Quantum bit mapping and quantum circuit synthesis methods for quantum simulation cores

Abstract

The invention discloses a quantum bit mapping and quantum circuit synthesis method for a quantum simulation kernel, relates to the field of quantum computing technology, and comprises the following steps: defining a quantum simulation kernel and a physical quantum bit connectivity graph, converting the quantum simulation kernel into the product of a plurality of exponential Pauli operators of equal length, constructing a logical quantum bit interaction matrix according to the exponential Pauli operators; calculating the pairwise interaction strength of the logical quantum bits according to the logical quantum bit interaction matrix; constructing a quantum bit mapping from the logical quantum bits to the physical quantum bits according to the physical quantum bit connectivity graph and the interaction strength of the logical quantum bits; traversing all the exponential Pauli operators, and generating a quantum circuit with the minimum depth for each exponential Pauli operator according to the quantum bit mapping and quantum circuit synthesis method; obtaining a quantum circuit with the minimum depth based on the quantum bit mapping and quantum circuit synthesis method, and at the same time, the quantum circuit has better parallelism.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing technology, and in particular to a quantum bit mapping and quantum circuit synthesis method for a quantum simulation kernel. Background Art

[0002] Quantum compilation is a technology that converts any quantum program into a quantum circuit that can be executed on a specific quantum computer. Among them, circuit transformation is one of the key links in quantum compilation. It transforms the hardware-independent quantum program into a quantum circuit composed of basic gates that can be executed in a quantum computer within an acceptable time, so that the transformed quantum circuit conforms to the coupled topology of the quantum computer and the circuit fidelity is as high as possible. Circuit transformation in quantum compilation is an indispensable bridge for implementing quantum algorithms in quantum computers.

[0003] The paper "Paulihedral: A Generalized Block-WiseCompiler Optimization Framework for QuantumSimulation Kernels" included in ACM ASPLOS 2022 proposes an open source compilation framework called Paulihedral to compile quantum simulation kernels into quantum circuits.

[0004] However, the quantum circuits generated by the Paulihedral compiler have poor parallelism because the Paulihedral compiler lacks depth estimation when generating circuits; secondly, the quantum bit mapping cost of the Paulihedral compiler is high because it lacks a quantum bit mapping method that is compatible with the circuit synthesis module, and uses a fixed quantum bit mapping that cannot be changed according to the input program. Summary of the invention

[0005] Based on the technical problems existing in the background technology, the present invention proposes a quantum bit mapping and quantum circuit synthesis method for a quantum simulation kernel, so as to obtain a quantum circuit with the smallest depth and better quantum circuit parallelism.

[0006] The quantum bit mapping and quantum circuit synthesis method for the quantum simulation kernel proposed in the present invention comprises the following steps:

[0007] Define a quantum simulation kernel and a physical qubit connectivity graph;

[0008] Converting the quantum simulation kernel into the product of a plurality of exponential Pauli operators of equal length, and constructing a logical quantum bit interaction matrix according to the exponential Pauli operators;

[0009] Calculate the pairwise interaction strength of logical qubits according to the logical qubit interaction matrix;

[0010] According to the physical qubit connectivity graph and the interaction strength of the logical qubit, a qubit mapping from the logical qubit to the physical qubit is constructed;

[0011] All exponential Pauli operators are traversed, and each exponential Pauli operator is formed into a quantum circuit with minimum depth according to the quantum bit mapping.

[0012] Furthermore, the quantum simulation kernel is constructed based on a linear combination of multiple Pauli strings of equal length, and the physical quantum bit connectivity graph is an undirected connectivity graph, in which the nodes are the physical quantum bits of the quantum computer and the edges are two-bit operations performed on the two connected physical quantum bits.

[0013] Furthermore, the definition process of the quantum simulation kernel is as follows:

[0014] Define the length as The Pauli string is any The tensor product of Pauli operators, where The Pauli operator acts on On logical qubits, The Pauli operators are called elements of the Pauli string;

[0015] Define the exponential Pauli operator as The operator of , where For the Pauli string, is a real number, For imaginary numbers, define the exponential Pauli operator The length is Length;

[0016] Define the quantum simulation kernel as The operator of , where is a real number, is a linear combination of multiple Pauli strings of equal length.

[0017] Further, constructing a logical quantum bit interaction matrix according to the exponential Pauli operator is specifically: based on the fact that The first Pauli series The Pauli operator is When Line The rule that the column elements are 0 and otherwise 1 is used to construct the logical quantum bit interaction matrix according to the exponential Pauli operator.

[0018] Furthermore, the pairwise interaction strength of the logical qubits is calculated according to the logical qubit interaction matrix, specifically: logical qubits and The interaction strength of the logical qubit is the first Column and The inner product of the columns is then used to calculate the pairwise interaction strength of the logical qubits according to the logical qubit interaction matrix.

[0019] Furthermore, the qubit mapping process from logical qubits to physical qubits is as follows:

[0020] (a1) Calculate the 1-norm of all columns in the logical qubit interaction matrix and arrange them in descending order, and map the logical qubit corresponding to the first column to the central node of the physical qubit connectivity graph;

[0021] (a2) Find the unmapped logical qubit with the largest sum of interaction strengths with the mapped logical qubits, denoted by ;

[0022] (a3) The mapped logical qubits are recorded as a set , mapping the found logical qubit to a node in the physical qubit connectivity graph , the node is and set The node with the lowest interaction cost for the logical qubits in ;

[0023] (a4) Repeat steps (a2) to (a3) ​​until all logical qubits are mapped.

[0024] Furthermore, in (a3), the node The interaction cost is defined as:

[0025] ;

[0026] in, is the quantum bit mapping, Representing logical qubits The node to which it is mapped, A node in the physical quantum bit connectivity graph and nodes The shortest path distance between Representing logical qubits and logical qubits The interaction intensity.

[0027] Furthermore, we define four Pauli operators: , , and ; In step 5, the exponential Pauli operator The process of synthesizing a quantum circuit with minimum depth is as follows:

[0028] (b1) Initialize an empty circuit C and traverse the Pauli string For all elements of The Pauli operator is , add an effect in Quantum gates on to line C; if the Pauli string The Pauli operator is , add an effect in Quantum gates on to the empty circuit; otherwise, no gate is added, where Indicates logical qubits The node to which it is mapped;

[0029] (b2) Find the Pauli string and finding the node to which the core quantum bit is mapped in the physical quantum bit connectivity graph;

[0030] (b3) Construct a qubit tree to cover all mapped nodes;

[0031] (b4) Traverse the edges of the qubit tree in (b3) from the bottom up, and add a CNOT gate acting on the two physical qubits at both ends of the edge to circuit C;

[0032] (b5) Add an action on the root node of the qubit tree Door;

[0033] (b6) Add the quantum gates added in (b4) to circuit C in reverse order;

[0034] (b7) Traversing the Pauli string For all elements of The Pauli operator is , add an effect in Quantum gates on to line C; if the Pauli string The Pauli operator is , add an effect in Quantum gates on to line C; otherwise, no gate is added, where Indicates logical qubits The nodes are mapped to, thereby synthesizing a quantum circuit with minimal depth.

[0035] Furthermore, in (b3), the construction process of the quantum bit tree is as follows:

[0036] (b3-1) Find the central node in the physical quantum bit connectivity graph as the root of the tree;

[0037] (b3-2) Define the connectivity cost function;

[0038] (b3-3) Based on the connectivity cost function, select the node that minimizes the cost function in the physical quantum bit connectivity graph;

[0039] (b3-4) Definition Respectively represent the depth and degree of the quantum bit tree, and define the parallel cost function as , if (b3-3) filters out multiple nodes, then filter out nodes that make The smallest node, if The smallest node screens out multiple nodes, and then randomly selects a node to add to the quantum bit tree, thereby constructing the quantum bit tree.

[0040] Furthermore, in (b3-2), the connectivity cost function The details are as follows:

[0041] ;

[0042] in, denote the set of nodes found in (b2) and the set of nodes that have been added to the qubit tree, respectively. yes The nodes in that have not been added to the qubit tree, for The nodes in , that is, the nodes in the quantum bit tree.

[0043] The advantages of the quantum bit mapping and quantum circuit synthesis method for the quantum simulation kernel provided by the present invention are: constructing a quantum bit mapping according to the input quantum simulation kernel and the hardware quantum bit connectivity graph; constructing a quantum bit tree for each exponential Pauli operator in the input quantum simulation kernel according to the constructed quantum bit mapping; for each quantum bit tree, generating a quantum circuit with the minimum depth for the corresponding exponential Pauli operator; therefore, this embodiment comprehensively considers the degree and depth of the tree when constructing the quantum bit tree, the constructed quantum bit tree is more balanced, and the corresponding quantum circuit has better parallelism. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the process of the present invention;

[0045] Figure 2 A schematic diagram of constructing a quantum bit tree based on a cost function;

[0046] Figure 3 A schematic diagram of constructing a qubit tree based on the depth and number of branches;

[0047] Figure 4 A schematic diagram of constructing a quantum circuit based on a quantum bit tree;

[0048] Figure 5 Schematic diagram of quantum bit mapping. DETAILED DESCRIPTION

[0049] Below, the technical solution of the present invention is described in detail through specific embodiments. Many specific details are set forth in the following description to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific implementation disclosed below.

[0050] like Figures 1 to 5 As shown, the quantum bit mapping and quantum circuit synthesis method for the quantum simulation kernel proposed in the present invention includes the following steps:

[0051] Step 1: define a quantum simulation kernel and a physical quantum bit connectivity graph, wherein the quantum simulation kernel is constructed based on a linear combination H of multiple Pauli strings of equal length, and the physical quantum bit connectivity graph is an undirected connectivity graph, wherein the nodes are physical quantum bits of a quantum computer, and the edges are two-bit operations performed on two connected physical quantum bits;

[0052] The matrix representations of the four Pauli operators are defined as follows:

[0053] ;

[0054] in Represents an imaginary unit.

[0055] Define the length as The Pauli string is any The tensor product of Pauli operators, where The Pauli operator acts on On logical qubits, The Pauli operators are called elements of the Pauli string;

[0056] Define the exponential Pauli operator as The operator of , where For the Pauli string, is a real number, For imaginary numbers, define the exponential Pauli operator The length is Length;

[0057] Define the quantum simulation kernel as The operator of , where is a real number, is a linear combination of multiple Pauli strings of equal length, that is ,in For a Pauli string, is a real number.

[0058] Define the quantum bit connectivity graph as an undirected connectivity graph , the nodes in the graph is the physical qubit of a quantum computer. The edge connecting two physical qubits in the figure Indicates that two-bit operations can be performed on this pair of physical quantum bits.

[0059] Step 2: Convert the quantum simulation kernel into the product of multiple exponential Pauli operators of equal length, based on the assumption that The first Pauli series The Pauli operator is When Line The rule that the column elements are 0 and otherwise are 1, constructs a logical quantum bit interaction matrix according to the exponential Pauli operator;

[0060] The quantum simulation kernel is converted into a product of exponential Pauli operators using the following formula (1):

[0061] (1);

[0062] is a real number.

[0063] The logical qubit interaction matrix is ​​a A 0 / 1 matrix, where is equal to the number of Pauli strings in H, is equal to the length of these Pauli strings if and only if the The first Pauli series When the Pauli operator is I, the logical quantum bit interaction matrix Line The column element is 0, otherwise it is 1. In the following description, The first Column vector, corresponding to logical qubits, The first Column vector, corresponding to logical qubits.

[0064] Assume that H contains the five Pauli strings of equation (2), as shown on the left side of the equation, and the corresponding logical quantum bit interaction matrix is ​​shown on the right side of the equation. Except for the eighth element of the first Pauli string which is I, the rest of the elements are not I. Therefore, in the first row of the corresponding matrix, only the eighth element is 0, and the rest of the elements are 1;

[0065] (2);

[0066] In formula (2), each row represents a Pauli string, so there are five Pauli strings in total, namely: YZZZZYYIY, XYIXXIZYZ, XXIIXXYXI, ZIIIXYYYY, XZYYXZXYI.

[0067] Step 3: Define logical qubits and The interaction strength of the logical qubit is the first Column and The inner product of the columns is used to calculate the pairwise interaction strength of the logical qubits according to the logical qubit interaction matrix;

[0068] In this embodiment, Indicates logical qubits and The interaction strength of logical qubits, .

[0069] In formula (2), ， , therefore, the interaction strength between the second logical qubit and the third logical qubit is .

[0070] Step 4: construct a quantum bit mapping from logical quantum bits to physical quantum bits based on the physical quantum bit connectivity graph and the interaction strength of the logical quantum bits;

[0071] The quantum bit mapping construction process is as follows (a1) to (a4):

[0072] (a1) Calculate the 1-norm of all columns in the logical qubit interaction matrix and arrange them in descending order, and map the logical qubit corresponding to the first column to the central node of the physical qubit connectivity graph;

[0073] Since the number of columns of the logical qubit interaction matrix corresponds to the logical qubit, the column number c with the largest 1-norm also corresponds to the cth logical qubit, and the cth logical qubit is mapped to the central node of the physical qubit connectivity graph. Since the nodes of the physical qubit connectivity graph are the physical qubits of the quantum computer, the mapping from the cth logical qubit to the cth physical qubit is realized.

[0074] (a2) Find the unmapped logical qubit with the largest sum of interaction strengths with the mapped logical qubits, denoted by .

[0075] (a3) The mapped logical qubits are recorded as a set , mapping the found logical qubit to a node in the physical qubit connectivity graph , the node is and set The node with the lowest interaction cost for the logical qubits in ;

[0076] node The interaction cost is defined as:

[0077] ;

[0078] in, is the quantum bit mapping, Representing logical qubits The node to which it is mapped, A node in the physical quantum bit connectivity graph and nodes The shortest path distance between Representing logical qubits and logical qubits The interaction intensity.

[0079] (a4) Repeat steps (a2) to (a3) ​​until all logical qubits are mapped.

[0080] Through (a1) to (a4), the construction of quantum bit mapping is realized.

[0081] Step 5: Traverse all exponential Pauli operators, and map the quantum bits obtained in step 3 to form a quantum circuit with the minimum depth for each exponential Pauli operator, including (b1) to (b6):

[0082] (b1) Initialize an empty circuit C and traverse the Pauli string For all elements of The Pauli operator is , add an effect in Quantum gates on to line C; if the Pauli string The Pauli operator is , add an effect in Quantum gates on to the empty circuit; otherwise, no gate is added, where Indicates logical qubits The node to which it is mapped;

[0083] (b2) Find the Pauli string , and find the nodes to which these core qubits are mapped in the physical qubit connectivity graph;

[0084] (b3) Construct a qubit tree to cover all mapped nodes;

[0085] The construction process of the quantum bit tree specifically includes (b3-1) to (b3-4):

[0086] (b3-1) Find the central node in the physical quantum bit connectivity graph as the root of the tree;

[0087] like Figure 2 The figure shows a physical quantum bit connectivity graph. The nodes with numbers represent the physical quantum bits found in (b2), and the numbers in the nodes represent the numbers of the logical quantum bits mapped to the nodes. The node where Set as the root node.

[0088] (b3-2) Define the connectivity cost function ;

[0089] ;

[0090] in, denote the set of nodes found in (b2) and the set of nodes that have been added to the qubit tree, respectively. yes The nodes in that have not been added to the qubit tree, for The nodes in , that is, the nodes in the quantum bit tree;

[0091] The geometric meaning of the connectivity cost function is The sum of the shortest distances from the nodes that have not been added to the qubit tree to the qubit tree. Figure 2 As shown, assuming The node where it is located has been added to the qubit tree. The node that has not been added to the qubit tree is , The node closest to the qubit tree is , the distance is 2, is also 2, so the connectivity cost function .

[0092] (b3-3) Based on the connectivity cost function, select the node that minimizes the cost function in the physical quantum bit connectivity graph;

[0093] like Figure 2 As shown, if The node above is added to the qubit tree, and the new connectivity cost function value can be calculated in the same way to be 3. The node on the right is added to the qubit tree, and the connectivity cost function is updated to 2. Therefore, this step will filter out The algorithm will follow the node on the right side of Figure 2 The steps shown by the solid arrows in the middle construct the quantum bit tree.

[0094] (b3-4) Definition Respectively represent the depth and degree of the quantum bit tree, and define the parallel cost function as , if (b3-3) filters out multiple nodes, then filter out nodes that make The smallest node, if The smallest node screens out multiple nodes, and then randomly selects a node to add to the quantum bit tree, thereby constructing the quantum bit tree.

[0095] like Figure 3 As shown, assuming have been added to the qubit tree, and further or or , the connectivity cost function D is equal to 2. However, their corresponding parallel cost functions are different. or Add a qubit tree, the degree of the qubit tree is 3 ( has three child nodes), the depth is 2, so, If you choose to Add a qubit tree, the degree and depth of the qubit tree are both 2, .therefore, is a better choice, the algorithm will follow Figure 3 The steps shown by the solid arrows in the middle construct the quantum bit tree.

[0096] (b4) Traverse the edges of the qubit tree in (b3) from the bottom up, and add a CNOT gate acting on the two physical qubits at both ends of the edge to circuit C;

[0097] For each edge that accesses the physical qubit connectivity graph , are two physical qubits connected by an edge, and a CNOT gate is added to act on these two physical qubits. Figure 4 In the example above, we traverse the edges of the quantum bit tree shown on the left from bottom to top. , add the corresponding quantum gates to Figure 4 Line C is shown to the right of the arrow.

[0098] (b5) Add an action on the root node of the qubit tree Door;

[0099] (b6) Add the quantum gates added in (b4) to the quantum circuit in reverse order;

[0100] (b7) Traversing the Pauli string For all elements of The Pauli operator is , add an effect in Quantum gates on to line C; if the Pauli string The Pauli operator is , add an effect in Quantum gates on to the empty circuit; otherwise, no gate is added, where Indicates logical qubits The node to which it is mapped, thus creating a quantum circuit with minimal depth.

[0101] The quantum circuit with the minimum depth is realized through (b1) to (b7) based on the obtained exponential Pauli operator.

[0102] According to steps one to five, this embodiment constructs a quantum bit mapping according to the input quantum simulation kernel and the hardware quantum bit connectivity graph; constructs a quantum bit tree for each exponential Pauli operator in the input quantum simulation kernel according to the constructed quantum bit mapping; for each quantum bit tree, generates a quantum circuit with the minimum depth for the corresponding exponential Pauli operator.

[0103] Compared with the Paulihedral compiler, the circuit depth obtained by compiling with the compilation framework proposed in this embodiment is shallower and contains fewer CNOT gates. A set of test quantum simulation kernels are compiled using this embodiment and the Paulihedral compiler respectively. This embodiment can reduce the number of CNOT gates and the circuit depth by 13% and 25% relative to the Paulihedral compiler. On the one hand, this is because the Paulihedral compiler uses a fixed quantum bit mapping, and the interaction of quantum bits requires more SWAP gates to assist, and one SWAP gate requires three CNOT gates to implement; and this embodiment constructs a quantum bit mapping according to the quantum bit interaction intensity. The stronger the interaction of quantum bits, the closer they will be mapped to, so it is conducive to their interaction, and the number of SWAP gates required is less. On the other hand, the Paulihedral compiler uses a depth-first tree as a quantum bit tree, which does not balance the degree and depth of the tree, resulting in poor circuit parallelism, and therefore, the depth of the circuit is deeper. However, this embodiment takes into account the degree and depth of the tree when constructing the quantum bit tree, so the constructed quantum bit tree is more balanced, and the corresponding quantum circuit parallelism is better.

[0104] As an example,

[0105] S1. Define a quantum simulation kernel and a physical qubit connectivity graph;

[0106] Assume that the input quantum simulation kernel ,in:

[0107] .

[0108] S2. According to step 2, the quantum simulation kernel Decompose into five exponential Pauli operators:

[0109] ;

[0110] Then, according to The Pauli string contained in constructs a logical quantum bit interaction matrix as shown in equation (2); according to step 2, the interaction strength of each pair of quantum bits is calculated;

[0111] S3. According to step 3, construct Figure 5 The qubit mapping shown;

[0112] S4: According to step 4, construct a qubit tree for each exponential Pauli, such as Figure 5 As shown, Figure 5 Each Pauli string in represents the corresponding exponential Pauli operator, such as the first Pauli string represent , according to step (b4), traverse the qubit tree from bottom to top and add a series of quantum gates to the empty circuit, Figure 5 To the right of each qubit tree in is the quantum gate added to the empty circuit in step (b4), resulting in a quantum circuit with the minimum depth for each exponential Pauli operator.

[0113] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A quantum bit mapping and quantum circuit synthesis method for a quantum simulation kernel, characterized in that: include: Define a quantum simulation kernel and a physical qubit connectivity graph; Converting the quantum simulation kernel into the product of a plurality of exponential Pauli operators of equal length, and constructing a logical quantum bit interaction matrix according to the exponential Pauli operators; Calculate the pairwise interaction strength of logical qubits according to the logical qubit interaction matrix; According to the physical qubit connectivity graph and the interaction strength of the logical qubit, a qubit mapping from the logical qubit to the physical qubit is constructed; Traversing all exponential Pauli operators, and mapping each exponential Pauli operator into a quantum circuit with minimum depth according to the quantum bit mapping; The qubit mapping process from logical qubits to physical qubits is as follows: (a1) Calculate the 1-norm of all columns in the logical qubit interaction matrix and arrange them in descending order, and map the logical qubit corresponding to the first column to the central node of the physical qubit connectivity graph; (a2) Find the unmapped logical qubit with the largest sum of interaction strengths with the mapped logical qubits, denoted by ; (a3) The mapped logical qubits are recorded as a set , mapping the found logical qubit to a node in the physical qubit connectivity graph , the node is and set The node with the lowest interaction cost for the logical qubits in The interaction cost is defined as: in, is the quantum bit mapping, Representing logical qubits The node to which it is mapped, A node in the physical quantum bit connectivity graph and nodes The shortest path distance between Representing logical qubits and logical qubits The interaction strength; (a4) Repeat steps (a2) to (a3) ​​until all logical qubits are mapped.

2. The method for quantum bit mapping and quantum circuit synthesis for a quantum simulation kernel according to claim 1, characterized in that: The quantum simulation kernel is constructed based on a linear combination of multiple Pauli strings of equal length. The physical quantum bit connectivity graph is an undirected connectivity graph, in which the nodes are the physical quantum bits of the quantum computer and the edges are two-bit operations performed on the two connected physical quantum bits.

3. The method for quantum bit mapping and quantum circuit synthesis for a quantum simulation kernel according to claim 2, characterized in that the quantum The simulation kernel is defined as follows: Define the length as The Pauli string is any The tensor product of Pauli operators, where The Pauli operator acts on On logical qubits, The Pauli operators are called elements of the Pauli string; Define the exponential Pauli operator as The operator of , where For the Pauli string, is a real number, For imaginary numbers, define the exponential Pauli operator The length is Length; Define the quantum simulation kernel as The operator of , where is a real number, is a linear combination of multiple Pauli strings of equal length.

4. The method for quantum bit mapping and quantum circuit synthesis for a quantum simulation kernel according to claim 2, characterized in that: The logical quantum bit interaction matrix is ​​constructed according to the exponential Pauli operator, specifically: based on the The first Pauli series The Pauli operator is When Line The rule that the column elements are 0 and otherwise 1 is used to construct the logical quantum bit interaction matrix according to the exponential Pauli operator.

5. The method for quantum bit mapping and quantum circuit synthesis for a quantum simulation kernel according to claim 1, characterized in that: The pairwise interaction strength of logical qubits is calculated based on the logical qubit interaction matrix. Specifically, define logical qubits and The interaction strength of the logical qubit is the first Column and The inner product of the columns is then used to calculate the pairwise interaction strength of the logical qubits according to the logical qubit interaction matrix.

6. The method for quantum bit mapping and quantum circuit synthesis for a quantum simulation kernel according to claim 3, characterized in that: Define four Pauli operators , , and ; Exponential Pauli Operator The process of synthesizing a quantum circuit with minimum depth is as follows: (b1) Initialize an empty circuit C and traverse the Pauli string For all elements of The Pauli operator is , add an effect in Quantum gates on to line C; if the Pauli string The Pauli operator is , add an effect in Quantum gates on to the empty circuit; otherwise, no gate is added, where Indicates logical qubits The node to be mapped; (b2) Find the Pauli string and finding the node to which the core quantum bit is mapped in the physical quantum bit connectivity graph; (b3) Construct a qubit tree to cover all mapped nodes; (b4) Traverse the edges of the qubit tree in (b3) from the bottom up, and add a CNOT gate acting on the two physical qubits at both ends of the edge to circuit C; (b5) Add an action on the root node of the qubit tree Door; (b6) Add the quantum gates added in (b4) to circuit C in reverse order; (b7) Traversing the Pauli string For all elements of The Pauli operator is , add an effect in Quantum gates on to line C; if the Pauli string The Pauli operator is , add an effect in Quantum gates on to line C; otherwise, no gate is added, where Indicates logical qubits The nodes are mapped to, thereby synthesizing a quantum circuit with minimal depth.

7. The method for quantum bit mapping and quantum circuit synthesis for a quantum simulation kernel according to claim 6, characterized in that: In (b3), the construction process of the qubit tree is as follows: (b3-1) Find the central node in the physical quantum bit connectivity graph as the root of the tree; (b3-2) Define the connectivity cost function; (b3-3) Based on the connectivity cost function, select the node that minimizes the cost function in the physical quantum bit connectivity graph; (b3-4) Definition Respectively represent the depth and degree of the quantum bit tree, and define the parallel cost function as , if (b3-3) filters out multiple nodes, then filter out nodes that make The smallest node, if The smallest node screens out multiple nodes, and then randomly selects a node to add to the quantum bit tree, thereby constructing the quantum bit tree.

8. The method for quantum bit mapping and quantum circuit synthesis for a quantum simulation kernel according to claim 7, characterized in that: In (b3-2), the connectivity cost function The details are as follows: in, denote the set of nodes found in (b2) and the set of nodes that have been added to the qubit tree, respectively. yes The nodes in that have not been added to the qubit tree, for The nodes in , that is, the nodes in the quantum bit tree.

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