一、项目初始化 # 创建项目结构 mkdir -p quantum_lab/{ core,experiments,ui} cd quantum_lab# 创建requirements.txt cat > requirements.txt<< 'EOF' streamlit>=1.28.0 numpy>=1.24.0 scipy>=1.11.0 matplotlib>=3.7.0 pandas>=2.0.0 plotly>=5.17.0 seaborn>=0.12.0 tqdm>=4.65.0 joblib>=1.3.0 EOF # 创建主文件 touch __init__.pytouch main.py二、核心后端实现 2.1 量子态模拟器基类 # core/backend.py from abcimport ABC, abstractmethodfrom typingimport List, Tuple, Dict, Anyimport numpyas npclass QuantumBackend ( ABC) : """量子计算后端抽象基类""" @abstractmethod def initialize ( self, n_qubits: int ) - > None : """初始化量子寄存器""" pass @abstractmethod def apply_gate ( self, gate_name: str , targets: List[ int ] , controls: List[ int ] = None , params: Dict= None ) - > None : """应用量子门""" pass @abstractmethod def get_statevector ( self) - > np. ndarray: """获取当前量子态""" pass @abstractmethod def measure ( self, shots: int = 1024 ) - > Dict[ str , int ] : """测量量子态""" pass @abstractmethod def reset ( self) - > None : """重置到|0>态""" pass @abstractmethod def expectation_value ( self, pauli_string: str ) - > float : """计算Pauli算符的期望值""" pass 2.2 Statevector模拟器实现 # core/statevector_backend.py import numpyas npfrom typingimport List, Dict, Anyimport itertoolsfrom . backendimport QuantumBackendclass StatevectorBackend ( QuantumBackend) : """纯Python实现的量子态矢量模拟器""" # Pauli矩阵定义 PAULI_MATRICES= { 'I' : np. array( [ [ 1 , 0 ] , [ 0 , 1 ] ] , dtype= complex ) , 'X' : np. array( [ [ 0 , 1 ] , [ 1 , 0 ] ] , dtype= complex ) , 'Y' : np. array( [ [ 0 , - 1j ] , [ 1j , 0 ] ] , dtype= complex ) , 'Z' : np. array( [ [ 1 , 0 ] , [ 0 , - 1 ] ] , dtype= complex ) , } # 基础量子门矩阵 GATE_MATRICES= { 'H' : np. array( [ [ 1 , 1 ] , [ 1 , - 1 ] ] , dtype= complex ) / np. sqrt( 2 ) , 'X' : np. array( [ [ 0 , 1 ] , [ 1 , 0 ] ] , dtype= complex ) , 'Y' : np. array( [ [ 0 , - 1j ] , [ 1j , 0 ] ] , dtype= complex ) , 'Z' : np. array( [ [ 1 , 0 ] , [ 0 , - 1 ] ] , dtype= complex ) , 'S' : np. array( [ [ 1 , 0 ] , [ 0 , 1j ] ] , dtype= complex ) , 'T' : np. array( [ [ 1 , 0 ] , [ 0 , np. exp( 1j * np. pi/ 4 ) ] ] , dtype= complex ) , 'CNOT' : None , # 特殊处理 'SWAP' : None , # 特殊处理 } def __init__ ( self, n_qubits: int ) : self. n_qubits= n_qubits self. state= np. zeros( 2 ** n_qubits, dtype= complex ) self. state[ 0 ] = 1.0 # |00...0⟩ self. gate_history= [ ] def initialize ( self, n_qubits: int = None ) - > None : """初始化量子寄存器""" if n_qubits: self. n_qubits= n_qubits self. state= np. zeros( 2 ** self. n_qubits, dtype= complex ) self. state[ 0 ] = 1.0 self. gate_history= [ ] def _tensor_product ( self, matrices: List[ np. ndarray] ) - > np. ndarray: """计算张量积""" result= matrices[ 0 ] for matin matrices[ 1 : ] : result= np. kron( result, mat) return resultdef _apply_single_qubit_gate ( self, gate: np. ndarray, target: int ) - > None : """应用单量子比特门""" # 构造完整的变换矩阵 matrices= [ self. PAULI_MATRICES[ 'I' ] ] * self. n_qubits matrices[ target] = gate full_matrix= self. _tensor_product( matrices) # 应用变换 self. state= full_matrix @ self. statedef _apply_controlled_gate ( self, gate: np. ndarray, control: int , target: int ) - > None : """应用受控门（CNOT, CZ等）""" # 构建受控门的矩阵表示 dim= 2 ** self. n_qubits matrix= np. eye( dim, dtype= complex ) # 遍历所有基态 for iin range ( dim) : # 将索引转换为二进制字符串 bits= format ( i, f'0 { self. n_qubits} b' ) # 检查控制位是否为1 if bits[ control] == '1' : # 计算目标位翻转后的索引 target_bit= bits[ target] new_target_bit= '0' if target_bit== '1' else '1' # 构造新的二进制字符串 new_bits= list ( bits) new_bits[ target] = new_target_bit new_bits_str= '' . join( new_bits) # 计算新索引 j= int ( new_bits_str, 2 ) # 对于CNOT，就是简单的交换振幅 matrix[ i, i] = 0 matrix[ i, j] = 1 # 应用变换 self. state= matrix @ self. statedef _rotation_gate ( self, axis: str , angle: float ) - > np. ndarray: """生成旋转门矩阵""" if axis== 'x' : return np. array( [ [ np. cos( angle/ 2 ) , - 1j * np. sin( angle/ 2 ) ] , [ - 1j * np. sin( angle/ 2 ) , np. cos( angle/ 2 ) ] ] , dtype= complex ) elif axis== 'y' : return np. array( [ [ np. cos( angle/ 2 ) , - np. sin( angle/ 2 ) ] , [ np. sin( angle/ 2 ) , np. cos( angle/ 2 ) ] ] , dtype= complex ) elif axis== 'z' : return np. array( [ [ np. exp( - 1j * angle/ 2 ) , 0 ] , [ 0 , np. exp( 1j * angle/ 2 ) ] ] , dtype= complex ) else : raise ValueError( f"Unknown rotation axis: { axis} " ) def apply_gate ( self, gate_name: str , targets: List[ int ] , controls: List[ int ] = None , params: Dict= None ) - > None : """应用量子门""" controls= controlsor [ ] params= paramsor { } # 记录门操作 self. gate_history. append( { 'gate' : gate_name, 'targets' : targets, 'controls' : controls, 'params' : params} ) # 处理旋转门 if gate_name. startswith( 'R' ) : axis= gate_name[ 1 ] . lower( ) angle= params. get( 'theta' , 0.0 ) gate_matrix= self. _rotation_gate( axis, angle) for targetin targets: self. _apply_single_qubit_gate( gate_matrix, target) # 处理标准单量子比特门 elif gate_namein self. GATE_MATRICESand self. GATE_MATRICES[ gate_name] is not None : gate_matrix= self. GATE_MATRICES[ gate_name] for targetin targets: self. _apply_single_qubit_gate( gate_matrix, target) # 处理CNOT门 elif gate_name== 'CNOT' : if len ( controls) != 1 or len ( targets) != 1 : raise ValueError( "CNOT gate requires exactly one control and one target" ) self. _apply_controlled_gate( self. GATE_MATRICES[ 'X' ] , controls[ 0 ] , targets[ 0 ] ) # 处理CZ门 elif gate_name== 'CZ' : if len ( controls) != 1 or len ( targets) != 1 : raise ValueError( "CZ gate requires exactly one control and one target" ) self. _apply_controlled_gate( self. PAULI_MATRICES[ 'Z' ] , controls[ 0 ] , targets[ 0 ] ) else : raise ValueError( f"Unsupported gate: { gate_name} " ) def get_statevector ( self) - > np. ndarray: """获取当前量子态""" return self. state. copy( ) def get_probabilities ( self) - > np. ndarray: """获取测量概率分布""" return np. abs ( self. state) ** 2 def measure ( self, shots: int = 1024 ) - > Dict[ str , int ] : """测量量子态""" probs= self. get_probabilities( ) counts= { } # 概率采样 samples= np. random. choice( len ( probs) , size= shots, p= probs) # 统计结果 for samplein samples: bitstring= format ( sample, f'0 { self. n_qubits} b' ) counts[ bitstring] = counts. get( bitstring, 0 ) + 1 return countsdef expectation_value ( self, pauli_string: str ) - > float : """计算Pauli算符的期望值""" # 解析Pauli字符串，如 "X0 Z1" terms= pauli_string. split( ) coeff= 1.0 if len ( terms) == 0 : return 1.0 # 检查是否有系数 if terms[ 0 ] . replace( '.' , '' ) . replace( '-' , '' ) . isdigit( ) : coeff= float ( terms[ 0 ] ) terms= terms[ 1 : ] # 构建Pauli算符的矩阵表示 matrices= [ self. PAULI_MATRICES[ 'I' ] ] * self. n_qubitsfor termin terms: pauli= term[ 0 ] qubit= int ( term[ 1 : ] ) matrices[ qubit] = self. PAULI_MATRICES[ pauli] # 计算张量积 pauli_matrix= self. _tensor_product( matrices) # 计算期望值 expectation= np. real( np. vdot( self. state, pauli_matrix @ self. state) ) return coeff* expectationdef reset ( self) - > None : """重置到|0>态""" self. initialize( self. n_qubits) def __str__ ( self) - > str : """字符串表示""" return f"StatevectorBackend(n_qubits= { self. n_qubits} )" 2.3 可视化工具 # core/visualization.py import numpyas npimport matplotlib. pyplotas pltfrom matplotlib. patchesimport FancyArrowPatchfrom mpl_toolkits. mplot3dimport proj3dimport plotly. graph_objectsas goclass QuantumVisualizer : """量子态可视化工具""" @staticmethod def plot_statevector ( statevector: np. ndarray, title: str = "Quantum State" ) : """绘制量子态振幅和相位""" fig, ( ax1, ax2) = plt. subplots( 1 , 2 , figsize= ( 12 , 4 ) ) n_qubits= int ( np. log2( len ( statevector) ) ) basis_states= [ format ( i, f'0 { n_qubits} b' ) for iin range ( len ( statevector) ) ] # 振幅图 amplitudes= np. abs ( statevector) ax1. bar( basis_states, amplitudes** 2 , alpha= 0.7 , color= 'blue' ) ax1. set_xlabel( 'Basis State' ) ax1. set_ylabel( 'Probability' ) ax1. set_title( f' { title} - Probabilities' ) ax1. tick_params( axis= 'x' , rotation= 45 ) # 相位图 phases= np. angle( statevector) ax2. bar( basis_states, phases, alpha= 0.7 , color= 'red' ) ax2. set_xlabel( 'Basis State' ) ax2. set_ylabel( 'Phase (radians)' ) ax2. set_title( f' { title} - Phases' ) ax2. tick_params( axis= 'x' , rotation= 45 ) plt. tight_layout( ) return fig@staticmethod def plot_bloch_vector ( theta: float , phi: float , title: str = "Bloch Sphere" ) : """在Bloch球上绘制量子态""" # 计算笛卡尔坐标 x= np. sin( theta) * np. cos( phi) y= np. sin( theta) * np. sin( phi) z= np. cos( theta) # 创建Bloch球 fig= plt. figure( figsize= ( 8 , 8 ) ) ax= fig. add_subplot( 111 , projection= '3d' ) # 绘制球体 u= np. linspace( 0 , 2 * np. pi, 100 ) v= np. linspace( 0 , np. pi, 100 ) xs= np. outer( np. cos( u) , np. sin( v) ) ys= np. outer( np. sin( u) , np. sin( v) ) zs= np. outer( np. ones( np. size( u) ) , np. cos( v) ) ax. plot_surface( xs, ys, zs, color= 'b' , alpha= 0.1 ) # 绘制坐标轴 ax. quiver( 0 , 0 , 0 , 1.5 , 0 , 0 , color= 'r' , arrow_length_ratio= 0.1 , label= 'X' ) ax. quiver( 0 , 0 , 0 , 0 , 1.5 , 0 , color= 'g' , arrow_length_ratio= 0.1 , label= 'Y' ) ax. quiver( 0 
