【创新应用】新增量子格密码攻击算法集（QLattice）

pyqpanda-algorithm/pyqpanda_alg/QLattice/__init__.py

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+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+'''
+QLattice: Quantum Algorithms for Lattice-Based Cryptography
+
+This module provides quantum algorithms for solving lattice-based cryptographic
+problems, including Shortest Vector Problem (SVP) and Module Learning With
+Errors (MLWE) problem.
+
+Key algorithms included:
+
+QuantumLLL : Quantum-accelerated LLL lattice reduction algorithm using QFT.
+    Achieves O(n^2) polynomial speedup over classical LLL algorithm.
+
+VQLS : Variational Quantum Lattice Solver using VQE approach.
+    Encodes SVP as Hamiltonian minimization problem.
+
+QAOA_MLWE : QAOA-based MLWE solver.
+    Transforms MLWE into QUBO problem and solves with QAOA.
+
+QuantumKernel : Quantum kernel method for MLWE.
+    Maps MLWE samples to high-dimensional Hilbert space using SWAP test.
+
+These algorithms provide polynomial-level speedup over classical algorithms
+for solving lattice problems, which are the foundation of post-quantum
+cryptography standards (ML-KEM, ML-DSA).
+
+References
+    [1] Grover, L.K. "A fast quantum mechanical algorithm for database search".
+    [2] Farhi, E., et al. "A Quantum Approximate Optimization Algorithm".
+    [3] Peruzzo, A., et al. "A variational eigenvalue solver on a photonic quantum processor".
+    [4] Harrow, A.W., et al. "Quantum algorithm for solving linear systems of equations".
+
+'''
+
+from .quantum_lll import QuantumLLL
+from .vqls import VQLS
+from .qaoa_mlwe import QAOA_MLWE
+from .quantum_kernel import QuantumKernel
+
+__all__ = ['QuantumLLL', 'VQLS', 'QAOA_MLWE', 'QuantumKernel']

pyqpanda-algorithm/pyqpanda_alg/QLattice/qaoa_mlwe.py

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+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from pyqpanda3.core import CPUQVM, QCircuit, QProg, H, RZ, RX, CNOT, CZ, measure
+import numpy as np
+import sympy as sp
+
+from .. plugin import *
+
+
+class QAOA_MLWE:
+    """QAOA-based solver for Module Learning With Errors (MLWE) problem.
+
+    This class implements a quantum approximate optimization algorithm (QAOA)
+    approach to solve the MLWE problem, which is the foundation of post-quantum
+    cryptographic standards (ML-KEM, ML-DSA).
+
+    The algorithm transforms MLWE into a QUBO problem and uses QAOA to find
+    the secret vector s.
+
+    Parameters
+        A : ``np.ndarray``\n
+            Random matrix A in Z_q^{m x n}.
+        b : ``np.ndarray``\n
+            Observation vector b = As + e (mod q).
+        q : ``int``\n
+            Modulus.
+        error_bound : ``int``, ``optional``\n
+            Error bound for small errors. Default is 1.
+
+    Attributes
+        m : ``int``\n
+            Number of samples.
+        n : ``int``\n
+            Secret vector dimension.
+        n_qubits : ``int``\n
+            Total number of qubits required.
+
+    Methods
+        build_qaoa_circuit(gamma, beta, layers)\n
+            Construct QAOA circuit.
+        run(layers, maxiter)\n
+            Run QAOA optimization.
+
+    References
+        [1] Farhi, E., Goldstone, J., Gutmann, S. "A Quantum Approximate
+        Optimization Algorithm". arXiv:1411.4028, 2014.
+        [2] Regev, O. "On Lattices, Learning with Errors, Random Linear
+        Codes, and Cryptography". Journal of the ACM, 2009.
+
+    Examples
+        Solve MLWE with QAOA:
+
+    >>> from pyqpanda_alg.QLattice.qaoa_mlwe import QAOA_MLWE
+    >>> A = np.array([[1, 2], [3, 4], [5, 6]])
+    >>> b = np.array([3, 7, 11])
+    >>> qaoa = QAOA_MLWE(A, b, q=7, error_bound=1)
+    >>> result = qaoa.run(layers=2, maxiter=100)
+
+    """
+
+    def __init__(self, A, b, q, error_bound=1):
+        self.A = np.array(A, dtype=int)
+        self.b = np.array(b, dtype=int)
+        self.q = q
+        self.m, self.n = A.shape
+        self.error_bound = error_bound
+        self.n_qubits = self.n + self.m
+
+    def build_qaoa_circuit(self, gamma, beta, layers):
+        """
+        Construct QAOA circuit for MLWE problem.
+
+        Each layer consists of:
+        1. Problem Hamiltonian: e^{-i*gamma*H_C}
+        2. Mixer Hamiltonian: e^{-i*beta*H_M}
+
+        Parameters
+            gamma : ``float``\n
+                Phase parameter for problem Hamiltonian.
+            beta : ``float``\n
+                Rotation parameter for mixer Hamiltonian.
+            layers : ``int``\n
+                Number of QAOA layers.
+
+        Return
+            circuit : ``QCircuit``\n
+                QAOA quantum circuit.
+
+        Examples
+            Build QAOA circuit with 2 layers:
+
+        >>> from pyqpanda_alg.QLattice.qaoa_mlwe import QAOA_MLWE
+        >>> qaoa = QAOA_MLWE(A, b, q=7)
+        >>> circuit = qaoa.build_qaoa_circuit(0.5, 0.3, layers=2)
+
+        """
+        n_qubits = self.n_qubits
+        circuit = QCircuit()
+
+        for i in range(n_qubits):
+            circuit << H(i)
+
+        for layer in range(layers):
+            for i in range(n_qubits - 1):
+                circuit << CZ(i, i + 1)
+                circuit << RZ(i, gamma)
+                circuit << RZ(i + 1, gamma)
+                circuit << CZ(i, i + 1)
+
+            for i in range(n_qubits):
+                circuit << RX(i, beta)
+
+        return circuit
+
+    def run(self, layers=2, maxiter=100, shots=10):
+        """
+        Run QAOA optimization for MLWE problem.
+
+        Parameters
+            layers : ``int``, ``optional``\n
+                Number of QAOA layers. Default is 2.
+            maxiter : ``int``, ``optional``\n
+                Maximum iterations. Default is 100.
+            shots : ``int``, ``optional``\n
+                Number of measurements. Default is 10.
+
+        Return
+            result : ``dict``\n
+                Dictionary containing:
+                - 'best_state': Best measurement result
+                - 'best_cost': Best cost function value
+                - 'secret': Recovered secret vector
+                - 'iterations': Total iterations
+
+        Examples
+            Run QAOA for MLWE:
+
+        >>> from pyqpanda_alg.QLattice.qaoa_mlwe import QAOA_MLWE
+        >>> qaoa = QAOA_MLWE(A, b, q=7)
+        >>> result = qaoa.run(layers=3, maxiter=200)
+
+        """
+        best_cost = float('inf')
+        best_state = None
+
+        gamma = np.random.uniform(0, np.pi)
+        beta = np.random.uniform(0, np.pi / 2)
+
+        for iteration in range(maxiter):
+            prog = QProg()
+            prog << self.build_qaoa_circuit(gamma, beta, layers)
+
+            qubits = list(range(self.n_qubits))
+            prog << measure(qubits, qubits)
+
+            qvm = CPUQVM()
+            qvm.run(prog, shots)
+            result = qvm.result().get_prob_dict(qubits)
+
+            for state_str, prob in result.items():
+                s = np.array([int(state_str[i]) for i in range(self.n)], dtype=int)
+                e = np.array([int(state_str[self.n + i]) for i in range(self.m)], dtype=int)
+
+                b_computed = (self.A @ s + e) % self.q
+                cost = np.sum((b_computed - self.b) ** 2)
+
+                if cost < best_cost:
+                    best_cost = cost
+                    best_state = state_str
+
+            gamma = gamma * 0.99
+            beta = beta * 0.99
+
+        if best_state:
+            s = np.array([int(best_state[i]) for i in range(self.n)], dtype=int)
+            e = np.array([int(best_state[self.n + i]) for i in range(self.m)], dtype=int)
+        else:
+            s = np.zeros(self.n, dtype=int)
+            e = np.zeros(self.m, dtype=int)
+
+        return {
+            'best_state': best_state,
+            'best_cost': best_cost,
+            'secret': s.tolist(),
+            'error': e.tolist(),
+            'iterations': maxiter
+        }