.

[0034] The tunable filter 16 and the 99:1 fiber beam splitter 17 are used in the actual optical path setup. The tunable filter 16 finely adjusts the center wavelength and bandwidth based on the actual operating bandwidth of the 2×2 lithium niobate intensity modulator 21 and the current time mode interval of the system, completely filtering out residual sideband noise and ensuring that the single-mode compressed state injected into the interference loop reaches the optimal spectral type. Subsequently, the optical field enters the 99:1 fiber beam splitter 17, which splits the finely filtered compressed optical field into two paths. 99% of the optical power serves as the main signal and continues to propagate forward, being injected into the 2×2 lithium niobate intensity modulator 21 for Gaussian boson sampling. The remaining 1% of weak optical power is extracted to an external conventional photodetector or spectrometer for real-time monitoring of the light source's output power and spectral state without interfering with the quantum evolution process of the main optical path.

[0035] This invention achieves ultimate purification of the input quantum state and non-destructive monitoring throughout the entire process by adding an adjustable filter 16 and a 99:1 fiber beam splitter 17 between the light source and the interference module. The adjustable filter 16 gives the system the ability to dynamically adjust the spectrum to adapt to different modulator parameters and experimental requirements, making up for the lack of flexibility of fixed filters; while the 99:1 fiber beam splitter 17, without significantly losing precious quantum signals, opens up a real-time optical field state feedback bypass, enabling the measurement and control system to monitor the stability of the light source at any time and provide early warnings, greatly improving the convenience of overall system debugging and the observability of the operation process.

[0036] In one embodiment, the first input of the 2×2 lithium niobate intensity modulator 21 is connected to the pulsed single-mode compressed state output by the quantum light source module 1, the second input is connected to the light field returned by the closed loop 22, the first output is connected to the detection link, and the second output is connected to the closed loop 22. The coupling ratio of the 2×2 lithium niobate intensity modulator 21 is controlled at high speed by an external radio frequency signal to achieve programmable coupling between the input light field and the loop light field at each time step. In actual operation, at the initial moment of each time step, an external arbitrary wave generator sends a radio frequency signal to change the internal interference state of the 2×2 lithium niobate intensity modulator 21, thereby setting a specific transmission and reflection ratio. At this time, the newly injected pulsed single-mode compressed state enters from the first input, while the light pulse that has completed its cycle in the closed loop 22 returns from the second input. The two are split and coherently superimposed inside the modulator according to the set ratio. Subsequently, part of the mixed light field is directly output to the detection link through the first output terminal for photon capture, while the other part is re-injected into the closed loop 22 through the second output terminal to start the next round of delay and interference, thereby realizing dynamic and controllable time pattern weaving and matrix evolution.

[0037] In one embodiment, the closed loop 22 includes an adjustable fiber delay line 221 for setting time pattern intervals. Δt During the actual system initialization phase, the measurement and control and data processing module 4, based on the dimension of the target matrix and the dead time of the single-photon detector 32, sends tuning commands to the tunable fiber delay line 221, precisely stretching or shortening the physical length of the internal fiber. This establishes, on a macroscopic scale, the absolute time reference required for the light field to complete one cycle in the closed loop 22, thereby ensuring the pulse period of the pulsed pump light is... T rep and Δt satisfy T rep = Δt or T rep =n· ΔtThe synchronization constraint relationship is established. At this time, the measurement and control and data processing module 4 synchronously triggers and controls the pulsed laser 14, ensuring that its output beat is strictly locked on the aforementioned time reference. When the newly generated pulsed single-mode compressed state arrives at the 2×2 lithium niobate intensity modulator 21, it perfectly meets the previous pulse that has undergone delay and phase modulation within the closed loop 22, achieving precise timing alignment. This ensures that different pulse timing modes can be distinguished and interfere with each other within the preset time window. Thus, within the preset time window, the photon number detection and counting module 3 can clearly distinguish each independent time slice, avoiding physical crosstalk and misjudgment caused by timing overlap between adjacent modes, while ensuring the strict phase matching required for coherent superposition, thereby accurately capturing multiphoton coincidence counting events with complex quantum interference characteristics.

[0038] This invention, by introducing an adjustable fiber delay line 221 and establishing strict timing synchronization constraints, achieves flexible customization and precise control of the time mode in a time-domain Gaussian boson sampling system. This design, on the one hand, endows the system with a strong adaptability to the light source pulse period and detector dead time, eliminating the system bottleneck caused by differences in hardware response speed; on the other hand, it fundamentally eliminates crosstalk ambiguity between time modes, significantly improving the visibility of multiphoton interference and the fidelity of the sampled data, laying a reliable physical foundation for the accurate solution of subsequent complex graph theory problems.

[0039] In one embodiment, a phase stabilization system 5 is also included. This system splits the auxiliary light output from the loop via a wavelength division multiplexing module 51 and sends it to a photodetector 52. During actual operation, the measurement, control, and data processing module 4 generates a pilot light with a wavelength different from the signal light and injects it into the closed loop 22. This pilot light cycles with the signal light and is then output. The wavelength division multiplexing module 51 separates this auxiliary light from the optical path to prevent it from interfering with subsequent quantum detection, and focuses it into the photodetector 52 to convert it into a level signal. This electrical signal is input to a lock-in amplifier 53, which provides feedback control to the piezoelectric ceramic phase shifter 23. The lock-in amplifier 53 extracts the low-frequency phase drift component caused by ambient temperature or mechanical vibration from the electrical signal, calculates the error value, and generates a corresponding compensation voltage signal in real time, outputting it to the piezoelectric ceramic phase shifter 23 to drive it to produce a small mechanical deformation. This compensates for the slow-drift phase of the loop and stabilizes the interference conditions. Through this continuous closed-loop feedback, the optical cavity length of the closed loop 22 is dynamically locked at the optimal operating point, ensuring that the return light field and the injected light field participating in each round of interference always maintain a constant phase difference, thereby maintaining a high-visibility quantum interference effect during long-term sampling.

[0040] This invention constructs a closed-loop active optical locking mechanism by introducing a phase-stabilized system 5, effectively overcoming the slow change in optical path length caused by environmental disturbances during long-term operation of the fiber optic closed loop 22. This design not only ensures the long-term stability and repeatability of the time-mode interferometry network and avoids sampling data distortion caused by phase drift, but also significantly reduces the dependence on the harsh laboratory constant temperature and vibration isolation environment, improving the system's robustness and continuous operation capability under actual complex working conditions.

[0041] In one embodiment, the phase-stabilizing system 5 uses classical continuous light with reverse input for loop phase stabilization: In actual system setup, to avoid interfering with the extremely weak quantum signal light, an external ordinary continuous laser 54 is introduced as a pilot light source. It is injected into the closed loop 22 via a fiber optic circulator at the loop output, ensuring its propagation path is completely opposite to the quantum squeezed state. The wavelength of the continuous laser 54 differs from the output band of the single-mode squeezed state and falls into the independent channel of the wavelength division multiplexing module 51. The measurement, control, and data processing module 4 sets the operating wavelength of the continuous laser 54 to be far from the band where the quantum light is located. Thus, when the reverse light circulates within the closed loop 22 and outputs again, the wavelength division multiplexing module 51 can easily intercept it like a sieve and guide it into a specific channel. Furthermore, its input direction is opposite to the propagation direction of the quantum light to reduce crosstalk to quantum sampling and improve the stability signal-to-noise ratio. This reverse and different wavelength design fundamentally blocks the impact of classical strong light on the single-photon detector 32, while using the reverse optical path to monitor the same physical optical path drift, making the phase error signal obtained by the photodetector 52 purer and clearer.

[0042] This invention employs classical continuous light of opposite wavelengths for phase stabilization, cleverly utilizing wavelength division multiplexing and directional isolation techniques. Without occupying quantum channel resources, it perfectly resolves the conflict between strong classical light and weak quantum light. This scheme protects the highly vulnerable single-photon detector 32 from stray strong light excitation and significantly improves the signal-to-noise ratio of the error signal received by the lock-in amplifier 53, thereby achieving high-precision, low-crosstalk closed-loop phase locking and ensuring the long-term reliability and accuracy of time-domain Gaussian boson sampling data.

[0043] In one embodiment, the photon number detection and counting module 3 achieves 1×N beam splitting and parallel detection by multiple detectors through an optical fiber splitter 31. In actual operation, the photon stream overflowing from the first output of the 2×2 lithium niobate intensity modulator 21 first enters the optical fiber splitter 31, is uniformly split into N independent optical signals, and is synchronously distributed to an array composed of multiple single-photon detectors 32. This ensures that when any single-photon detector 32 records a photon event, these detectors are arranged side by side in space. Once a detector in the array is triggered, the generated electrical pulse is immediately transmitted to the time-correlated single-photon counting device 33 for high-precision timestamp marking. The event is mapped to photon detection in the corresponding time mode. The measurement, control, and data processing module 4 accurately analyzes the specific time slice to which the timestamp belongs based on the preset synchronization sequence and delay calibration, seamlessly converting the multi-channel detection response in physical space into the photon distribution state in the time domain. Thus, under the single detector recovery time constraint, multi-photon number pseudo-resolution detection and effective coincidence counting in dense time mode are achieved. By employing this space-for-time hardware reuse strategy, even if two or more photons arrive in succession within a very short time interval, they can be captured separately by different detectors that are in a ready state, completely breaking the dead time bottleneck of a single detector, thereby accurately recording high photon coincidence events.

[0044] This invention cleverly resolves the physical contradiction between high-density time modes and detector dead time by using an optical fiber splitter 31 in conjunction with a multi-detector parallel detection mechanism. This pseudo-resolution detection architecture not only significantly increases the system's capture probability of high-photon-number events and greatly expands the available dimensions of the time-domain Gaussian boson sampling matrix, but also drastically reduces the data loss rate caused by detector saturation, providing a solid guarantee for extracting high-quality quantum interference probability distributions.

[0045] In one embodiment, a polarization controller 34 is also disposed upstream of the single-photon detector 32. In the actual optical path, after the interference light field output by the quantum interference module 2 is split into 1×N beams by the fiber splitter 31, the optical signals of each branch pass through the polarization controller 34 connected in series on their respective optical paths before entering the corresponding single-photon detector 32. The polarization controller 34 is used to adjust the polarization state of the input light field to align it with the polarization response sensitive axis of the single-photon detector 32, so as to maximize the detection efficiency.

[0046] In one embodiment, the measurement, control, and data processing module 4 obtains the adjacency matrix A of the graph in the dense subgraph task, performs Takagi-Autonne decomposition on A to obtain the parameter set required for graph encoding. Specifically, the classical computer 41 first receives the actual graph theory data to be solved and constructs a symmetric adjacency matrix. Then, it calls the built-in efficient numerical algorithm to perform matrix diagonalization processing, extracts the eigenvalues ​​and phase angle information that can characterize the graph topology, and packages them into an instruction package that can be recognized by hardware. The parameter set is then encoded into the compression degree of the quantum light source module 1 and the electro-optic modulation parameters of the quantum interference module 2. During this process, the measurement, control, and data processing module 4 dynamically adjusts the driving current of the pulsed laser 14 to change the intensity of the compressed light field according to the magnitude of the eigenvalues ​​obtained by analysis. At the same time, it sends precise radio frequency control voltage sequences to the 1×1 lithium niobate phase modulator 24 and the 2×2 lithium niobate intensity modulator 21, seamlessly mapping the complex graph structure information into the physical evolution trajectory of the light field. In this system, the number of vertices in the graph equals the number of time patterns. This means that the number of time slices set by the adjustable fiber delay line 221 directly corresponds to the total number of nodes in the network to be analyzed, transforming the macroscopic graph dimension into the microscopic time-domain pulse sequence length. Furthermore, the number of detected photons equals the number of vertices in the output dense subgraph seed graph. After the sampling operation is completed, the photon count and detection module 3 summarizes the output results of the single-photon detector 32, and the measurement, control, and data processing module 4 statistically analyzes the frequency and distribution of photons within a specific time window. High-photon-count coincidence events are directly decoded into the most densely connected subnetwork node set in the original graph, thus quickly outputting the dense subgraph seed graph.

[0047] This invention establishes a complete computational closed loop—from graph theory data input to quantum state evolution and graph theory result output—through deep integration of classical computer 41 and quantum hardware. This mapping mechanism fully leverages the scalability of time-domain multiplexing architecture, enabling finite physical optical paths to characterize large-scale graph structures, effectively avoiding the exponential time complexity bottleneck of classical algorithms when solving NP-hard problems in dense subgraphs. Simultaneously, based on the intuitive mapping relationship between photon number and vertex number, it significantly reduces the difficulty of post-processing sampled data, substantially improving the solution efficiency and practical application value of complex network analysis.

[0048] In one embodiment, after the measurement, control, and data processing module 4 performs statistical analysis on the coincidence count sampling data to obtain the seed graph, in actual operation, the classical computer 41 collects multi-channel timestamp data uploaded by the time-correlated single-photon counting device 33, calculates the coincidence probability of high photon counts under each time pattern combination, and directly translates the time pattern index corresponding to the probability peak into the initial node set of the original graph, establishing the preliminary boundary of the dense subgraph. The seed graph is further expanded on the original graph through classical random search or heuristic optimization. Subsequently, the classical computer 41 calls a pre-written heuristic algorithm to evaluate the connection weights of candidate nodes around the seed graph based on the adjacency matrix A of the original graph, attempting to include edge nodes in the set or remove internal sparse nodes. The density index is improved by iteratively adding and deleting vertices, thereby obtaining the final dense subgraph. During this iterative process, the classical computer 41 continuously recalculates the edge density and other evaluation indices of the current subgraph, retaining the optimal solution for density improvement after each iteration until the density index converges to an extreme value, finally outputting the most tightly connected core node group in the network.

[0049] This invention constructs a quantum-classical hybrid processing architecture by combining the fast global search of quantum sampling with the refined local optimization of classical computation. This design leverages the inherent advantage of quantum interference networks in rapidly locking high-density core regions within a vast solution space, while also utilizing the high controllability of classical algorithms in local adjustments. This effectively compensates for the insufficient accuracy of pure quantum sampling due to hardware noise or dimensionality limitations, thereby efficiently approximating the optimal solution in a shorter computation time and significantly improving the accuracy and practicality of dense subgraph mining in large-scale complex networks.

[0050] The present invention also provides a time-domain Gaussian boson sampling method, which uses the above-described time-domain Gaussian boson sampling system and includes the following steps: S1, Generate or read the graph adjacency matrix A for the target problem, and perform Takagi-Autonne decomposition on the adjacency matrix A to obtain the parameter set required for graph encoding; In actual execution, the classical computer 41 receives the externally input network data to be solved and constructs a symmetric adjacency matrix A, and then calls the built-in efficient numerical algorithm to perform diagonalization decomposition on the matrix, extracting the eigenvalues ​​and phase angle parameters that can accurately characterize the graph topology, and packaging them into a modulation control instruction set that can be directly recognized by hardware.

[0051] S2, the parameter set is mapped to the compression degree of the quantum light source module 1 and the modulation parameters of the quantum interference module 2, so that the time mode evolution is equivalent to the target unitary matrix or its corresponding Gaussian transformation; the measurement, control and data processing module 4 dynamically adjusts the driving parameters of the pulsed laser 14 according to the received instruction set to control the intensity of the compressed light field, and at the same time sends a precise radio frequency control voltage sequence to the 2×2 lithium niobate intensity modulator 21 and the 1×1 lithium niobate phase modulator 24, so that the light pulse injected into the closed loop 22 perfectly reproduces the Gaussian transformation characteristics of the target graph structure in the cycle evolution.

[0052] S3, within a preset time window, the photon number detection and counting module 3 collects multi-photon coincidence counting sampling data; the single-photon detector 32 array captures photon events overflowing from the interference network in real time and converts them into high-speed electrical pulses; the time-correlated single-photon counting device 33 then timestamps these pulses with high precision, converting the massive and random quantum interference results into a time-series data stream that can be computed.

[0053] S4. The sampled data is preprocessed, coincidence count statistics are performed, and post-processing analysis is conducted to output the sampling distribution and its corresponding task results. The classical computer 41 first performs time window alignment and noise filtering on the collected timestamp data, then performs multi-channel coincidence count statistics to extract higher-order correlation features and probability distributions, and finally maps the event with the highest photon number coincidence probability back to the original graph space, directly outputting the solution results for specific graph theory problems such as dense subgraphs.

[0054] The time-domain Gaussian boson sampling method provided by this invention achieves an efficient transformation of complex graph theory problems into time-domain quantum light field evolution through a clear algorithmic decomposition and physical mapping process. This method fully leverages the advantages of time-domain multiplexing architecture, transforming large-scale matrix operations into high-frequency cyclic evolution within a single closed loop, significantly reducing the hardware scale threshold for realizing high-dimensional quantum computing. Simultaneously, the fully automated measurement and control and systematic data processing ensure the fidelity and reliability of the sampling results, providing a practical and feasible technical path for the standardized implementation of quantum computing in real-world applications such as graph theory optimization.

[0055] In one embodiment, such as Figure 10As shown, the system performs initialization and timing synchronization calibration. The measurement, control, and data processing module 4, based on the dimension of the target matrix and the dead time of the single-photon detector 32, sends tuning commands to the adjustable fiber delay line 221 to establish the time mode interval Δt required for the light field to cycle once in the closed loop 22. In actual operation, the classical computer 41 first analyzes the scale of the problem to be solved, calculates the total number of required time modes, and, considering the maximum reset period of the single-photon detector 32, calculates the optimal time mode interval Δt without crosstalk. This is then converted into electronic control commands and sent to the piezoelectric motor inside the adjustable fiber delay line 221 to precisely adjust the physical stretch of the fiber. Simultaneously, the pulsed laser 14 is triggered, ensuring that the pulse period T_rep strictly satisfies the synchronization constraint relationship of T_rep=Δt or T_rep=n·Δt, thus completing the locking of the time domain reference. At this time, the measurement and control and data processing module 4 generates a high-frequency clock signal and hardwires it with the internal trigger of the pulsed laser 14, forcing the output beat of the pump light to be synchronized with the delay period of the closed loop 22 at the nanosecond level, ensuring that each newly generated pulsed single-mode compressed state can arrive at the input port of the 2×2 lithium niobate intensity modulator 21 on time.

[0056] This invention establishes an unambiguous physical time reference for time-domain Gaussian boson sampling by introducing precise system initialization and timing synchronization calibration in the pre-sampling stage. This step effectively avoids the overlap and confusion of adjacent time modes during the interferometry and detection stages, while maximizing the utilization of the detector's response window, laying a solid hardware triggering foundation for subsequent high-fidelity multiphoton interferometry and coincidence counting.

[0057] In one embodiment, during parameter mapping and optical field evolution, the measurement, control, and data processing module 4 continuously operates the phase-stabilizing system 5, which separates the classical continuous light injected into the closed loop 22 by the wavelength division multiplexing module 51 and sends it to the photodetector 52. During long-term sampling cycles, minute fluctuations in ambient temperature and mechanical micro-vibrations can cause sub-micron-level deformation of the optical fiber in the closed loop 22. The measurement, control, and data processing module 4 triggers an external continuous laser to emit a pilot light with a wavelength completely different from and opposite in direction to the quantum signal light into the loop. This pilot light carries optical path drift information and cycles along with the signal light. The lock-in amplifier 53 extracts low-frequency phase drift errors in real time and feeds back to control the piezoelectric ceramic phase shifter 23 to dynamically compensate for slow optical path drift, ensuring long-term phase stability of multi-time mode interference. The photodetector 52 converts the intensity fluctuation of the pilot light into a weak AC voltage signal and inputs it into the lock-in amplifier 53. The amplifier uses the reference frequency to perform coherent demodulation, filter out high-frequency white noise, accurately extract the error envelope representing the slow drift of the environment, and convert it into a reverse correction voltage applied to the piezoelectric ceramic phase shifter 23, causing it to produce micron-level stretching to counteract the natural deformation of the optical fiber.

[0058] This invention constructs an adaptive closed-loop optical path locking mechanism by implementing dynamic phase-stable control during optical field evolution. This design effectively overcomes the phase random walk problem of the fiber closed loop 22 during long-term continuous sampling, ensuring that multiple time modes can maintain the preset phase relationship after dozens or even hundreds of cyclic interferences, greatly improving the long-term stability and repeatability of the Gaussian boson sampling distribution.

[0059] In one embodiment, during the acquisition of multiphoton coincidence count sampling data, the measurement and control and data processing module 4 simultaneously records the optical loss parameters of the closed loop 22 and the dark count rate of the single-photon detector 32. During actual data acquisition, the photon number detection and counting module 3 sends a massive number of electrical pulses to the time-correlated single-photon counting device 33 to generate raw timestamps, while the classical computer 41 simultaneously reads the pre-calibrated insertion loss table of each optical element and the background dark count distribution of the single-photon detector 32, establishing a channel transmission model for the current hardware state. In the background, background noise is subtracted and detection efficiency is normalized in real time on the raw timestamp data, and it is determined whether the current accumulated sampling rounds have reached the preset statistical confidence level requirement. If not, cyclic sampling continues. The classical computer 41 uses the aforementioned channel model to verify the authenticity of each timestamp in the background, eliminate false alarms that may be caused by dark counting, and mathematically compensate for the probability of photon loss due to fiber coupling loss. At the same time, it dynamically calculates the confidence interval of the histogram of the current higher-order correlation events. If the statistical significance does not reach the set threshold, it automatically extends the sampling time and adds data collection batches.

[0060] This invention achieves real-time purification of raw quantum data into a high-fidelity statistical distribution by introducing a companion-type data correction and sampling control mechanism. This step effectively removes the masking effect of hardware imperfections (such as dark counting and transmission loss) on quantum interference characteristics, and optimizes the total sampling time through adaptive confidence evaluation, avoiding waste of computational resources and ensuring the physical accuracy and computational availability of the output dataset.

[0061] In one embodiment, after extracting the photon distribution events with the highest probability according to counting statistics as the seed graph, the classical computer 41 further invokes a heuristic optimization algorithm to iteratively add and delete vertices on the boundaries of the seed graph on the original graph. When quantum sampling provides an initial high-density node set, due to potential misjudgments of individual edge nodes caused by detection noise or a limited number of sampling times, the classical computer 41 imports the seed graph into a local analysis engine to evaluate external nodes adjacent to the seed graph in the original graph, calculating the impact of merging them or removing weakly connected internal nodes on the overall edge density. The subgraph density index is continuously evaluated and improved until convergence to a global or local optimum, ultimately outputting an accurate dense subgraph result. In each iteration, the classical computer 41 dynamically updates the candidate node list and calculates the average degree and other density evaluation functions in real time using a greedy strategy or simulated annealing algorithm. The topological change is retained only when the subgraph density produces a positive gain. Convergence is determined when the density no longer increases after multiple consecutive iterations, and the final node set is mapped to the actual physical labels in the original graph and output.

[0062] This invention integrates the global sampling advantage of quantum hardware with the local fine-grained search capability of classical heuristic algorithms, constructing a complementary quantum-classical hybrid computing architecture. This scheme effectively compensates for the insufficient fine-grainedness of pure quantum sampling due to hardware limitations and noise, enabling it to approximate the theoretical optimal solution of NP-hard problems with extremely high efficiency. It significantly enhances the solution accuracy and engineering practical value of time-domain Gaussian boson sampling systems in real-world complex network analysis tasks.

[0063] refer to Figure 7 This diagram illustrates the time-correlated single-photon counting device 33's technology process for time marking and coincidence counting statistics. The diagram includes two core processes: the single-photon counting process and the time-correlation (coincidence event) process. In the single-photon counting process, photons first enter a superconducting nanowire single-photon detector. The detector converts the photon signal into an electrical pulse signal. After processing by a subsequent processing module, the electrical pulses are counted using the "pulse accumulation counting" principle, ultimately outputting the statistical result of the single-photon count. In the time-correlation process, two photons enter the superconducting nanowire single-photon detector separately, each generating an electrical pulse, which is then processed by the processing module. The time difference Δt between the two electrical pulses is calculated through "time-correlation" analysis. If Δt is less than a preset window, it is determined to be a coincidence event. This determination result is recorded by a multi-channel coincidence technology acquisition card for subsequent statistical analysis. The entire process clearly presents the complete process from photon detection to single-photon counting and multi-channel coincidence event determination, demonstrating the key aspects of the time-correlation single-photon counting device 33's technology in time marking and coincidence counting.

[0064] Reference Appendix Figure 8This figure illustrates the process of mapping the graph adjacency matrix A to Takagi-Autonne decomposition and device parameters. First, the graph's adjacency matrix is ​​input into the "algorithm and mapping layer," which uses Takagi-Autonne decomposition as its mathematical core, decomposing the adjacency matrix into three key parameters: singular values ​​λ. i The graph contains the number of vertices M and the unitary matrix U. These parameters are then mapped to the corresponding operations in the "device control layer": singular values ​​λ. i By adjusting parameters such as power, the number of graph vertices M is used to set the number of time modes M, and the unitary matrix U is used to change the splitting ratio of the 2×2 lithium niobate electro-optic modulator, thereby realizing the conversion from graph structure to quantum hardware parameters. Reference Appendix Figure 9 This figure illustrates the post-processing workflow for dense subgraph applications. Starting with the output samples from a time-domain Gaussian boson sampling system, the workflow is divided into two stages: "seed graph extraction" and "random search and expansion optimization." In the seed graph extraction stage, data acquisition begins by collecting sampled data that conforms to the photon number K. Next, a sample-node mapping relationship is constructed, establishing a mapping between time patterns and vertex numbers. Then, seed graph selection is performed, statistically analyzing the sampling results and selecting vertex sets with high-frequency or high-scoring functions. In the random search and expansion optimization stage, the seed graph undergoes classical post-processing, employing classical random search or heuristic search methods. Then, iterative optimization is initiated, determining whether to update the optimal solution. If the conditions are met, the optimal solution is updated and iteration continues; otherwise, the iteration terminates and the optimal dense subgraph is output.

[0065] To verify the overall performance of the time-domain Gaussian boson sampling system and establish a consistency evaluation model between experiments and theory, this embodiment proposes and implements a time-mode encoded Gaussian boson sampling numerical simulation algorithm to reproduce experimental measurement results and statistical characteristics. Due to the low four-photon coincidence count rate in the experiment, this embodiment collects 100,000 two-photon coincidence count samples as a verification dataset and conducts the following verification process: Step 1: Obtain the experimental probability distribution of two-photon modes based on the statistical analysis of two-photon coincidence count samples; Step 2: Calculate the theoretical two-photon mode probability distribution based on the actual system parameters (including light source compression, interference matrix, and detection efficiency, etc.); Step 3: Use Total Variation Distance (TVD) to characterize the distribution difference. The TVD value range is [0,1]. The smaller the value, the better the experiment matches the theoretical model.

[0066] In the theoretical model, the system's equivalent transmittance is initially set to 0.653. A comparison of the experimental two-photon probability distribution and the theoretical two-photon mode probability distribution is shown in the figure below. Figure 11As shown. To further verify the accuracy of the model, a systematic scan of the equivalent transmittance parameter was performed, with values ​​of 1.0, 0.9, 0.8, 0.7, 0.6, and 0.5. For each parameter value, the corresponding theoretical two-photon mode probability distribution was calculated using a numerical simulation algorithm and compared with the experimental distribution. TVD was calculated as a measure of distribution difference, and the results are shown in the figure. Figure 12 As shown in the results, the TVD corresponding to an equivalent transmittance of 0.653 is very close to that of 0.6 and 0.7, and is significantly smaller than that of other parameter values ​​(such as 0.8, 0.9, and 1.0). This indicates that the theoretical model and experimental data agree best when the equivalent transmittance is approximately 0.65 ± 0.05, verifying the rationality of this parameter setting and the accuracy of the numerical simulation model.

[0067] In summary, the following conclusions can be drawn from the comparative analysis of numerical simulation and experiments: 1. The Gaussian boson sampling numerical simulation algorithm based on time-mode coding can accurately characterize the statistical behavior and photon interference properties of the experimental system while taking into account the actual system loss and noise factors.

[0068] 2. The experimental results of the two-photon mode probability distribution are in high agreement with the theoretical simulation. The model and experiment have the best agreement when the equivalent transmittance is about 0.65±0.05.

[0069] 3. This numerical simulation method is reliable in terms of system modeling accuracy and parameter adjustability, and can provide theoretical and computational support for subsequent multiphoton interference experiment design and complex graph theory tasks.

[0070] The constructed time-domain Gaussian boson sampling system consists of a programmable single-mode squeezed state source and a fiber optic loop interferometer. Thanks to its programmability, this system can not only generate and manipulate multimode Gaussian quantum states, but also be used to solve a typical combinatorial optimization problem in graph theory—the dense subgraph problem.

[0071] Introduction to the Dense Subgraph Problem. The dense subgraph problem refers to finding a subset of vertices in a given undirected weighted graph that maximizes the density (sum of weights) of its internal edges. Specifically, let... For an undirected weighted graph, its density is defined as:

[0072] in This represents the total number of vertices. This problem has wide applications in network analysis, community detection, chemical reaction networks, bioinformatics, and financial correlation analysis. The dense subgraph problem is NP-hard in classical computation; its solution complexity increases dramatically with the size of the graph. Quantum algorithms based on Bosonic sampling can naturally encode the adjacency matrix of a graph as a covariance structure of Gaussian states, making the sampling probability directly related to the square of the Haffni determinant of the subgraph. Through this mechanism, time-domain Gaussian Bosonic sampling systems can perform biased sampling of the structure of dense subgraphs at the physical level, thereby accelerating the discovery of the densest subgraph to some extent.

[0073] The flow of a dense subgraph search algorithm based on a time-domain Gaussian boson sampling system. Let the given... Undirected weighted graph of nodes The adjacency matrix is Using Takagi-Autonne decomposition to... Expanded to:

[0074] in for Takagi eigenvalues, Diagonalization function, and It is a unitary matrix. Takagi eigenvalues ​​are encoded into the single-mode compressed state source of the time-domain Gaussian boson sampling system, and the unitary matrix... The fiber optic loop interferometer is encoded into the time-domain Gaussian boson sampling system. Specifically, the programming and operation process of the time-domain Gaussian boson sampling system is as follows: Calculation parameters , making Takagi eigenvalues ​​obtained after Takagi-Autonne decomposition All in Interval. For the resulting unitary matrix. Reck decomposition was performed to obtain a list of propagation rate parameters for the fiber optic loop interferometer. By default, the fiber optic loop interferometer corresponding to the first time mode is a fully transparent interferometer, while the fiber optic loop interferometer corresponding to the last time mode is a fully reflective interferometer. All calculations above are performed on a classical computer.

[0075] The first step of the time-domain Gaussian boson sampling system The compression parameters of a single-mode compressed source are set to...

[0076] The first step of the time-domain Gaussian boson sampling system The propagation rate of the fiber optic loop interferometer is set to... .

[0077] Run the coded boson sampling system, which will sample from the following distribution. in Indicates the first The number of photons measured by the time-mode, and Subgraph The Haffney determinant. This time-domain Gaussian boson sampling system uses a pseudo-photon number-resolved detector, therefore the photon number measured in each time mode takes the value of .

[0078] After performing post-selection on the above sampled data, a total of A sample set of photons was detected in each of the different time modes. Each sample corresponds to an undirected weighted graph. The number of vertices is The subgraph, corresponding to the following method: if Then from Select the first A vertex and its associated edges.

[0079] The Haffni determinant of a subgraph is equal to the number of its perfect matches. The post-selected samples output by the above time-domain Gaussian boson sampling system represent different... The system samples subgraphs with a higher probability of having more perfect matches. Furthermore, the number of perfect matches in a subgraph is positively correlated with the density of the graph. Therefore, the system samples subgraphs with a higher probability of having a large number of perfect matches (i.e., a denser structure, or a denser subgraph). Vertex subgraph.

[0080] The time-domain Gaussian boson sampling system uses a Charikar hybrid algorithm. The above sampling process can only sample dense subgraphs with a relatively high probability, but it cannot guarantee obtaining the densest subgraph. To solve this problem, the classic Charikar greedy subgraph adjustment strategy needs to be integrated into the time-domain Gaussian boson sampling system. Based on the sampled dense subgraph, vertices are dynamically added or removed according to the vertex degree (i.e., the weight of the edges connected to that vertex) to further optimize the subgraph density. The algorithm process is as follows: Through the adjacency matrix of the graph The graph information is encoded into a time-domain Gaussian boson sampling system, and multiple [databases] are generated using the above process. Vertex subgraph sample.

[0081] Select subgraph size , which is the number of fixed points in the target dense subgraph.

[0082] 3) If Then repeatedly delete the corresponding samples The node with the smallest degree in the vertex subgraph (if there are ties, choose randomly) is selected until the number of remaining nodes is [value missing]. .

[0083] 4) If Then repeatedly add the corresponding samples The node with the highest degree in the vertex subgraph (if there are ties, choose randomly) is used until the number of nodes reaches a certain threshold. .

[0084] 5) Output the subgraph with the highest density among the multiple dense subgraphs obtained.

[0085] In this hybrid algorithm, the main role of the time-domain Gaussian boson sampling system is to provide initial candidate samples (i.e., "seeds") for dense subgraphs, and to pre-select samples with high-density structures through quantum sampling. The initial subgraph significantly accelerates the classical optimization process. Subsequently, the Charikar algorithm performs local adjustments based on these initial subgraphs, enabling a comprehensive search of dense subgraphs at different scales.

[0086] Dense Subgraph Application Examples This embodiment applies a time-domain Gaussian boson sampling system to solve graph theory problems, where the graph size (i.e., the number of vertices) is 20 and the constitutive photon number is 4. Based on the aforementioned experimental parameters, the corresponding undirected weighted graph structure is calculated, with an adjacency matrix of size 20×20, which is not fully listed here due to space limitations. For ease of demonstration, the visualization structure of this graph is as follows: Figure 13 As shown (for clarity, self-loop edges at each vertex are omitted in the diagram). Algorithm flow: Step 1: Run the runtime Gaussian boson sampling system to obtain the four-photon coincidence count results for 20 time modes as shown in the table below.

[0087]

[0088] Table 1. Four-photon coincidence count record for 20 time patterns Step 2: Post-process the coincidence count samples and construct the corresponding subgraph structure. For example, the subgraph corresponding to the coincidence count sample [9,11,13,15] contains these four vertices and their corresponding weighted edges. The visualization structure of this subgraph is as follows: Figure 14 As shown. Step 3: Use the obtained four-vertex subgraph as the initial seed to input the classic random search algorithm for dense subgraphs. This algorithm runs on a complete graph with 20 vertices, and optimizes the search for locally and globally optimal dense subgraphs through random perturbation and multiple rounds of iteration. The system records the candidate vertex set, average edge weight, and density index output in each iteration.

[0089] Typical search results: Search results for an eight-node subgraph are as follows Figure 15 As shown, the density of this subgraph is 0.021739, making it the densest subgraph with eight nodes found so far.

[0090] Nine-node subgraph search results are as follows Figure 16 As shown. This subgraph has a density of 0.019889, which is not the densest subgraph; it is only used as an example.

[0091] 10-node subgraph search results Figure 17 As shown, the density of this subgraph is 0.020539, making it the densest subgraph with ten nodes found so far.

[0092] The experimental results above demonstrate that the time-mode encoded time-domain Gaussian boson sampling system can effectively extract and reconstruct complex graph structure information even with a limited number of experimental photons (four-photon coincidence count). Combined with post-processing analysis of the classic dense subgraph algorithm, the subgraphs corresponding to the four-photon samples generated by the system show high consistency with the theoretically optimal dense subgraph in terms of structure density, verifying the feasibility and scalability of boson sampling in graph theory optimization problems. Furthermore, the experimental results also show that: The constructed time-domain Gaussian boson sampling system has the ability to process graph structures with a vertex size of not less than 20.

[0093] By combining with classical algorithms, it is possible to effectively identify and approximate the densest substructure.

[0094] The time-coded Gaussian boson sampling platform can serve as an experimental quantum acceleration framework for solving combinatorial optimization problems, providing a feasible path and technical verification basis for subsequent multiphoton interference-level application research.

[0095] The above description is merely an embodiment and does not constitute any limitation on the present invention. Any person skilled in the art can make many possible variations, modifications, or alterations to the technical solutions of the present invention without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the present invention, should fall within the protection scope of the present invention.

Claims

1. A time-domain Gaussian boson sampling system, characterized in that, include: The quantum light source module (1) is used to generate pulsed single-mode compressed states, including a nonlinear waveguide quantum light source (11) based on lithium niobate material, a pump filter unit (12), and a bandpass filter or wavelength division filter unit (13). The bandpass filter or wavelength division filter unit (13) is used to select the target frequency band or target frequency channel and suppress non-target spectral modes. The quantum interference module (2) is used to realize coherent coupling and unitary matrix evolution in the time mode dimension. It includes a 2×2 lithium niobate intensity modulator (21) and a closed loop (22) composed of optical fibers and devices. The closed loop (22) connects one output end and one input end of the 2×2 lithium niobate intensity modulator (21) to form a cyclic time delay interference structure. In the closed loop (22), a piezoelectric ceramic phase shifter (23) and a 1×1 lithium niobate phase modulator (24) are set in series to realize stable phase and programmable phase modulation, so that the input single-mode compressed state forms multiple mutually interfering time mode outputs after multiple cycles. The photon number detection and counting module (3) is used to acquire multi-photon coincidence count sampling data within a preset time window. It includes an optical fiber splitter (31) and N single-photon detectors (32). The optical fiber splitter (31) splits the output light into 1×N beams to input the N single-photon detectors (32) in parallel. The time-correlated single-photon counting device (33) performs time marking and coincidence count statistics on the detection events. The measurement and control and data processing module (4) is used to encode the graph data, control the modulator, stabilize the loop, preprocess and postprocess the sampled data and output the task results; the measurement and control and data processing module (4) maps the target problem to the setting of the compression degree of the quantum light source module (1) and the modulation parameters of the quantum interference module (2), and outputs the task results based on coincidence counting sampling.

2. The time-domain Gaussian boson sampling system according to claim 1, characterized in that, The center wavelength and bandwidth of the bandpass filter or wavelength division filter unit (13) are set according to at least one of the spectrum of the pulse pump light, the phase matching bandwidth of the nonlinear waveguide quantum light source (11), the time mode interval, the modulator operating passband, and the detector response range, so as to improve the spectral purity, time mode matching degree and multiphoton interference visibility of the output compressed state.

3. The time-domain Gaussian boson sampling system according to claim 1, characterized in that, The first input terminal of the 2×2 lithium niobate intensity modulator (21) is connected to the pulsed single-mode compressed state output by the quantum light source module (1), the second input terminal is connected to the light field returned by the closed loop (22), the first output terminal is connected to the detection link, and the second output terminal is connected to the closed loop (22). The coupling ratio of the 2×2 lithium niobate intensity modulator (21) is controlled at high speed by an external radio frequency signal to realize programmable coupling between the input light field and the loop light field at each time step.

4. The time-domain Gaussian boson sampling system according to claim 1, characterized in that, The closed loop (22) includes an adjustable fiber delay line (221), which is used to set the time pattern interval. Δt This makes the pulse period of the pulse pump light... T rep and Δt satisfy T rep = Δt or T rep =n· Δt The synchronization constraint relationship ensures that different pulse time modes can be distinguished and interfere with each other within a preset time window.

5. The time-domain Gaussian boson sampling system according to claim 1, characterized in that, It also includes a phase stabilization system (5), which sends the auxiliary light output from the loop to the photodetector (52) after being split by the wavelength division multiplexing module (51). Its electrical signal is input to the lock-in amplifier (53), which performs feedback control on the piezoelectric ceramic phase shifter (23) to compensate for the slow drift phase of the loop and stabilize the interference conditions.

6. The time-domain Gaussian boson sampling system according to claim 5, characterized in that, The phase-stabilized system (5) uses classical continuous light with reverse input for loop stabilization: the wavelength of the continuous laser (54) is different from the output band of the single-mode compressed state and falls into the independent channel of the wavelength division multiplexing module (51), and its input direction is opposite to the direction of quantum light propagation, so as to reduce crosstalk to quantum sampling and improve the stability signal-to-noise ratio.

7. The time-domain Gaussian boson sampling system according to claim 1, characterized in that, The photon number detection and counting module (3) achieves 1×N beam splitting and parallel detection of multiple detectors through the fiber optic splitter (31), so that when any single photon detector (32) records a photon event, the event is mapped to the photon detection of the corresponding time mode, thereby realizing multi-photon number pseudo-resolution detection and effective coincidence counting in dense time mode under the single detector recovery time limit.

8. The time-domain Gaussian boson sampling system according to claim 1, characterized in that, The measurement and control and data processing module (4) obtains the adjacency matrix A of the graph in the dense subgraph task, performs Takagi-Autonne decomposition on A to obtain the parameter set required for graph encoding, and encodes the parameter set into the compression degree of the quantum light source module (1) and the electro-optic modulation parameters of the quantum interference module (2); wherein, the number of vertices of the graph is equal to the number of time modes, and the number of detected photons is equal to the number of vertices of the output dense subgraph seed graph.

9. The time-domain Gaussian boson sampling system according to claim 8, characterized in that, The measurement and control and data processing module (4) performs statistical analysis on the coincident count sampling data to obtain a seed graph, and then further expands the seed graph on the original graph through classical random search or heuristic optimization. Iterative addition and deletion of vertices are used to improve the density index, thereby obtaining the final dense subgraph.

10. A time-domain Gaussian boson sampling method, using the time-domain Gaussian boson sampling system as described in any one of claims 1-9, characterized in that, Includes the following steps: S1, Generate or read the graph adjacency matrix A for the target problem, and perform Takagi-Autonne decomposition on the adjacency matrix A to obtain the parameter set required for graph encoding; S2, map the parameter set to the compression of the quantum light source module (1) and the modulation parameters of the quantum interference module (2), so that the time pattern evolution is equivalent to the target unitary matrix or its corresponding Gaussian transformation; S3, within a preset time window, multiphoton coincidence counting sampling data is collected by the photon number detection and counting module (3); S4. Perform preprocessing, coincidence counting, and post-processing analysis on the sampled data, and output the sampled distribution and its corresponding task results.

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