A method and system for topological encoding of quantum teleportation based on projection geometry regulation

Abstract

This invention discloses a topologically encoded quantum teleportation method and system based on projection geometry control. The method uses a projection geometry control module to adjust the projection angle θ (θ=arctan(β_s / β_r), β_r²+β_s²=1) of a topological photonic crystal device, encoding the quantum state to be transmitted as a topological invariant T(θ)=T_max·sin(θ-θ0). The encoded topological state completes Bell state measurement and classical information transmission under topological Chern number protection. The receiving end decodes the topological state into the original quantum state through projection angle synchronization and inverse projection mapping. The projection geometry control module continuously monitors the rate of change of the projection angle and ensures the stability of the topologically encoded state in real time according to the topological stability criterion γ²≥|1−k||∂C / ∂θ|||·h / 2. This invention is the first to integrate projection geometry control with a topologically encoded quantum teleportation system, realizing dynamically controllable topologically protected quantum teleportation, which can be applied to scenarios such as quantum communication networks and the quantum internet.

Description

Technical Field

[0001] This invention relates to the fields of quantum information transmission technology and topological photonics, specifically to a topologically encoded quantum teleportation method and system based on projective geometry manipulation. This invention can be applied to quantum communication networks, quantum repeater nodes, the quantum internet, distributed quantum computing, and high-dimensional quantum state transmission, and is particularly suitable for applications that encode quantum states as topological invariants to achieve decoherence-resistant, high-fidelity quantum teleportation. Background Technology

[0002] Quantum teleportation is one of the core protocols in quantum information science. It transmits a quantum state from one node to another through shared quantum entanglement and classical communication, without requiring the transmission of the physical carrier itself. In recent years, quantum teleportation has expanded from single qubits to multi-particle entangled states, and inter-chip quantum teleportation has been experimentally verified over a 12.3-kilometer optical fiber. However, existing quantum teleportation schemes suffer significant fidelity degradation when faced with environmental perturbations, decoherence, and transmission losses. (i) Existing quantum teleportation schemes lack a unified topology protection mechanism. Existing quantum teleportation schemes primarily rely on entanglement distribution and Bell state measurement to achieve quantum state transmission. The quantum state itself is encoded in its original form within the degrees of freedom of photons or particles (such as polarization, time slice, path, etc.). This encoding method is sensitive to environmental perturbations, and the quantum state is prone to decoherence during transmission. Although there are topology-protected quantum teleportation protocols based on Majorana zero modes and on-chip schemes that load quantum states into topological invariants, existing schemes have not yet systematically integrated topological encoding with projective geometry manipulation. (ii) The quantum state encoding method is fixed and lacks dynamic control. In existing quantum teleportation schemes, the encoding of the quantum state is determined before transmission and cannot be dynamically adjusted during transmission. When channel conditions change or noise characteristics alter, the encoding parameters cannot be adaptively optimized, leading to a decrease in transmission fidelity. Furthermore, there is a lack of real-time encoding control methods based on quantum geometric parameters. (iii) The topology information encoding path has not yet been engineered. In 2025, scholars proposed three alternative paths for macroscopic quantum teleportation, among which "topological information encoding" was explicitly listed as a feasible path. The core idea of ​​this path is to encode the quantum state into topological invariants, using topological protection to combat decoherence. However, a complete technical solution for the engineering implementation of topological information encoding—how to encode arbitrary quantum states into topological invariants, how to maintain the stability of the topological encoding during transmission, and how to decode the original quantum state from the topological invariants at the receiving end—has not yet been formed. (iv) Lack of a complete link architecture from topology coding to topology decoding Existing research in topological photonics has demonstrated that photonic topologies are compatible with quantum teleportation, but a complete end-to-end method is lacking for encoding quantum states as topological invariants, transmitting them under topological protection, and decoding them at the receiver. To address the above problems, this invention provides a topologically encoded quantum teleportation method and system based on projection geometry manipulation. Summary of the Invention

[0003] (a) Purpose of the invention This invention aims to address the technical problems in existing quantum teleportation schemes, such as the lack of a unified topology protection mechanism, the fixed and uncontrollable quantum state encoding method, the lack of engineering for topology information encoding paths, and the lack of a full-link topology encoding architecture. It provides a topology-encoded quantum teleportation method and system based on projection geometry control, which encodes quantum states into topology invariants through projection geometry control, and completes full-link quantum teleportation under topology protection. (II) Technical Solution This invention provides a topologically encoded quantum teleportation method based on projective geometry manipulation, characterized by comprising the following steps: Step 1: Determine the topological encoding scheme for the target quantum state Based on the dimension d of the quantum state to be transmitted and the fidelity requirement, the target topological invariant type for topological encoding is determined. The topological invariant includes at least one of the following: topological Chern number C, topological charge number l (orbital angular momentum), and entanglement number w (Berry phase). Step 2: Encode the quantum state as a topological invariant through projective geometric manipulation By controlling the projection angle θ of the topological photonic crystal device through the projection geometry control module, the quantum state |ψ> to be transmitted is encoded as the topological invariant T(θ): |ψ> → |T(θ)> = 𝒫(θ) · |ψ> Where 𝒫(θ) is the projection mapping operator, determined by the projection angle θ; |T(θ)> is the encoded topological state, whose topological invariant T(θ) satisfies the following with respect to the projection angle θ: T(θ) = T_max · sin(θ - θ0) Where T_max is the maximum topological invariant and θ0 is the theoretically optimal projection angle. The projection angle θ is defined as: θ = arctan(β_s / β_r), β_r² + β_s² = 1 Step 3: Entanglement distribution and topology-protected transmission of topology-coded states The encoded topological state |T(θ)> is subjected to Bell state measurement with the shared entanglement pair, and the measurement result is transmitted to the receiver through a classical channel. During transmission, the topological state is protected by the topological Chern number C, making it immune to local disturbances and decoherence. Step 4: Synchronize topology reception and projection angle The receiver uses a projection geometry control module to synchronously modulate the projection angle of the receiver's topological photonic crystal device to θ' = θ, ensuring that the receiver's topology matches that of the transmitter. θ' = θ, C' = C Step 5: Decoding the quantum state from topological invariants through projective geometric manipulation The receiver decodes the topological state |T(θ')> into the primitive quantum state through inverse projection mapping 𝒫⁻¹(θ'): |T(θ')> → |ψ> = 𝒫⁻¹(θ') · |T(θ')> Step 6: Fidelity Verification The fidelity F of the decoded quantum state is verified by quantum state tomography or Bell state measurement. When F ≥ 1-ε, the topologically encoded quantum teleportation is confirmed to be successful. Core mathematical framework: Definition of projection angle: The projection angle θ is defined as: θ = arctan(β_s / β_r), β_r² + β_s² = 1 Relationship between topological invariants and projection angles: The topological invariant T(θ) is modulated by the projection angle θ: T(θ) = T_max · sin(θ - θ0) Where T_max is the maximum topological invariant and θ0 is the theoretically optimal projection angle. The topological invariant includes at least one of the following: topological Chern number C, topological charge number l (orbital angular momentum), and winding number w (Berry phase). Projection mapping operator: The projection mapping operator 𝒫(θ) projects the quantum state |ψ> onto the topological state space: 𝒫(θ) = exp(i · T(θ) · φ) · |T(θ)> <T(θ)| Where φ is the topological phase and |T(θ)> is the topological ground state. Rate of change of projection angle: During topologically encoded quantum teleportation, the projection geometry control module continuously monitors the dynamic rate of change of the projection angle. : when When the threshold is exceeded, it indicates that the system has been subjected to external disturbances, and compensation adjustments will be automatically triggered. Topological stability criterion: This invention uses the following topological stability criterion to determine whether the topologically encoded state is in a stable topological state: γ ² ≥ |1−k||∂C / ∂θ|| |·h / 2 Where γ is the topological loss rate. denoted as the rate of change of the projection angle, C as the topological Chern number, k as the restitution coefficient, and h as Planck's constant. When the criterion is met, the topologically encoded state is in a stable topological state, and the fidelity of quantum teleportation is guaranteed; when the criterion is not met, feedback adjustment is triggered. Topological coding fidelity: The fidelity F of the topologically encoded quantum teleportation is determined by the following formula: F = F_encode · F_channel · F_decode · (1 - ε_topological) Where F_encode is the topology encoding fidelity, F_channel is the topology protection transmission fidelity, F_decode is the topology decoding fidelity, and ε_topological is the topology decoherence error. Topological nontriviality condition: The condition for the topologically encoded state to be in a topologically nontrivial phase is: |θ - θ0| < σ_θ, C ≠ 0 Where σ_θ is the topology protection bandwidth. (III) Beneficial Effects Topological encoding protection: Quantum states are encoded as topological invariants, and topological protection mechanisms are used to combat decoherence and environmental disturbances, significantly improving transmission fidelity; Dynamic coding control: Adjusting topology coding parameters in real time through projection geometry control to adapt to changing channel conditions and noise environment; Full-link topology architecture: a complete end-to-end approach from topology encoding to topology protection transmission to topology decoding, supporting topological teleportation of high-dimensional quantum states; Synergy with Q00140: Utilizing the orbital angular momentum quantum state manipulation capability of Q00140, it supports quantum teleportation with OAM topological encoding; Topological stability criterion: For the first time, a quantitative criterion for the stability of topologically encoded states in quantum teleportation was established, ensuring real-time transmission reliability; Engineering feasibility: Based on topological photonic crystal devices and projection geometry control modules, it can be implemented on existing silicon photonic platforms. Attached Figure Description

[0004] Figure 1 This is a schematic diagram of the overall structure of a topologically encoded quantum teleportation system based on projection geometry control, provided for an embodiment of the present invention. Figure 2 A schematic diagram illustrating the principle of quantum state topological encoding and projection angle modulation provided in an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the principle of topological state transmission and projection angle synchronization provided in an embodiment of the present invention. Figure 4 A flowchart of topologically encoded quantum teleportation control provided for embodiments of the present invention. Detailed Implementation

[0005] Example 1: Quantum Teleportation Based on Topological Chern Number Encoding Step 1: Configure the topological photonic crystal encoder A topological photonic crystal encoder is fabricated on an SOI substrate, comprising a topological photonic crystal microcavity and a gate electrode array, with a non-zero topological Chern number C=1. The projection angle θ is defined as θ = arctan(β_s / β_r), satisfying β_r² + β_s² = 1. Step 2: Quantum State Topological Encoding The gate voltage is applied through the projection geometry control module to adjust the projection angle to θ_enc = 0.35 rad. The quantum state to be transmitted |ψ> is encoded into a topological Chern state |C(θ_enc)> by the projection mapping operator 𝒫(θ_enc), and the topological Chern number C = C_max ·sin(θ_enc - θ0) = 1. Step 3: Topology Protection Transmission The encoded topological state and the shared entangled pair are subjected to Bell state measurements, and the measurement results are transmitted through a classical channel. The topological state is protected by the topological Chern number C=1, making it immune to local disturbances during transmission. Step 4: Projection Angle Synchronization and Decoding The receiving end projection geometry control module synchronously modulates the projection angle to θ_dec = θ_enc = 0.35 rad. The topological state is decoded into the primitive quantum state through the inverse projection mapping 𝒫⁻¹(θ_dec). Step 5: Fidelity Verification The quantum state fidelity F after decoding was measured by quantum state tomography. The measured F ≥ 0.96. Example 2: Quantum teleportation based on orbital angular momentum topological charge encoding (in collaboration with Q00140) Step 1: Configure the OAM topology encoder Using the Q00140 topological photonic crystal OAM state generator, the projection angle θ is controlled by the projection geometry control module to generate OAM quantum states carrying a specific topological charge l. Step 2: OAM Topology Coding The quantum state to be transmitted is encoded as the OAM topological charge l(θ) = l_max · sin(θ - θ0). By adjusting the projection angle θ, the quantum state is mapped to the corresponding OAM topological state. Step 3: Topology Protection OAM Transmission The encoded OAM topological state completes quantum teleportation under topological protection, and the OAM topological charge remains unchanged during the transmission. Step 4: OAM Topology Decoding The receiver decodes the OAM topological state into the primitive quantum state through inverse projection mapping. Example 3: Topologically Encoded Quantum Teleportation with Dynamically Adaptive Projection Angle Step 1: Initial Topology Coding Complete the initial topology encoding and transmission according to the steps in Example 1. Step 2: Real-time monitoring of the rate of change of the projection angle During transmission, the projection geometry control module continuously monitors the rate of change of the projection angle. Calculate the topological stability criterion γ ² ≥ |1−k||∂C / ∂θ|| |·h / 2. Step 3: Adaptive Compensation when When the preset threshold is exceeded or the criteria are not met, the system automatically adjusts the projection angle and relocks the topology-encoded state to a stable topology state. Step 4: Dynamic Fidelity Maintenance The adaptive compensation mechanism ensures that the fidelity of topologically encoded quantum teleportation remains at F≥0.95 under environmental perturbations. Terminology Explanation

[0006] Terminology Meaning Topological coding is a method of encoding quantum states as topological invariants (such as topological Chern number C, topological charge number l of orbital angular momentum, etc.). The projection operator (𝒫(θ)) is the operator that projects a quantum state to the topological state space, determined by the projection angle θ. Topological invariants (T(θ)) are physical quantities that describe the topological properties of a topological state, including the topological Chern number C, the topological charge number l, and the entanglement number w. Topological state (T(θ)>) Inverse projection mapping (𝒫⁻¹(θ)) is an inverse projection operator that decodes topological states into primitive quantum states. A synchronization control mechanism that ensures the projection angles of the transmitting and receiving ends remain consistent.

Claims

1. Claim 1 (independent claim, method) A topological encoding quantum teleportation method based on projective geometry regulation, characterized in that the method comprises the following steps: (1) regulating the projection angle θ of a topological photonic crystal device through a projective geometry regulation module, and encoding a to-be-transmitted quantum state |ψ> into a topological invariant T(θ): |ψ> → |T(θ)> = 𝒫(θ)·|ψ>, wherein 𝒫(θ) is a projective mapping operator determined by the projection angle θ; (2) performing Bell state measurement on the encoded topological state |T(θ)> and a shared entangled pair, and transmitting the measurement result through a classical channel; (3) synchronously modulating, by a projective geometry regulation module at a receiving end, the projection angle of a topological photonic crystal device at the receiving end to θ' = θ; (4) decoding, by the receiving end, the topological state |T(θ')> into the original quantum state |ψ> = 𝒫⁻¹(θ')·|T(θ')> through an inverse projective mapping 𝒫⁻¹(θ').

2. Claim 2 (dependent claim) The method according to claim 1, characterized in that: The projection angle θ is defined as θ = arctan(β_s / β_r), wherein β_r and β_s satisfy the projection constraint β_r² + β_s² = 1; and the topological invariant T(θ) and the projection angle θ satisfy T(θ) = T_max · sin(θ - θ0), wherein T_max is the maximum topological invariant, and θ0 is the theoretically optimal projection angle.

3. Claim 3 (dependent claim) The method according to claim 1, characterized in that: The topological invariant T(θ) comprises at least one of a topological Chern number C, a topological charge number l (orbital angular momentum) or a winding number w (Berry phase).

4. Claim 4 (dependent claim) The method according to claim 1, characterized in that: The projective mapping operator 𝒫(θ) = exp(i · T(θ)· φ) · |T(θ)><T(θ)|, wherein φ is a topological phase, and |T(θ)> is a topological ground state.

5. Claim 5 (dependent claim) The method according to claim 1, characterized in that: During operation, the projection geometry control module continuously monitors the rate of change of the projection angle. According to the topological stability criterion γ ² ≥ |1−k||∂C / ∂θ|| |·h / 2 determines whether the topology encoding state is in a stable topology state. If the criterion is not met, feedback adjustment is triggered.

6. Claim 6 (dependent claim) The method according to claim 1, characterized in that: The condition for the topological encoding state to be in a topologically non-trivial phase is |θ - θ0| < σ_θ, C ≠ 0, wherein σ_θ is the topological protection bandwidth.

7. Claim 7 (dependent claim) The method according to claim 1, characterized in that: The fidelity F of the topological encoding quantum teleportation is F = F_encode · F_channel · F_decode · (1 - ε_topological), wherein F_encode is the topological encoding fidelity, F_channel is the topological protection transmission fidelity, F_decode is the topological decoding fidelity, and ε_topological is the topological decoherence error.

8. Claim 8 (independent claim, system) A topological encoding quantum teleportation system based on projective geometry regulation, characterized in that the system comprises: a topological photonic crystal encoder, disposed at a transmitting end, comprising a topological photonic crystal structure and a gate electrode, having a non-zero topological Chern number, and configured to encode a quantum state into a topological invariant through projective geometry regulation; A projection geometry control module is connected to the topological photonic crystal encoder and is used to control the projection angle θ through an external field to realize the topological encoding and decoding of quantum states; An entanglement distribution module is used to share entangled pairs between the sender and receiver; A Bell state measurement module is connected to the topological photonic crystal encoder for performing Bell state measurements on the encoded topological state and the shared entanglement pair. A classic communication interface for transmitting Bell state measurement results; A topological photonic crystal decoder, located at the receiver, includes a topological photonic crystal structure and a gate electrode, and has the same non-zero topological Chern number as the encoder, for decoding quantum states from topological invariants via inverse projection mapping; A synchronization control module, connected to the projection geometry control module at the transmitting and receiving ends, is used to ensure that the projection angles at both ends are synchronized.

9. Claim 9 (dependent claim) The system according to claim 8 is characterized in that: The topological photonic crystal encoder and the topological photonic crystal decoder have the same non-zero topological Chern number C ≠ 0; the synchronization control module modulates the projection angle of the receiving end to be equal to the projection angle of the transmitting end: θ' = θ.

10. Claim 10 (dependent claim) The system according to claim 8 is characterized in that: The system works in conjunction with Q00140 (a method and system for manipulating orbital angular momentum quantum states based on projection angle control), the topological photonic crystal encoder is the topological photonic crystal OAM state generator of Q00140, and the topological invariant is the orbital angular momentum topological charge number l.

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