... | ... |
@@ -10,7 +10,7 @@ by the associated classical bitstring. |
10 | 10 |
|
11 | 11 |
import numpy as np |
12 | 12 |
|
13 |
-__all__ = ["from_classical", "is_normalized", "num_qubits", "zero"] # type: ignore |
|
13 |
+__all__ = ["from_classical", "is_normalized", "is_normalizable", "normalize", "num_qubits", "zero"] # type: ignore |
|
14 | 14 |
|
15 | 15 |
|
16 | 16 |
def from_classical(bitstring): |
... | ... |
@@ -59,7 +59,22 @@ def num_qubits(state): |
59 | 59 |
|
60 | 60 |
def is_normalized(state: np.ndarray) -> bool: |
61 | 61 |
"""Return True if and only if 'state' is normalized.""" |
62 |
- return np.allclose(np.linalg.norm(state), 1) |
|
62 |
+ return np.isclose(np.linalg.norm(state), 1) |
|
63 |
+ |
|
64 |
+ |
|
65 |
+def is_normalizable(v: np.ndarray) -> bool: |
|
66 |
+ """Return True if and only if 'v' is normalizable.""" |
|
67 |
+ # If the norm is too small then normalizing a vector using |
|
68 |
+ # the norm will yield a vector that is not normalized to machine |
|
69 |
+ # precision. |
|
70 |
+ return bool(np.linalg.norm(v) ** 2 > np.finfo(float).smallest_normal) |
|
71 |
+ |
|
72 |
+ |
|
73 |
+def normalize(state: np.ndarray) -> np.ndarray: |
|
74 |
+ """Return a normalized state, given a potentially un-normalized one.""" |
|
75 |
+ if not is_normalizable(state): |
|
76 |
+ raise ValueError("State is not normalizable") |
|
77 |
+ return state / np.linalg.norm(state) |
|
63 | 78 |
|
64 | 79 |
|
65 | 80 |
def _check_valid_state(state): |
... | ... |
@@ -68,7 +68,7 @@ def _check_valid_state(state): |
68 | 68 |
isinstance(state, np.ndarray) |
69 | 69 |
# is complex |
70 | 70 |
and np.issubdtype(state.dtype, np.complex128) |
71 |
- # is square |
|
71 |
+ # is a vector |
|
72 | 72 |
and len(state.shape) == 1 |
73 | 73 |
# has size 2**n, n > 1 |
74 | 74 |
and np.log2(state.shape[0]).is_integer() |
... | ... |
@@ -10,7 +10,7 @@ by the associated classical bitstring. |
10 | 10 |
|
11 | 11 |
import numpy as np |
12 | 12 |
|
13 |
-__all__ = ["from_classical"] # type: ignore |
|
13 |
+__all__ = ["from_classical", "is_normalized", "num_qubits", "zero"] # type: ignore |
|
14 | 14 |
|
15 | 15 |
|
16 | 16 |
def from_classical(bitstring): |
... | ... |
@@ -28,7 +28,6 @@ def from_classical(bitstring): |
28 | 28 |
The state vector in the computational basis. |
29 | 29 |
Has :math:`2^n` components. |
30 | 30 |
""" |
31 |
- |
|
32 | 31 |
bitstring = "".join(map(str, bitstring)) |
33 | 32 |
n_qubits = len(bitstring) |
34 | 33 |
try: |
... | ... |
@@ -39,3 +38,41 @@ def from_classical(bitstring): |
39 | 38 |
state = np.zeros(1 << n_qubits, dtype=complex) |
40 | 39 |
state[index] = 1 |
41 | 40 |
return state |
41 |
+ |
|
42 |
+ |
|
43 |
+def zero(n: int): |
|
44 |
+ """Return the zero state on 'n' qubits.""" |
|
45 |
+ state = np.zeros(1 << n, dtype=complex) |
|
46 |
+ state[0] = 1 |
|
47 |
+ return state |
|
48 |
+ |
|
49 |
+ |
|
50 |
+def num_qubits(state): |
|
51 |
+ """Return the number of qubits in the state. |
|
52 |
+ |
|
53 |
+ Raises ValueError if 'state' does not have a shape that is |
|
54 |
+ an integer power of 2. |
|
55 |
+ """ |
|
56 |
+ _check_valid_state(state) |
|
57 |
+ return state.shape[0].bit_length() - 1 |
|
58 |
+ |
|
59 |
+ |
|
60 |
+def is_normalized(state: np.ndarray) -> bool: |
|
61 |
+ """Return True if and only if 'state' is normalized.""" |
|
62 |
+ return np.allclose(np.linalg.norm(state), 1) |
|
63 |
+ |
|
64 |
+ |
|
65 |
+def _check_valid_state(state): |
|
66 |
+ if not ( |
|
67 |
+ # is an array |
|
68 |
+ isinstance(state, np.ndarray) |
|
69 |
+ # is complex |
|
70 |
+ and np.issubdtype(state.dtype, np.complex128) |
|
71 |
+ # is square |
|
72 |
+ and len(state.shape) == 1 |
|
73 |
+ # has size 2**n, n > 1 |
|
74 |
+ and np.log2(state.shape[0]).is_integer() |
|
75 |
+ and state.shape[0].bit_length() > 1 |
|
76 |
+ and is_normalized(state) |
|
77 |
+ ): |
|
78 |
+ raise ValueError("State is not valid") |
This avoids problems with testing against the wrong package version
Joseph Weston authored on 30/11/2019 18:31:571 | 1 |
new file mode 100644 |
... | ... |
@@ -0,0 +1,41 @@ |
1 |
+"""Quantum state vectors |
|
2 |
+ |
|
3 |
+The quantum state of :math:`n` quantum bits is represented as a 1D array of complex |
|
4 |
+numbers of length :math:`2^n`; the components of the state vector in the |
|
5 |
+computational basis. |
|
6 |
+ |
|
7 |
+The computational basis for :math:`n` qubits is ordered by the number represented |
|
8 |
+by the associated classical bitstring. |
|
9 |
+""" |
|
10 |
+ |
|
11 |
+import numpy as np |
|
12 |
+ |
|
13 |
+__all__ = ["from_classical"] # type: ignore |
|
14 |
+ |
|
15 |
+ |
|
16 |
+def from_classical(bitstring): |
|
17 |
+ """Return a quantum state corresponding to a classical bitstring. |
|
18 |
+ |
|
19 |
+ Parameters |
|
20 |
+ ---------- |
|
21 |
+ bitstring : sequence of bits |
|
22 |
+ Can be a string like "01011", or a sequence of |
|
23 |
+ integers. |
|
24 |
+ |
|
25 |
+ Returns |
|
26 |
+ ------- |
|
27 |
+ state : ndarray[(2**n,), complex] |
|
28 |
+ The state vector in the computational basis. |
|
29 |
+ Has :math:`2^n` components. |
|
30 |
+ """ |
|
31 |
+ |
|
32 |
+ bitstring = "".join(map(str, bitstring)) |
|
33 |
+ n_qubits = len(bitstring) |
|
34 |
+ try: |
|
35 |
+ index = int(bitstring, base=2) |
|
36 |
+ except ValueError: |
|
37 |
+ raise ValueError("Input is not a classical bitstring") from None |
|
38 |
+ |
|
39 |
+ state = np.zeros(1 << n_qubits, dtype=complex) |
|
40 |
+ state[index] = 1 |
|
41 |
+ return state |