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src/samplers/mixed.py

+"""
+Contain methods to sample mixed density matrices
+"""
+
+import numpy as np
+
+from ..types import DMStack
+from .utils import RandomGinibre, RandomUnitary, dagger, balanced
+
+class RandomInduced :
+    """
+    Random mixed states from the Induced measure
+    """
+    def __init__(self, k_params):
+        """
+        :param k_params: a int or an array of int
+        """
+        self.k_params = k_params
+
+    def states(self, n_states, dims):
+        """
+        sample n_states density matrices from the Induced measure
+        :param n_states: number of density matrices
+        :param dims: dimensions of the subsystems
+        :return: a set of states (DMStack), a dictionary of information (k param : key 'ks')
+        """
+        if isinstance(self.k_params, int):
+            return RandomInduced.states_k(self.k_params, n_states, dims)
+        else :
+            return RandomInduced.states_ks(self.k_params, n_states, dims)
+
+    @staticmethod
+    def states_k(k, n_states, dims):
+        dim = np.product(dims)
+        gin = RandomGinibre.matrices(n_states, [dim, k])
+        gin = gin @ dagger(gin)
+        gin /= np.trace(gin, axis1=1, axis2=2)[:,None,None]
+
+        return gin, {'ks' : np.full(n_states, k)}
+
+
+    @staticmethod
+    def states_ks(vals_k, n_states, dims):
+        dim = np.product(dims)
+
+        per_k = balanced(n_states, len(vals_k))
+        states = np.zeros((n_states, dim, dim), dtype=complex)
+        ks = np.zeros(n_states, dtype=int)
+        idx = 0
+        for i in range(len(per_k)):
+            if per_k[i]==0 :
+                continue
+            states[idx : idx + per_k[i]] = RandomInduced.states_k(vals_k[i], per_k[i], dims)[0]
+            ks[idx : idx + per_k[i]] = vals_k[i]
+            idx += per_k[i]
+
+        return DMStack(states, dims), {'ks' : ks}
+
+
+class RandomBures :
+    """
+    Random mixed states from the Bures measure
+    """
+
+    @staticmethod
+    def states(n_states, dims):
+        """
+        sample n_states density matrices from the Bures measure
+        :param n_states: number of density matrices
+        :param dims: dimensions of the subsystems
+        :return: a set of states (DMStack), a dictionary of information (empty)
+        """
+        dim = np.product(dims)
+        G = RandomGinibre.matrices(n_states, [dim, dim])
+        U = RandomUnitary().matrices(n_states, dims) + np.full((n_states, dim, dim), np.eye(dim))
+
+        # state : (ID + U) G G^dag (ID + U^dag)
+        G = U @ G
+        G = G @ dagger(G)
+        G /= np.trace(G, axis1=1, axis2=2)[:, None, None]
+
+        return DMStack(G, dims), {}
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