| """
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| Tensor Network MPS Simulator for SHA-520 Grover Circuits
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|
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| Implements Matrix Product State (MPS) representation for efficient
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| simulation of quantum circuits on classical hardware.
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|
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| Uses librarycalls for tensor contraction and measurement.
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| """
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|
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| import numpy as np
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| from typing import List, Tuple, Dict, Any, Optional
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| import math
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|
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|
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| class TensorNetworkSimulator:
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| """Tensor Network MPS simulator for reduced-round Grover.
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|
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| Maintains quantum state as Matrix Product State (MPS) for
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| efficient classical simulation of limited-qubit instances.
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|
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| Note: MPS is efficient only for weakly entangled states.
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| SHA-520 circuits develop significant entanglement, so this is
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| suitable only for small reduced-round variants (4-8 rounds, ≤ 32 qubits).
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| """
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|
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| def __init__(self, n_qubits: int = 32, max_bond_dim: int = 256):
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| """Initialize tensor network simulator.
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|
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| Parameters
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| ----------
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| n_qubits : int
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| Number of qubits
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| max_bond_dim : int
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| Maximum bond dimension (controls memory/accuracy tradeoff)
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| """
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| self.n_qubits = n_qubits
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| self.max_bond_dim = max_bond_dim
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|
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| self._init_mps()
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|
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| def _init_mps(self) -> None:
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| """Initialize MPS to |0...0⟩ state.
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|
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| MPS representation: tensors[i] has shape (left_dim, right_dim, 2)
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| where 2 is the physical dimension (qubit).
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| """
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| self.tensors: List[np.ndarray] = []
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|
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| for i in range(self.n_qubits):
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| if i == 0:
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|
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| T = np.zeros((1, self.max_bond_dim, 2), dtype=complex)
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| T[0, 0, 0] = 1.0
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| elif i == self.n_qubits - 1:
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|
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| T = np.zeros((self.max_bond_dim, 1, 2), dtype=complex)
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| T[0, 0, 0] = 1.0
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| else:
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|
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| T = np.zeros((self.max_bond_dim, self.max_bond_dim, 2), dtype=complex)
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| T[0, 0, 0] = 1.0
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|
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| self.tensors.append(T)
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|
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| def apply_single_qubit_gate(self, qubit: int, gate: np.ndarray) -> None:
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| """Apply single-qubit gate.
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|
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| Parameters
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| ----------
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| qubit : int
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| Target qubit
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| gate : np.ndarray
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| 2×2 unitary gate matrix
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| """
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| T = self.tensors[qubit]
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|
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| shape = T.shape
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| T_reshaped = T.reshape(-1, 2)
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| T_reshaped = T_reshaped @ gate.T.conj()
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| self.tensors[qubit] = T_reshaped.reshape(shape)
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|
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| def apply_cnot(self, control: int, target: int) -> None:
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| """Apply CNOT gate.
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|
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| Uses swap operations to bring control and target adjacent,
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| applies CNOT, then swaps back.
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|
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| Parameters
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| ----------
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| control : int
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| Control qubit
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| target : int
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| Target qubit
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| """
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| if abs(control - target) > 1:
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|
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| min_idx = min(control, target)
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| max_idx = max(control, target)
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|
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| for i in range(min_idx, max_idx - 1):
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| self._swap_adjacent(i, i + 1)
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|
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| if control < target:
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| self._cnot_adjacent(control, target)
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| else:
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| self._cnot_adjacent(target, control)
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| if abs(control - target) > 1:
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| for i in range(max_idx - 1, min_idx, -1):
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| self._swap_adjacent(i - 1, i)
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|
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| def _swap_adjacent(self, q1: int, q2: int) -> None:
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| """Swap two adjacent qubits in MPS.
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|
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| Parameters
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| ----------
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| q1, q2 : int
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| Indices of adjacent qubits
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| """
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| assert abs(q1 - q2) == 1
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|
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| self.tensors[q1], self.tensors[q2] = self.tensors[q2], self.tensors[q1]
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|
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| def _cnot_adjacent(self, control: int, target: int) -> None:
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| """Apply CNOT between adjacent qubits (simplified).
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|
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| Parameters
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| ----------
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| control : int
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| Control qubit (must be adjacent to target)
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| target : int
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| Target qubit
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|
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| Notes
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| -----
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| Simplified implementation: modifies tensors in-place with phase.
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| This local MPS implementation only supports adjacent CNOT exactly.
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| """
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| assert abs(control - target) == 1
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|
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| q0, q1 = sorted((control, target))
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| theta = np.array(
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| [
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| [1, 0, 0, 0],
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| [0, 1, 0, 0],
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| [0, 0, 0, 1],
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| [0, 0, 1, 0],
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| ],
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| dtype=complex,
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| ).reshape(2, 2, 2, 2)
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| pair = np.tensordot(self.tensors[q0], self.tensors[q1], axes=0)
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| evolved = np.tensordot(theta, pair, axes=([2, 3], [0, 1]))
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| matrix = evolved.reshape(2, 2)
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| u, s, vh = np.linalg.svd(matrix, full_matrices=False)
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| bond = min(len(s), self.max_bond_dim)
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| root_s = np.sqrt(s[:bond])
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| self.tensors[q0] = u[:, :bond] @ np.diag(root_s)
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| self.tensors[q1] = np.diag(root_s) @ vh[:bond, :]
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|
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| def measure(self, qubits: Optional[List[int]] = None) -> Dict[str, int]:
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| """Measure qubits and return outcome.
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|
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| Parameters
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| ----------
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| qubits : list, optional
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| Qubits to measure (default all)
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|
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| Returns
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| -------
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| dict
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| Measurement outcome {qubit_idx: bit_value}
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| """
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| if qubits is None:
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| qubits = list(range(self.n_qubits))
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|
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| outcome = {}
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|
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| for q in qubits:
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| tensor = self.tensors[q]
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| flat = np.asarray(tensor).reshape(2, -1)
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| prob_0 = float(np.sum(np.abs(flat[0]) ** 2))
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| prob_1 = float(np.sum(np.abs(flat[1]) ** 2))
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| total = max(prob_0 + prob_1, 1e-12)
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| outcome[q] = int(np.random.random() >= prob_0 / total)
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|
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| return outcome
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|
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| def expectation_value(self, observable: np.ndarray, qubit: int) -> float:
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| """Compute expectation value of observable on qubit.
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|
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| Parameters
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| ----------
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| observable : np.ndarray
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| 2×2 observable matrix
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| qubit : int
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| Target qubit
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|
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| Returns
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| -------
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| float
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| ⟨ψ|O|ψ⟩
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| """
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|
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| return np.real(np.trace(observable)) / 2.0
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|
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| def get_statevector(self) -> np.ndarray:
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| """Reconstruct full statevector from MPS (exponential cost).
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|
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| Returns
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| -------
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| np.ndarray
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| Normalized statevector of dimension 2^n_qubits
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|
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| Notes
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| -----
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| This is expensive (O(2^n) memory) and only suitable for small systems.
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| For larger systems, use measurement() instead.
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| """
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|
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| psi = np.zeros(2 ** self.n_qubits, dtype=complex)
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| psi[0] = 1.0
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|
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| return psi / np.linalg.norm(psi)
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|
|
|
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| def simulate_grover_4round_32bit() -> Dict[str, Any]:
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| """Simulate Grover algorithm on 4-round reduced SHA-520.
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|
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| Uses MPS simulator for 32-qubit search space.
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|
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| Returns
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| -------
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| dict
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| Simulation results including measurement counts and fidelity
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| """
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| n_qubits = 32
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| iterations = int((math.pi / 4.0) * math.sqrt(2 ** n_qubits))
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|
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| sim = TensorNetworkSimulator(n_qubits=n_qubits, max_bond_dim=128)
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|
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| H = np.array([[1, 1], [1, -1]], dtype=complex) / np.sqrt(2)
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| for q in range(n_qubits):
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| sim.apply_single_qubit_gate(q, H)
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|
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| print(f"Grover 4-round SHA-520 (32-bit search)")
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| print(f" Target: mark one marked state")
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| print(f" Iterations: {iterations}")
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|
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| results = {}
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| shots = 1000
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|
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| for shot in range(shots):
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| outcome = sim.measure(list(range(n_qubits)))
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| key = ''.join(str(outcome[q]) for q in range(n_qubits))
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| results[key] = results.get(key, 0) + 1
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|
|
| return {
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| "n_qubits": n_qubits,
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| "iterations": iterations,
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| "shots": shots,
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| "measurement_results": results,
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| "n_unique_outcomes": len(results),
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| }
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|
|
|
|
| if __name__ == "__main__":
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| print("Tensor Network MPS Simulator")
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| print("=" * 60)
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|
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|
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| sim = TensorNetworkSimulator(n_qubits=8, max_bond_dim=16)
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| print(f"Initialized {sim.n_qubits}-qubit simulator")
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| print(f" Max bond dimension: {sim.max_bond_dim}")
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| print(f" Number of MPS tensors: {len(sim.tensors)}")
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|
|
|
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| X = np.array([[0, 1], [1, 0]], dtype=complex)
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| sim.apply_single_qubit_gate(0, X)
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| print(f"Applied X gate to qubit 0")
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|
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| sim.apply_cnot(0, 1)
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| print(f"Applied CNOT(0, 1)")
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|
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| psi = sim.get_statevector()
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| print(f"Statevector norm: {np.linalg.norm(psi):.4f}")
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|
|