A quantum circuit semi-cutting mechanism for a distributed quantum computing environment

Abstract

The application provides a quantum circuit semi-cutting mechanism for a distributed quantum computing environment, comprising: an isomorphic sub-circuit multiplexing mechanism, which is used for identifying isomorphic sub-circuits in a quantum circuit, and cutting the quantum circuit into isomorphic sub-circuits so as to multiplex execution results of the isomorphic sub-circuits; and a quantum circuit semi-cutting mechanism, which eliminates remote operations by cutting key quantum bits and gate operations in the quantum circuit, and reduces the classical post-processing overhead when cutting a large quantum circuit. The mechanism solves the problems that the isomorphic sub-circuits cannot be multiplexed and the number of cutting operations is large in the prior art; reduces remote communication operations in distributed quantum computing, and improves the execution reliability of the quantum circuit.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of quantum computing, in particular to a quantum circuit cutting mechanism, more particularly to a quantum circuit semi-cutting mechanism for distributed quantum computing environment. BACKGROUND

[0002] Quantum computing exhibits strong computing acceleration capability for specific tasks, and can accelerate the solution of intractable problems in classical computing. Solving practical problems using quantum computers requires a large number of reliable qubits. For example, breaking RSA-2048 requires about 4000 logical qubits. However, due to manufacturing process limitations, it is currently impossible to integrate too many qubits on a single quantum chip. The current quantum computer has at most a few hundred qubits, which cannot support the running of large quantum circuits. Distributed quantum computing (DQC) is an effective method to achieve large-scale quantum computing. In DQC, multiple small quantum chips (quantum processing units, QPUs) work together to form a large quantum computing system. The physical qubits of each QPU can be divided into two categories: the first category is data qubits, which are used to map logical qubits in the quantum circuit. The second category is communication qubits, which are used to build EPR (Einstein-Podolsky-Rosen) pairs required for remote communication between QPUs. Compared with local communication operations occurring within the QPU, the error rate of remote communication operations is higher and the time consumption is longer. Therefore, the number of remote communication operations should be reduced to improve the execution reliability of the quantum circuit in the DQC environment.

[0003] Quantum circuit cutting is another method to achieve large-scale quantum computing. A large quantum circuit can be cut into multiple sub-circuits with fewer qubits and executable on QPUs. By executing each sub-circuit separately and merging the execution results of these sub-circuits, the execution result of the original circuit can be obtained. The process of merging the execution results of sub-circuits is called "classical post-processing". Quantum circuit cutting can be performed in two ways: qubit cutting and quantum gate cutting. Figure 1 An example of cutting a 4-qubit GHZ (Greenberger-Horne-Zeilinger) quantum circuit into two sub-circuits using a qubit cutting operation is shown. Qubit cutting introduces a new qubit and moves all two-qubit gate operations after the cutting position to the new qubit for execution. Figure 2 An example of cutting a GHZ quantum circuit using a quantum gate cutting operation is shown. Quantum gate cutting cuts a two-qubit gate operation into two single-qubit gate operations, which are executed in two sub-circuits, respectively. The merging overhead of sub-circuit execution results (i.e., the classical post-processing overhead) increases exponentially with the number of cuts, so the number of quantum circuit cuts should be reduced.

[0004] Quantum circuit cutting can be used to remove the remote communication operations between QPUs in the DQC environment. The existing quantum circuit cutting mechanism mainly has the following problems:

[0005] (1) There is currently no efficient isomorphic sub-circuit reuse mechanism. If a quantum circuit is cut into multiple isomorphic sub-circuits, the execution results of these isomorphic sub-circuits can be reused in the classical post-processing process. Only one of the multiple isomorphic sub-circuits needs to be executed, and the execution result can be reused as the execution result of the other isomorphic sub-circuits. There is currently no efficient isomorphic sub-circuit reuse mechanism, which cannot detect and reuse isomorphic sub-circuits in a large quantum circuit, and the isomorphic sub-circuit needs to be executed multiple times.

[0006] (2) The existing quantum circuit cutting mechanism always cuts a quantum circuit into multiple completely independent sub-circuits. This results in a large number of cutting operations when cutting a large quantum circuit, resulting in high classical post-processing overhead. The inventors have observed that when cutting a quantum circuit, some cutting operations are unnecessary. Because these cutting operations can only remove a small number of remote communication operations, but result in high classical post-processing overhead. Therefore, these unnecessary cutting operations do not need to be performed, and the quantum circuit does not need to be cut into multiple completely independent sub-circuits. SUMMARY

[0007] To solve the problems existing in the prior art, the present application proposes a quantum circuit semi-cutting mechanism for a distributed quantum computing environment, which is used to reduce the remote communication operations in the DQC environment. The present application consists of the following two parts.(1) Isomorphic sub-circuit reuse mechanism, which is used to cut the quantum circuit into isomorphic sub-circuits and reuse the execution results of the isomorphic sub-circuits.(2) Quantum circuit semi-cutting mechanism, which does not need to cut the quantum circuit into multiple completely independent sub-circuits, but only eliminates the remote communication operations in the DQC environment by cutting the key qubits and gate operations in the quantum circuit, thereby reducing the classical post-processing overhead when cutting a large quantum circuit. The specific steps of each part are as follows:

[0008] (I) Isomorphic sub-circuit reuse mechanism

[0009] Step 1, obtain a large quantum circuit to be cut, and construct an interaction graph. The nodes in the interaction graph represent a logical qubit used by a two-qubit gate operation. The edges in the interaction graph represent a logical qubit shared by a two-qubit gate operation or two adjacent two-qubit gate operations. Cutting an edge in the interaction graph is equivalent to performing a cutting operation on the quantum circuit.

[0010] Step 2, detect isomorphic sub-circuits in the large quantum circuit, and construct an isomorphic-aware interaction graph. Specifically, it includes the following steps:

[0011] Step 2.1, Identifying isomorphic sub-circuits. The VF2++ algorithm is used to obtain the matching scheme of isomorphic sub-circuits with no quantum gate operation intersection in large quantum circuits. In order to avoid cutting out sub-circuits across QPU mapping, the number of qubits in each isomorphic sub-circuit cannot exceed the number of qubits in the largest QPU. The scheme that cuts the large quantum circuit into isomorphic sub-circuits with the least number of cuts is selected as the final scheme.

[0012] Step 2.2, collapsing the nodes corresponding to isomorphic sub-circuits in the interaction graph to construct an isomorphism-aware interaction graph. For each isomorphic sub-circuit, all nodes corresponding to the sub-circuit in the interaction graph are collapsed into a supernode. The supernode cannot be cut. Therefore, when cutting the circuit, the qubits and gate operations in the isomorphic sub-circuit will not be cut, which helps to cut the large quantum circuit into isomorphic sub-circuits. In addition, by collapsing the nodes corresponding to isomorphic sub-circuits, the number of edges in the interaction graph is reduced, the search space of the cutting scheme is reduced, and the search speed is improved.

[0013] (B) Quantum circuit semi-cutting mechanism

[0014] Step 3, Construct a small root heap to store candidate cutting schemes. The small root heap can return the cutting scheme with the lowest cutting cost in the candidate cutting scheme. The lower the cutting cost, the lower the classical post-processing overhead of the scheme, and the fewer the remote communication operations generated after mapping to DQC. A Boolean value list s = {s1, s2, …, s n} represents a candidate cutting scheme, where s i value of true indicates that the i-th edge in the interaction graph is cut, and s i value of false indicates that the i-th edge in the interaction graph is not cut. The length of s represents the number of edges in the interaction graph that have made cutting decisions. An empty list (i.e., a candidate cutting scheme that does not make cutting decisions for any edge in the interaction graph) is added to the small root heap as the initial scheme.

[0015] Step 4, iteratively update the lowest cost cutting scheme until the small root heap storing candidate cutting schemes is empty. Each iteration includes the following steps:

[0016] Step 4.1, take out a candidate cutting scheme from the small root heap storing candidate cutting schemes.

[0017] Step 4.2, check if the extracted candidate partitioning scheme is feasible. If the candidate partitioning scheme is not feasible, skip this scheme and continue the next iteration. The following three types of candidate partitioning schemes are not feasible: (1) If the candidate partitioning scheme results in a subcircuit with more qubits than the maximum QPU, the candidate partitioning scheme is not feasible. (2) If the candidate partitioning scheme has a higher cost than the lowest cost partitioning scheme, the candidate partitioning scheme is not feasible. Because further iterations will not produce a better scheme than the lowest cost partitioning scheme. (3) If the candidate partitioning scheme has made a decision for all edges in the interaction graph (i.e., the candidate partitioning scheme has a Boolean value list of length equal to the number of edges in the interaction graph), but the large quantum circuit is not partitioned into completely independent subcircuits, the candidate partitioning scheme is not feasible.

[0018] Step 4.3, update the lowest cost partitioning scheme. When a candidate partitioning scheme is feasible and has made a decision for all edges in the interaction graph, compare the candidate partitioning scheme with the lowest cost partitioning scheme. If the candidate partitioning scheme has a lower cost, set the candidate partitioning scheme as the new lowest cost partitioning scheme. The cost of a partitioning scheme is represented as a tuple of four values. The first item in the tuple is the number of remote communication operations that would be generated when mapping the partitioned subcircuits to a DQC. The second item is the sampling overhead (i.e., the number of times the subcircuits need to be executed), which is calculated as O(16 k1 9 k2 ), where k1 represents the number of qubit partitions and k2 represents the number of gate partitions. If there are reusable isomorphic subcircuits, the sampling overhead will be reduced. The third item is the classical post-processing overhead, which is calculated as O(4 k1 6 k2 ). The last item is -1 x the search depth (i.e., the length of the candidate partitioning scheme s). In the min-heap, the candidate partitioning schemes are ordered according to the lower indexed item in the tuple. If the lower indexed items in two tuples are equal, the higher indexed items are compared.

[0019] Step 4.4, construct new candidate partitioning schemes. For a feasible candidate partitioning scheme, if it has not made a decision for all edges in the interaction graph, add a true to the candidate partitioning scheme to generate the first new candidate partitioning scheme, and add a false to the candidate partitioning scheme to generate the second new candidate partitioning scheme. Add the two new candidate partitioning schemes to the min-heap that stores candidate partitioning schemes.

[0020] Step 4.5, if the min-heap that stores candidate partitioning schemes is not empty, repeat steps 4.1 to 4.4. Otherwise, return the lowest cost partitioning scheme.

[0021] Step 5, removing non-key cutting operations in the minimum cost cutting scheme, constructing a semi-cutting scheme. For each cutting operation in the minimum cost cutting scheme, the number of remote communication operations that can be removed by performing the cutting operation is obtained. The average value of the number of remote communication operations that can be removed by all cutting operations is calculated. If the number of remote communication operations that can be removed by a cutting operation is greater than or equal to the average value, the cutting operation is recorded as a key cutting operation, otherwise it is recorded as a non-key cutting operation. The semi-cutting scheme containing only the key cutting operation is output.

[0022] The application further provides a storage medium for storing a program for executing the quantum circuit semi-cutting mechanism for the distributed quantum computing environment.

[0023] The application has the advantages that: the application designs the isomorphic sub-circuit multiplexing mechanism and the quantum circuit semi-cutting mechanism for the quantum circuit cutting problem in the distributed quantum computing environment. The isomorphic sub-circuit multiplexing mechanism can identify the isomorphic sub-circuit in the quantum circuit, construct an isomorphic-aware interaction graph, cut the quantum circuit into isomorphic sub-circuits, and reduce the number of sub-circuits that need to be executed. In the quantum circuit semi-cutting mechanism, only key qubits and gate operations are cut, the number of cutting operations required for cutting a large quantum circuit is reduced, and the classical post-processing overhead is reduced. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 A schematic diagram of a qubit cutting operation performed on a GHZ quantum circuit;

[0025] Figure 2 A schematic diagram of a quantum gate cutting operation performed on a GHZ quantum circuit;

[0026] Figure 3 A flowchart of a quantum circuit semi-cutting mechanism for the distributed quantum computing environment proposed by the application;

[0027] Figure 4 An interaction graph constructed for a large quantum circuit in an embodiment of the application;

[0028] Figure 5 A schematic diagram of identifying isomorphic sub-circuits and constructing an isomorphic-aware interaction graph;

[0029] Figure 6 A schematic diagram of updating the minimum cost cutting scheme;

[0030] Figure 7 A schematic diagram of removing non-key cutting operations in the minimum cost cutting scheme and constructing a semi-cutting scheme. DETAILED DESCRIPTION

[0031] In order to make the above features and effects of the application more explicit and easy to understand, the following embodiments are given, and the accompanying drawings are referred to.Figures 1 to 7 ) are described in detail as follows.

[0032] A quantum circuit semi-cutting mechanism for a distributed quantum computing environment includes the following steps: step 1, based on an isomorphic sub-circuit multiplexing mechanism, obtaining a large quantum circuit to be cut, and constructing an interaction graph; step 2, based on the isomorphic sub-circuit multiplexing mechanism, detecting isomorphic sub-circuits in the large quantum circuit, and constructing an isomorphic-aware interaction graph; step 3, constructing a small root heap storing candidate cutting schemes; step 4, iteratively updating the lowest cost cutting scheme until the small root heap storing the candidate cutting schemes is empty; and step 5, removing non-critical cutting operations in the lowest cost cutting scheme to construct a semi-cutting scheme, without cutting the quantum circuit into multiple completely independent sub-circuits, only by cutting the critical quantum bits and gate operations in the quantum circuit to eliminate the remote communication operations in the DQC environment, and reducing the classical post-processing overhead when cutting the large quantum circuit.

[0033] Step 1 includes: a node in the interaction graph represents a double-qubit gate operation using a logical qubit; an edge in the interaction graph represents a double-qubit gate operation, or a logical qubit shared by two adjacent double-qubit gate operations; and cutting an edge in the interaction graph is equivalent to performing a cutting operation on the quantum circuit.

[0034] Step 2 includes: step 2.1, identifying isomorphic sub-circuits: using the VF2++ algorithm to obtain an isomorphic sub-circuit matching scheme with no quantum gate operation intersection in the large quantum circuit; to avoid cutting sub-circuits across QPU mapping, the number of qubits of each isomorphic sub-circuit must not exceed the number of qubits of the largest QPU; and selecting the scheme with the least number of cutting operations for cutting the large quantum circuit into isomorphic sub-circuits as the final scheme; and step 2.2, merging the nodes corresponding to the isomorphic sub-circuits in the interaction graph to construct an isomorphic-aware interaction graph. For each isomorphic sub-circuit, all nodes corresponding to the sub-circuit are merged into a super node in the interaction graph.

[0035] The present application provides a quantum circuit semi-cutting mechanism for a distributed quantum computing environment, which includes: an isomorphic sub-circuit multiplexing mechanism for identifying isomorphic sub-circuits in a quantum circuit and cutting the quantum circuit into isomorphic sub-circuits to facilitate multiplexing the execution results of the isomorphic sub-circuits; and a quantum circuit semi-cutting mechanism for eliminating remote operations by cutting critical qubits and gate operations in the quantum circuit to reduce the classical post-processing overhead when cutting the large quantum circuit. The mechanism solves the problem of being unable to multiplex isomorphic sub-circuits and the large number of cutting operations in the prior art; reduces the remote communication operations in distributed quantum computing, and improves the execution reliability of the quantum circuit.

[0036] The present application consists of two parts.(1) Isomorphic sub-circuit multiplexing mechanism, used for cutting quantum circuits into isomorphic sub-circuits, and multiplexing the execution results of isomorphic sub-circuits.(2) Quantum circuit semi-cutting mechanism, without cutting quantum circuits into multiple completely independent sub-circuits, only by cutting the key quantum bits and gate operations in the quantum circuit to eliminate the remote communication operation in the DQC environment, reduce the classical post-processing overhead when cutting large quantum circuits.

[0037] 1. Operating environment. The present application is based on open source software development kit Qiskit and Circuit knitting toolbox, and realizes the quantum circuit splitting mechanism in the distributed quantum computing system. The interface provided by Qiskit is used to obtain large quantum circuits and the interaction information between quantum bits, and an interaction graph is constructed. The locally constructed quantum circuit cutting mechanism is used to cut the large quantum circuit, the Circuit_knitting_toolbox and Qiskit are used to run the split sub-circuit, the execution results of the sub-circuit are merged, and the execution result of the original circuit is obtained.

[0038] 2. Specific steps. Figure 3 The flowchart of one embodiment of the present application is shown. The present application mainly includes the following steps:

[0039] (I) Isomorphic sub-circuit multiplexing mechanism

[0040] Step 1, obtaining a large quantum circuit to be cut, and constructing an interaction graph. Figure 4 An example of constructing an interaction graph for a large quantum circuit is shown. The method of constructing an interaction graph is as follows: for each two-qubit gate operation, two nodes representing the two logical qubits used by the two-qubit gate operation are added to the interaction graph. For two nodes belonging to the same two-qubit gate operation in the interaction graph, there is an edge between the nodes, representing the two-qubit gate operation, that is, Figure 4 The horizontal solid edge in the figure. Cutting a horizontal solid edge in the interaction graph is equivalent to performing a qubit cutting on the quantum circuit. Figure 1 An example of cutting a 4-qubit GHZ quantum circuit using a qubit cutting operation is shown. If two adjacent two-qubit gate operations use the same logical qubit, there is an edge between the corresponding nodes, representing the logical qubit shared by the two two-qubit gate operations, that is, Figure 4 The vertical dashed edge in the figure. Cutting a vertical dashed edge in the interaction graph is equivalent to performing a gate cutting on the quantum circuit. Figure 2 An example of cutting a 4-qubit GHZ quantum circuit using a gate cutting operation is shown.

[0041] Step 2, detecting isomorphic sub-circuits in the large quantum circuit, and constructing an isomorphic-aware interaction graph, which includes:

[0042] Step 2.1, Identify isomorphic subcircuits. Use VF2++ algorithm to obtain the matching scheme of quantum gate operation disjoint isomorphic subcircuits in large quantum circuits. Figure 5 -(a) shows an example of identifying isomorphic subcircuits. The identified isomorphic subcircuits are marked with a gray dashed line box.

[0043] Step 2.2, Collapse the nodes corresponding to isomorphic subcircuits in the interaction graph, and construct an isomorphism-aware interaction graph. Figure 5 -(b) shows an example of constructing an isomorphism-aware interaction graph. For each isomorphic subcircuit in (a), all nodes corresponding to the subcircuit are collapsed into a supernode in the interaction graph, and an isomorphism-aware interaction graph is constructed. The supernode cannot be further cut, i.e., the qubits and gate operations in the isomorphic subcircuit cannot be cut, which helps to cut large quantum circuits into isomorphic subcircuits. Figure 5 -(a), all nodes corresponding to the subcircuit are collapsed into a supernode in the interaction graph, and an isomorphism-aware interaction graph is constructed. The supernode cannot be further cut, i.e., the qubits and gate operations in the isomorphic subcircuit cannot be cut, which helps to cut large quantum circuits into isomorphic subcircuits.

[0044] (II) Quantum circuit semi-cutting mechanism

[0045] Step 3, Construct a small root heap to store candidate cutting schemes.

[0046] Step 4, Update the lowest cost cutting scheme iteratively until the small root heap storing candidate cutting schemes is empty. Each iteration includes the following steps:

[0047] Step 4.1, Take out a candidate cutting scheme from the small root heap storing candidate cutting schemes.

[0048] Step 4.2, Detect whether the candidate cutting scheme is feasible. If the candidate cutting scheme is not feasible, skip the scheme and continue the next iteration.

[0049] Step 4.3, Update the lowest cost cutting scheme. Figure 6 An example of updating the lowest cost cutting scheme is shown. Figure 6 -(a) shows a 4-qubit quantum supremacy circuit and its interaction graph. If each QPU in DQC has only 3 qubits, the circuit needs to be mapped across QPUs, resulting in remote communication operations. Figure 6- (b) shows the current lowest cost cutting scheme. This scheme uses two qubit cutting operations to cut the circuit into a 4-qubit subcircuit 1 and a 2-qubit subcircuit 2. Mapping subcircuit 1 requires at least one remote operation, so the first term of the lowest cost cutting scheme is 1. The candidate circuit cutting scheme obtained from the min-heap cuts the circuit into two 3-qubit subcircuits, each of which can be mapped to a QPU without any remote operations. So the first term of the cutting cost is 0. In contrast, the cutting cost of the candidate circuit cutting scheme obtained from the min-heap is lower, so this scheme is set as the new lowest cost cutting scheme.

[0050] Step 4.4, construct a new candidate cutting scheme.

[0051] Step 4.5, return the lowest cost cutting scheme.

[0052] Step 5, remove non-critical cutting operations in the lowest cost cutting scheme to construct a semi-cutting scheme. Figure 7 An example of removing non-critical operations in the lowest cost cutting scheme to construct a semi-cutting scheme is shown. If a 4-qubit Quantum Fourier Transformation (QFT) circuit is to be mapped into a DQC environment with only 3-qubit QPUs, at least six remote operations need to be performed without cutting the quantum circuit. The lowest cost cutting scheme returned by step 4.5 is shown in Figure 7 - (a), which uses two qubit cutting operations and two quantum gate cutting operations. Figure 7 - (b) shows the circuit generated after using only the No. 1 cutting operation. Mapping this circuit requires at least four remote operations. Therefore, the number of remote gate operations that can be removed using the No. 1 cutting operation is 6-4 = 2. Similarly, using only the No. 2, No. 3, and No. 4 cutting operations, the number of remote operations that can be removed is 2, 1, and 1, respectively. The average number of remote operations that can be removed by all cutting operations is (2+2+1+1) / 4 = 1.5. When the number of remote operations that can be removed by a cutting operation is greater than or equal to the average, the cutting operation is considered a critical cutting operation. Figure 7 - (c), the No. 1 and No. 2 cutting operations are critical cutting operations. Otherwise, the cutting operation is considered a non-critical cutting operation. Figure 7 - (c), the No. 3 and No. 4 cutting operations are non-critical cutting operations. The semi-cutting scheme output contains only the critical cutting operations No. 1 and No. 2. This scheme does not cut the quantum circuit into completely independent subcircuits.

[0053] The present application also provides a storage medium for storing a program for executing any one of the semi-cutting mechanisms for quantum circuits in a distributed quantum computing environment.

Claims

1. A method for half-cutting quantum circuits in a distributed quantum computing environment, characterized in that, Includes the following steps: Step 1: Based on the homogeneous sub-circuit reuse mechanism, obtain the large quantum circuit to be cut and construct the interaction graph; Step 2: Based on the homogeneous sub-circuit reuse mechanism, detect homogeneous sub-circuits in large-scale quantum circuits and construct a homogeneous sensing interaction graph; Step 3: Construct a min-heap to store candidate cutting schemes; Step 4: Iteratively update the lowest cost cutting scheme until the min-heap storing candidate cutting schemes is empty; Step 5: Remove non-critical cutting operations from the lowest-cost cutting scheme and construct a semi-cutting scheme. This eliminates the need to cut the quantum circuit into multiple completely independent sub-circuits. Instead, it eliminates remote communication operations in the DQC environment by cutting the critical qubits and gate operations in the quantum circuit, thereby reducing the classical post-processing overhead when cutting large quantum circuits. Step 1 includes: a node in the interaction graph represents a two-qubit gate operation that uses a logical qubit; an edge in the interaction graph represents a two-qubit gate operation, or two adjacent two-qubit gate operations sharing a logical qubit; cutting an edge in the interaction graph is equivalent to performing a cutting operation on the quantum circuit. Step 2 includes: Step 2.1, Identify isomorphic sub-circuits: Use the VF2++ algorithm to obtain matching schemes for isomorphic sub-circuits with no intersection of quantum gate operations in large quantum circuits; to avoid cross-QPU mapping of the cut sub-circuits, the number of qubits of each isomorphic sub-circuit must not exceed the number of qubits of the largest QPU; select the scheme that requires the fewest cuts to cut the large quantum circuit into isomorphic sub-circuits as the final scheme. Step 2.2: In the interaction graph, merge the nodes corresponding to the isomorphic sub-lines to construct an isomorphic perception interaction graph. For each isomorphic sub-line, merge all the nodes corresponding to the sub-line into a super node in the interaction graph. In step 4, the splitting cost is represented by a tuple containing four values; the first item in the tuple is the number of remote communication operations generated when mapping the split sub-line to DQC; the second item is the sampling overhead, i.e., the number of times the sub-line needs to be executed, calculated as O(16^6). k1 9 k2 The sampling overhead is calculated as follows: k1 represents the number of qubit cuts, k2 represents the number of quantum gate cuts, and if reusable isomorphic subcircuits exist, the sampling overhead will be reduced. The third term is the classical post-processing overhead, calculated as O(4^2). k1 6 k2 The last term is -1 × search depth, which is the length of the candidate cutting scheme s.

2. The quantum circuit half-cutting method for distributed quantum computing environments as described in claim 1, characterized in that, Step 3 includes: a min-heap can return the cutting scheme with the lowest cutting cost among the candidate cutting schemes; the lower the cutting cost, the lower the classical post-processing overhead of the scheme, and the fewer remote communication operations generated after mapping to DQC; a Boolean list s = {s1, s2, ..., s...} is used. n } represents a candidate cutting scheme, where s i A value of true indicates that the i-th edge in the interaction graph is cut, s i A value of false indicates that the i-th edge in the interaction graph has not been cut; the length of s represents the number of edges in the interaction graph that have made a cutting decision; an empty list, i.e., candidate cutting schemes that have not made a cutting decision for any edge in the interaction graph, is added to the min-heap as the initial scheme.

3. The quantum circuit half-cutting method for distributed quantum computing environments as described in claim 1, characterized in that, Step 4 includes: Step 4.1: Take a candidate cutting scheme from the min-heap storing candidate cutting schemes; Step 4.2, check whether the selected candidate cutting scheme is feasible: if the candidate cutting scheme is not feasible, skip the scheme and continue to the next iteration; the following three types of candidate cutting schemes are not feasible: (1) if cutting the line with the candidate cutting scheme results in the number of qubits of a sub-line exceeding the number of qubits of the maximum QPU, the candidate cutting scheme is not feasible; (2) if the cutting cost of the candidate cutting scheme exceeds the minimum cost cutting scheme, the candidate cutting scheme is not feasible, because further iteration will not produce a better scheme than the minimum cost cutting scheme; (3) if the candidate cutting scheme has made cutting decisions for all edges in the interaction graph, that is, the length of the Boolean list of the candidate cutting scheme is equal to the number of edges in the interaction graph, but the large quantum line has not been cut into completely independent sub-lines, the candidate cutting scheme is not feasible; Step 4.3, Update the lowest-cost cutting scheme: When a candidate cutting scheme is feasible and has made cutting decisions for all edges in the interaction graph, compare the candidate cutting scheme with the lowest-cost cutting scheme; if the cutting cost of the candidate cutting scheme is lower, set the candidate cutting scheme as the new lowest-cost cutting scheme; in the min-heap, sort the candidate cutting schemes according to the item with the lower index value in the tuple; if the items with the lower index values ​​in two tuples are equal, compare the items with the higher index value. Step 4.4, construct new candidate cutting schemes: For a feasible candidate cutting scheme, if it does not make a cutting decision for all edges in the interaction graph, add a true value to the candidate cutting scheme to generate the first new candidate cutting scheme; add a false value to the candidate cutting scheme to generate the second new candidate cutting scheme; add the two new candidate cutting schemes to the min-heap storing candidate cutting schemes. Step 4.5: If the min-heap storing candidate cutting schemes is not empty, repeat steps 4.1 to 4.4; otherwise, return the lowest cost cutting scheme.

4. The quantum circuit half-cutting method for distributed quantum computing environments as described in claim 1, characterized in that, Step 5 includes: for each cutting operation in the lowest cost cutting scheme, obtaining the number of remote communication operations that can be removed by executing the cutting operation; calculating the average number of remote communication operations that can be removed by all cutting operations; if the number of remote communication operations that can be removed by a cutting operation is greater than or equal to the average, then the cutting operation is recorded as a critical cutting operation, otherwise it is recorded as a non-critical cutting operation, and the output is a half cutting scheme that only contains critical cutting operations.

5. A storage medium for storing a program that executes a quantum circuit half-cutting method for a distributed quantum computing environment as described in any one of claims 1 to 4.

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