Fival encoding

fival_encoding.py

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+# "Fival encoding"
+# https://arxiv.org/abs/hep-th/9409150 adopts a definition of a "maximally-entangled" state
+# that relies on two qudits with the same (but otherwise arbitrary) dimensional cardinality.
+# If padded with 0-amplitude entries so that the new dimensionality of the modified state
+# has a cardinality that factors as only first powers of unique prime numbers, then the
+# Schmidt rank becomes 1, and the state appears separable in the "Fival encoding."
+
+import sys
+import numpy as np
+
+from pyqrack import QrackSimulator
+
+
+def main():
+    qsim = QrackSimulator(2)
+    qsim.h(0)
+    qsim.h(1)
+    qsim.mcz([0], 1)
+    qsim.h(1)
+
+    ket = qsim.out_ket() + [0, 0]
+    print(ket)
+
+    r = np.reshape(ket, (2, 3))
+    U, S, Vh = np.linalg.svd(r)
+    ket1 = U[:, [0]]
+    ket2 = Vh[:, [0]]
+
+    print("2 by 3:")
+    print(np.kron(ket1, ket2))
+    print(S)
+
+if __name__ == '__main__':
+    sys.exit(main())