Path planning method based on constrained quantum random walk and non-global quantum state enhancement

Abstract

The invention discloses a path planning method based on constrained quantum random walk and non-global quantum state enhancement, and the method comprises the steps: coding a two-dimensional discrete environment containing an obstacle into a quantum register system, introducing an environment constraint mechanism in a quantum state evolution stage, and only allowing a path state to be transmitted to a non-obstacle position, therefore, illegal path branches are directly inhibited in the quantum random walk process. Constructing a path effectiveness judgment operator and a reflection operator based on an evolutionary state, and performing amplitude enhancement on path branches meeting environmental constraints and target constraints on the premise of not depending on full-space uniform superposition search; according to the method, the path planning efficiency is improved by using quantum parallelism, and the method has good engineering realizability and expansibility in a complex environment.

Description

Technical Field

[0001] This invention belongs to the field of robot motion planning and quantum computing technology, specifically relating to a path planning method based on constrained quantum random walk and non-global quantum state enhancement. Background Technology

[0002] Traditional mobile robot path planning commonly employs sampling-based random tree algorithms. These methods achieve path search by randomly sampling in the configuration space and progressively expanding the tree structure. They offer advantages such as simplicity and applicability to high-dimensional spaces. However, in complex, large-scale grid maps, they often suffer from the following problems: High computational complexity: To ensure feasible and near-optimal solutions are found, the number of sampling points increases exponentially with environmental complexity, leading to a significant increase in time overhead; Prone to local suboptimal conditions: In narrow passages or high obstacle density scenarios, sampling efficiency decreases, making it difficult to guarantee path quality and success rate; Difficulty in fully utilizing parallelism: Classical algorithms inherently rely on sequential sampling and detection operations, making it difficult to achieve large-scale parallel exploration at the algorithm level. Existing quantum path planning research is mostly based on quantum search frameworks such as Grover's search, or introduces quantum parallel extensions on top of classical sampling. However, these methods typically rely on uniform superposition and global reflection operations across the entire path space, making it difficult to effectively incorporate path constraint information in complex obstacle environments. Furthermore, they have high requirements for the number of qubits, gate depth, and coherence time, which is not conducive to implementation on noisy medium-scale quantum devices (NISQ). Furthermore, existing methods often lack effective decoupling between the search phase and collision constraints and target guidance, resulting in limited path selection efficiency and difficulty in balancing search success rate and computational complexity. Summary of the Invention

[0003] Objective: To overcome the problems of low efficiency, high algorithm complexity, and high requirements for quantum hardware resources in existing path planning technologies, this invention proposes a path planning method based on constrained two-dimensional quantum random walks and non-global search-type quantum state enhancement. Environmental constraints are introduced during the quantum state evolution stage to suppress path branches pointing to obstacle regions. Furthermore, non-global search-type quantum state enhancement is used to strengthen the path quantum states that satisfy the target guidance conditions, achieving efficient path planning from the starting cell to the ending cell in complex two-dimensional grid maps, while simultaneously considering path search success rate and adaptability to medium-scale quantum devices with high noise levels.

[0004] Technical Solution: The present invention discloses a path planning method based on constrained quantum random walk and non-global quantum state enhancement, used to plan collision-free paths from a starting cell to an ending cell in a two-dimensional grid map containing obstacles. The path planning method employs a non-global search-type quantum state enhancement mechanism, which constructs a reflection operator using the quantum random walk evolution state as a reference state to selectively enhance the measurement probability of path quantum states that satisfy preset conditions. The method includes the following steps:

[0005] (1) Obtain a two-dimensional grid map, starting cell and ending cell, and calculate the Manhattan distance from the starting point to the ending point as the basic planning steps;

[0006] (2) Construct a quantum system, including a position register for encoding the current position, a map register for representing map obstacle information, a target register for encoding the destination information, and a quantum coin register for encoding the direction of each step of movement;

[0007] (3) Encode the starting point, ending point, and map information into the quantum system to form an initial quantum state;

[0008] (4) Constructing a constrained two-dimensional quantum random walk operator, including: a coin operator for generating a superposition state of motion direction using a quantum coin register; a conditional move operator for controlling the update of the position register state according to the motion direction and map obstacle information; wherein, the conditional move operator is configured to perform a legality determination before performing displacement, and to perform unitary substitution evolution to maintain the unitary nature of the system when the target position is an obstacle; by applying the constrained two-dimensional quantum random walk operator to the initial quantum state, an evolution state containing a superposition of candidate paths that satisfy environmental constraints is generated;

[0009] (5) Based on the information of the position register and the target register, construct a Boolean function for parallel judgment of whether the candidate path meets the preset conditions; wherein, the preset conditions include at least that the path termination position meets the target guidance requirements and whether the path collides during the quantum state evolution process, which is guaranteed by the constrained two-dimensional quantum random walk operator through the environmental constraint mechanism during the state evolution stage;

[0010] (6) Based on Boolean functions, a phase marking operator is constructed to perform phase modulation marking on path quantum states that meet preset conditions;

[0011] (7) Constructing a reflection operator for the evolution state: Constructing a reflection operator for the evolution state obtained after the constrained two-dimensional quantum random walk operator is applied to the initial state, wherein the reflection operator is configured to perform a reflection transformation on the quantum state distribution with the evolution state as the reference state;

[0012] (8) Perform non-global search type quantum state enhancement: Combine the phase tagging operator with the reflection operator about the evolution state to construct a non-global search type quantum state enhancement operator; and iteratively apply the operator to selectively enhance the measurement probability of the path quantum state that satisfies the preset conditions without relying on the uniform superposition state in the whole space.

[0013] Furthermore, in step (4), the conditional movement operator performs controlled operations based on the direction of motion indicated by the quantum coin register and the map register information: when the target position is not an obstacle, the position register is updated; when the target position is an obstacle, the position is not updated, but a preset unitary evolution (such as identity mapping or direction reflection) is applied to the current state, thereby suppressing path diffusion towards the obstacle area while maintaining the overall unitaryity.

[0014] Furthermore, in step (4), the coin operator is implemented by applying a Hadamard gate or a rotation gate to the qubit corresponding to each planning step, so that each direction of motion is superimposed with a preset probability, thereby realizing quantum parallel exploration of the feasible path space.

[0015] Furthermore, in step (5), the preset conditions include: the path termination position is equal to the endpoint unit; the number of steps of the constrained two-dimensional quantum random walk operator is equal to the Manhattan distance from the starting point to the endpoint; and the global collision free path is directly output through a quantum state enhancement process and subsequent measurement.

[0016] Furthermore, the preset conditions include that the ending position of the path is closer to the endpoint unit than the starting position of the plan; the path planning is carried out in stages, including the following steps:

[0017] (s1) Set a single-stage quantum random walk step size that is smaller than the total number of planning steps;

[0018] (s2) Starting from the current starting position, execute steps (4)-(8), but construct a constrained quantum random walk operator with a single-stage step size, and use a Boolean function to determine the termination position is closer to the endpoint;

[0019] (s3) Measure to obtain the new intermediate position and the corresponding sub-path;

[0020] (s4) Using the new intermediate position as the starting position of the next stage, repeat steps (s2) and (s3) until the endpoint cell is reached, and then splice the sub-paths obtained in each stage to form a complete collision free path.

[0021] Furthermore, determining whether a position is closer to the endpoint is achieved by calculating and comparing the Manhattan distances from the termination position and the starting position to the endpoint, and the distance reduction must meet a preset threshold.

[0022] The path planning system of the present invention is used to implement any of the methods described herein, comprising:

[0023] The map acquisition module is used to acquire a two-dimensional grid map containing obstacles, as well as start and end point information; the encoding module is used to encode the map, start and end point information into a quantum register;

[0024] The quantum random walk module is used to construct and execute constrained two-dimensional quantum random walk operators to generate quantum states containing path superpositions subject to environmental constraints.

[0025] The quantum state enhancement module is used to construct and iteratively execute non-global search quantum state enhancement operators to increase the probability of path quantum states that satisfy the target guidance conditions appearing in the measurement results.

[0026] The measurement decoding module is used to measure the quantum state and decode the result into a path sequence.

[0027] An electronic device according to the present invention includes a processor and a memory, wherein the memory stores a computer program, and the computer program, when executed by the processor, implements any of the methods described herein.

[0028] The present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements any of the methods described herein.

[0029] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: It utilizes quantum superposition and parallelism to explore a large-scale path space in parallel, significantly reducing the time complexity of path search; it directly embeds environmental constraints into the evolution operator and combines a non-global search-type quantum state enhancement mechanism to avoid searching for and reflecting invalid obstacle paths, greatly improving the success rate of the algorithm in complex environments; it addresses the needs of both "global one-time planning" and "low-circuit-depth phased planning" through both full-path and target-guided modes, effectively reducing the quantum circuit depth and making it more suitable for current NISQ quantum devices; in experiments, it exhibits shorter average planning time and smaller time fluctuations, and better adaptability to changes in obstacle density. Attached Figure Description

[0030] Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram illustrating the path planning results generated based on constrained quantum random walks under different obstacle distribution density parameters r, serving as an example to demonstrate that the method of this invention can generate collision-free paths under different environmental conditions; wherein, for example... Figure 2 In the given information, (a) represents r = 0.2. Figure 2In (b), r is 0.3; Figure 2 In the equation (c), r is 0.4. Detailed Implementation

[0031] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0032] like Figure 1 As shown, this invention provides a path planning method based on constrained quantum random walk and non-global quantum state enhancement, used to plan a collision-free path from a starting cell to an ending cell in a two-dimensional grid map containing obstacles, including the following steps:

[0033] Step 1: Obtain a grid map of size N×N, the starting cell and the ending cell, and calculate the Manhattan distance M from the starting point to the ending point;

[0034] Step 2: Construct a quantum register, including: a position register p, used to encode the current grid coordinates, with a bit length of 2log2N;

[0035] Map register m is used to represent obstacle distribution information in a two-dimensional grid map. This obstacle distribution information is provided through register encoding or an equivalent quantum decision operator. Target register g is used to encode the endpoint coordinates, with a bit depth of 2log2N; quantum coin register c is used to encode the direction of movement for each step, with a bit depth of 2M.

[0036] Step 3: Encode the start point, end point, and map information into the aforementioned register, initialize the system's quantum state, and set the initial state of the system to... ;

[0037] Step 4: Construct a constrained two-dimensional quantum random walk operator. The operator is built based on a position register, a quantum coin register, and a map register, and is configured to introduce environmental constraints during the quantum state evolution process to control the transfer behavior of the quantum state probability amplitude between grid positions.

[0038] The constrained two-dimensional quantum random walk operator includes a coin operator for constructing a quantum superposition state of motion directions before position updating, and a conditional move operator for updating the position register. The coin operator generates a quantum superposition state of multiple candidate motion directions in each evolution step. In one implementation, by applying a superposition or rotation-like quantum gate to the quantum coin register, the path search can simultaneously cover four orthogonal directions (up, down, left, and right) with a preset probability amplitude distribution, thereby utilizing the quantum superposition property to explore multiple candidate motion directions in parallel.

[0039] The conditional movement operator is implemented by introducing map-aided control logic: for each state update of the position register, a controlled displacement operation is performed on the position register according to the movement direction indicated by the quantum coin register and the obstacle state of the corresponding target position in the map register; when the target position is marked as non-obstacle state in the map register, an update operation of incrementing or decrementing the position register is activated, and the corresponding quantum state probability amplitude transition is performed; when the target position is marked as obstacle state in the map register, no position update is performed, but a unitary substitution evolution related to the movement direction is applied to the current position and its corresponding movement direction state, so that the quantum state probability amplitude remains at the current position or evolves according to a preset unitary rule.

[0040] Through the aforementioned constrained movement mechanism, while maintaining the unitarity of the overall quantum state evolution of the system, path diffusion towards the obstacle region is suppressed, so that the quantum random walk process introduces environmental constraints at the quantum state evolution stage, thereby forming a non-uniform path distribution structure in the feasible region that is constrained by environmental constraints.

[0041] Step 5: Initial state Applying the two-dimensional quantum random walk operator yields a quantum state containing a superposition of candidate paths of length M that satisfy environmental constraints. ;

[0042] Step 6: Construct a path validity determination function based on the position register p and the destination register g.

[0043]

[0044] The path validity determination function is used to determine whether the path termination position satisfies the target constraints, which include the path termination position being equal to the endpoint unit or satisfying a preset target guidance criterion. At the implementation level, the path validity determination function can be implemented in Boolean logic form to output whether the path satisfies the target constraints. Whether a collision occurs during the path evolution process is guaranteed by the constrained two-dimensional quantum random walk operator in step 4 through exclusive environment constraints.

[0045] Step 7: Determine the validity of the path based on the aforementioned path validity function. Construct a path validity phase marking operator to apply phase modulation to the path quantum state at the termination position that satisfies the target constraint;

[0046] Step 8: Construct a reflection operator for the evolved state obtained after the constrained two-dimensional quantum random walk operator is applied to the initial state. The reflection operator is used to perform a reflection transformation on the quantum state distribution with the evolved state as the reference state, thereby selectively enhancing the probability amplitude of the target path quantum state that satisfies the path validity determination condition without introducing a uniform superposition state in the entire space.

[0047] Step 9: Combine the path validity phase marker operator with the reflection operator regarding the evolution state to form a non-global search quantum state enhancement operator; based on the distribution characteristics of obstacles in the map or the statistical characteristics of the path validity state, adaptively determine the number of iterations of the quantum state enhancement operator, and repeatedly apply the quantum state enhancement operator to the quantum state to increase the measurement probability of the target path quantum state that meets the path validity determination condition; wherein, the path feasibility constraint is directly embedded in the position update operator in the state evolution stage of the quantum random walk, rather than being filtered through subsequent determinations or energy functions of the generated path;

[0048] Step 10: Measure the coin register c and decode the measurement result into a classical path composed of a sequence of motion directions. The classical path corresponds to the collision free path from the starting unit to the ending unit.

[0049] This invention also provides a phased goal-guided path planning method based on constrained quantum random walks, used to plan a collision-free path from a starting cell to an ending cell in a two-dimensional grid map containing obstacles, including the following steps:

[0050] S1: Set the quantum random walk step size t for staged path search, where t is less than or equal to the Manhattan distance M from the starting point to the ending point;

[0051] S2: When constructing the quantum register, add a position information register p′ from the previous stage to store the starting reference point for the current stage search;

[0052] S3: Write the global starting point to register p′, and encode the ending point and map information into the corresponding registers to obtain the initial state. ;

[0053] S4: Construct a constrained two-dimensional quantum random walk operator with a step size of t. During the evolution process, the operator performs a preset unitary substitution evolution on the evolution component pointing to the obstacle position through map-aided environmental constraint control logic. This restricts the diffusion of quantum states to the obstacle region and applies it to the current state while maintaining the overall unitary nature of the system, so as to generate a quantum state superposition containing local candidate sub-paths of length t starting from the current starting point p′.

[0054] S5: Construct a heuristic path validity determination function to determine whether the path termination position after t-step evolution is closer to the endpoint unit than the previous stage position p', or whether it meets the preset target guidance criterion, so as to serve as the basis for subsequent phase marking and quantum state enhancement operations.

[0055] S6: Construct a phase marker operator based on the heuristic path validity determination function, which is used to apply phase modulation to the quantum state of the sub-path that satisfies the target guidance condition;

[0056] S7: Combine the phase marker operator with the reflection operator about the evolution state to form a non-global search type quantum state enhancement operator; adaptively determine the number of iterations based on the distribution characteristics of environmental obstacles and the staged search state, and selectively enhance the measurement probability of the path quantum state that satisfies the target guidance condition;

[0057] S8: Measure the position register and the quantum coin register to obtain the new intermediate position and the corresponding sub-path sequence, and write the new position back to the previous stage position information register p′ as the starting point for the next stage search;

[0058] S9: Repeat steps S4 to S9 until the measured current position information is consistent with the endpoint cell; then, splice the sub-path sequences obtained in each stage to obtain a complete collision free path from the starting cell to the endpoint cell.

[0059] Specific examples illustrate:

[0060] Example 1: Constrained Quantum Random Walk Path Planning Method Based on Full Path Search: This example describes a constrained quantum random walk path planning method based on full path search, based on steps 1 to 10. First, the position register p, map register m, target register, and quantum coin register g are initialized, and the starting unit, ending unit, and obstacle distribution information are encoded into the corresponding quantum registers to obtain the initial state of the system. .

[0061] Subsequently, a constrained two-dimensional quantum random walk operator is constructed based on a position register, a quantum coin register, and a map register. During the quantum state evolution process, this operator restricts the diffusion of the quantum state to obstacle locations through unitary substitution evolution by environmental constraint control logic, allowing the quantum state to evolve only within the feasible region. By cascading single-step constrained two-dimensional quantum random walk processes according to a preset number of steps, a quantum state superposition containing multiple candidate paths starting from the starting unit and covering the entire path length range is generated.

[0062] Based on this, a path validity determination process is constructed using the position register and the target register to determine whether the path termination position satisfies the requirement of reaching the endpoint unit or conforms to the preset target guidance criteria. For path quantum states that satisfy the target constraints, a non-global search-type quantum state enhancement process is constructed by applying phase modulation and combining it with state transformation operations related to the evolution state, in order to increase the probability of the target path quantum state appearing in the measurement results.

[0063] Finally, the quantum coin register is measured, and the measurement result is decoded into a classical path output consisting of a sequence of motion directions, thereby obtaining a collision-free path from the starting unit to the ending unit.

[0064] Example 2: Goal-guided phased constrained quantum random walk path planning method: This example describes a goal-guided phased constrained quantum random walk path planning method based on steps S1-S9.

[0065] In this embodiment, the overall path planning process is divided into multiple stages. First, a position register, a previous stage position information register, a map register, a target register, and a quantum coin register are constructed. The starting position, ending unit, and obstacle distribution information of the current stage are encoded into the corresponding registers to obtain the initial quantum state.

[0066] Subsequently, a constrained two-dimensional quantum random walk operator with a preset step size is constructed and applied to the quantum state of the current stage. During the evolution process, this operator performs unitary substitution evolution on the evolution component pointing to the obstacle location through environmental constraint control logic, thereby restricting the diffusion of the quantum state to the obstacle region and generating a superposition of quantum states of local candidate paths starting from the starting position of the current stage.

[0067] After the local path is generated, the path validity determination process is used to determine whether the path termination position is closer to the endpoint unit than the previous stage position. For path quantum states that meet the target guidance conditions, a quantum state enhancement process is constructed through phase modulation and state transformation operations related to the evolution state to increase the probability of path branches that meet the target guidance conditions appearing in the measurement results.

[0068] By measuring the quantum register, a new intermediate position and its corresponding sub-path sequence are obtained. This intermediate position is then written back to the previous stage's position information register as the starting position for the next stage's path search. This process is repeated until the measured current position matches the endpoint unit, thus forming a complete collision-free path by splicing together multiple sub-path sequences.

[0069] In one optional implementation, when the target position is determined to be an obstacle state during a quantum random walk, the conditional move operator does not perform a position update. Instead, it applies a preset unitary evolution operation to the current position and its corresponding direction state, keeping the quantum state probability amplitude at the current node or evolving according to a predetermined direction rule to maintain the unitarity of the overall quantum state evolution process. In a preferred implementation, when the target position is determined to be an obstacle, the conditional move operator performs an identity mapping on the position register, keeping the quantum state at its original position.

[0070] In another alternative implementation, the unitary evolution operation can be manifested as a phase flip or direction reflection of the motion direction state to enhance the interference suppression effect on the obstacle boundary, thereby suppressing path diffusion pointing to the obstacle region while maintaining quantum state normality.

[0071] like Figure 2 The diagram shows the path results generated by the constrained quantum random walk path planning method under different obstacle distribution density parameters r. Black squares represent obstacle units, white squares represent passable units, blue broken lines represent the planned collision-free paths, triangles represent starting units, and stars represent ending units. Figure 2 (a) Figure 2 (b) and Figure 2 (c) in the diagram corresponds to different obstacle density scenarios, illustrating that the method of the present invention can still stably generate effective paths that meet the constraints under varying obstacle density conditions.

Claims

1. A method for path planning based on constrained quantum random walks and non-global quantum state amplification, characterized in that, The application relates to a method for planning a collision-free path from a starting cell to a terminal cell in a two-dimensional grid map containing obstacles, which adopts a non-global search type quantum state enhancement mechanism, and selectively enhances the measurement probability of a path quantum state satisfying a preset condition by constructing a reflection operator with a quantum random walk evolution state as a reference state, and comprises the following steps: (1) obtaining a two-dimensional grid map, a starting cell and a terminal cell, and calculating the Manhattan distance from the starting cell to the terminal cell as a basic planning step number; (2) constructing a quantum system, including a position register for encoding the current position, a map register for representing the obstacle information of the map, a target register for encoding the terminal information, and a quantum coin register for encoding the motion direction of each step; (3) encoding the starting point, the terminal point and the map information into the quantum system to form an initial quantum state; (4) constructing a constrained two-dimensional quantum random walk operator, including: a coin operator for generating a motion direction superposition state by using the quantum coin register; and a conditional movement operator for controlling the state update of the position register according to the motion direction and the obstacle information of the map; wherein the conditional movement operator is configured to perform a legality judgment before performing the displacement, and performs an identity replacement evolution when the target position is an obstacle to maintain the system identity; the evolution state containing a candidate path superposition satisfying the environmental constraint is generated by applying the constrained two-dimensional quantum random walk operator to the initial quantum state; (5) based on the information of the position register and the target register, a Boolean function for judging whether the candidate path satisfies the preset condition in parallel is constructed; wherein the preset condition is specifically that the path termination position satisfies the target guiding requirement and whether the path collides in the quantum state evolution process; the environmental constraint mechanism is used to ensure that the preset condition is met in the state evolution stage by the constrained two-dimensional quantum random walk operator; (6) based on the Boolean function, a phase marker operator is constructed for phase modulation marking of the path quantum state satisfying the preset condition; (7) constructing a reflection operator about the evolution state: the reflection operator about the evolution state obtained by applying the constrained two-dimensional quantum random walk operator to the initial state is constructed, and the reflection operator is configured to perform a reflection transformation on the quantum state distribution with the evolution state as a reference state; (8) non-global search type quantum state enhancement: the phase marker operator and the reflection operator about the evolution state are combined to construct a non-global search type quantum state enhancement operator; and the operator is iteratively applied to selectively enhance the measurement probability of the path quantum state satisfying the preset condition without relying on the uniform superposition state of the whole space.

2. The method of claim 1, wherein, In step (4), the conditional movement operator performs a controlled operation according to the motion direction indicated by the quantum coin register and the map register information: when the target position is a non-obstacle, the coordinate of the position register is updated; when the target position is an obstacle, no position update is performed, but a preset identity evolution is applied to the current state, so that the path diffusion pointing to the obstacle region is inhibited while the overall identity is maintained.

3. The method of claim 1, wherein, The identity evolution includes an identity mapping or a direction reflection.

4. The method of claim 1, wherein, In step (4), the coin operator is implemented by applying Hadamard gates or rotation gates on the corresponding quantum bits at each planning step, so that each movement direction is superimposed with a preset probability, thereby realizing quantum parallel exploration of the feasible path space.

5. The method of claim 1, wherein, In step (5), the preset conditions include that the termination position of the path is equal to the end cell; the step number of the constrained two-dimensional quantum random walk operator is equal to the Manhattan distance from the start point to the end point; and the global collision-free path is directly output by one quantum state enhancement process and subsequent measurement.

6. The method of claim 5, wherein, The preset conditions include that the termination position of the path is closer to the end cell than the planned start position; The path planning is performed in a staged manner, including the following steps: (s1) setting a single-stage quantum random walk step length smaller than the total planning step number; (s2) taking the current start position as the start point, performing steps (4)-(8), but using the single-stage step length to construct the constrained quantum random walk operator, and using a Boolean function that judges whether the termination position is closer to the end point; (s3) measuring to obtain a new intermediate position and a corresponding sub-path; (s4) taking the new intermediate position as the start position of the next stage, repeating steps (s2) and (s3) until the end cell is reached, and splicing the sub-paths obtained in each stage to form a complete collision-free path.

7. The method of claim 1, wherein, Whether the position is closer to the end point is determined by calculating and comparing the Manhattan distances from the termination position and the start position to the end point, and the distance reduction amplitude needs to meet a preset threshold.

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