GitList
Browse code

Add basic quantum gates

Joseph Weston authored on 10/11/2019 16:33:08
Showing 3 changed files
pyproject.toml
History View file @ 0a4b3d0
... ... 
@@ -30,7 +30,7 @@ test = [
30 30 
     "pytest-flake8",
31 31 
     "pytest-mypy",
32 32 
     "pytest-black",
33 
-    "hypothesis",
33 
+    "hypothesis[numpy]",
34 34 
     "tox",
35 35 
     "flake8-per-file-ignores",
36 36 
 ]
qsim/gate.py
History View file @ 0a4b3d0
... ... 
@@ -1,3 +1,128 @@
1 
-"""Quantum gate operations"""
1 
+"""Quantum gate operations
2 2
3 
-__all__ = []  # type: ignore
3 
+A quantum gate acting on :math:`n` qubits is a :math:`2^n×2^n` unitary
4 
+matrix written in the computational basis.
5 
+"""
6 
+
7 
+import numpy as np
8 
+
9 
+__all__ = [
10 
+    "n_qubits",
11 
+    "controlled",
12 
+    # -- Single qubit gates --
13 
+    "id",
14 
+    "x",
15 
+    "y",
16 
+    "z",
17 
+    "not_",
18 
+    "sqrt_not",
19 
+    "phase_shift",
20 
+    # -- 2 qubit gates --
21 
+    "cnot",
22 
+    "swap",
23 
+    # -- 3 qubit gates --
24 
+    "toffoli",
25 
+    "cswap",
26 
+    "fredkin",
27 
+    "deutsch",
28 
+]  # type: ignore
29 
+
30 
+
31 
+def _check_valid_gate(gate):
32 
+    if not (
33 
+        # is an array
34 
+        isinstance(gate, np.ndarray)
35 
+        # is complex
36 
+        and np.issubdtype(gate.dtype, np.complex128)
37 
+        # is square
38 
+        and gate.shape[0] == gate.shape[1]
39 
+        # has size 2**n, n > 1
40 
+        and np.log2(gate.shape[0]).is_integer()
41 
+        and np.log2(gate.shape[0]) > 0
42 
+        # is unitary
43 
+        and np.allclose(gate @ gate.conjugate().transpose(), np.identity(gate.shape[0]))
44 
+    ):
45 
+        raise ValueError("Gate is not valid")
46 
+
47 
+
48 
+def n_qubits(gate):
49 
+    """Return the number of qubits that a gate acts on.
50 
+
51 
+    Raises ValueError if 'gate' does not have a shape that is
52 
+    an integer power of 2.
53 
+    """
54 
+    _check_valid_gate(gate)
55 
+    n = np.log2(gate.shape[0])
56 
+    assert n.is_integer()
57 
+    return int(n)
58 
+
59 
+
60 
+def controlled(gate):
61 
+    """Return a controlled quantum gate, given a quantum gate.
62 
+
63 
+    If 'gate' operates on :math:`n` qubits, then the controlled gate operates
64 
+    on :math:`n+1` qubits, where the most-significant qubit is the control.
65 
+
66 
+    Parameters
67 
+    ----------
68 
+    gate : np.ndarray[complex]
69 
+        A quantum gate acting on :math:`n` qubits;
70 
+        a :math:`2^n×2^n` unitary matrix in the computational basis.
71 
+
72 
+    Returns
73 
+    -------
74 
+    controlled_gate : np.ndarray[(2**(n+1), 2**(n+1)), complex]
75 
+    """
76 
+    _check_valid_gate(gate)
77 
+    n = gate.shape[0]
78 
+    zeros = np.zeros((n, n))
79 
+    return np.block([[np.identity(n), zeros], [zeros, gate]])
80 
+
81 
+
82 
+# -- Single qubit gates --
83 
+
84 
+#: The identity gate on 1 qubit
85 
+id = np.identity(2, complex)
86 
+#: Pauli X gate
87 
+x = np.array([[0, 1], [1, 0]], complex)
88 
+#: NOT gate
89 
+not_ = x
90 
+#: Pauli Y gate
91 
+y = np.array([[0, -1j], [1j, 0]], complex)
92 
+#: Pauli Z gate
93 
+z = np.array([[1, 0], [0, -1]], complex)
94 
+#: SQRT(NOT) gate
95 
+sqrt_not = 0.5 * (1 + 1j * id - 1j * x)
96 
+#: Hadamard gate
97 
+hadamard = np.sqrt(0.5) * (x + z)
98 
+
99 
+
100 
+def phase_shift(phi):
101 
+    "Return a gate that shifts the phase of :math:`|1⟩` by :math:`φ`."
102 
+    return np.array([[1, 0], [0, np.exp(1j * phi)]])
103 
+
104 
+
105 
+# -- Two qubit gates --
106 
+
107 
+#: Controlled NOT gate
108 
+cnot = controlled(x)
109 
+#: SWAP gate
110 
+swap = np.identity(4, complex)[:, (0, 2, 1, 3)]
111 
+
112 
+# -- Three qubit gates --
113 
+
114 
+#: Toffoli (CCNOT) gate
115 
+toffoli = controlled(cnot)
116 
+#: Controlled SWAP gate
117 
+cswap = controlled(swap)
118 
+#: Fredkin gate
119 
+fredkin = cswap
120 
+
121 
+
122 
+def deutsch(phi):
123 
+    "Return a Deutsch gate for angle :math:`φ`."
124 
+    gate = np.identity(8, complex)
125 
+    gate[-2:, -2:] = np.array(
126 
+        [[1j * np.cos(phi), np.sin(phi)], [np.sin(phi), 1j * np.cos(phi)]]
127 
+    )
128 
+    return gate
tests/test_gate.py
History View file @ 0a4b3d0
4 129 
new file mode 100644
... ... 
@@ -0,0 +1,103 @@
1 
+from hypothesis import given
2 
+import hypothesis.strategies as st
3 
+import hypothesis.extra.numpy as hnp
4 
+import numpy as np
5 
+import pytest
6 
+
7 
+import qsim.gate
8 
+
9 
+
10 
+def unitary(n):
11 
+    valid_complex = st.complex_numbers(allow_infinity=False, allow_nan=False)
12 
+    return (
13 
+        hnp.arrays(complex, (n, n), valid_complex)
14 
+        .map(lambda a: np.linalg.qr(a)[0])
15 
+        .filter(lambda u: np.all(np.isfinite(u)))
16 
+    )
17 
+
18 
+
19 
+n_qubits = st.shared(st.integers(min_value=1, max_value=6))
20 
+phases = st.floats(
21 
+    min_value=0, max_value=2 * np.pi, allow_nan=False, allow_infinity=False
22 
+)
23 
+single_qubit_gates = unitary(2)
24 
+two_qubit_gates = unitary(4)
25 
+n_qubit_gates = n_qubits.map(lambda n: 2 ** n).flatmap(unitary)
26 
+
27 
+
28 
+@given(n_qubits, n_qubit_gates)
29 
+def test_n_qubits(n, gate):
30 
+    assert qsim.gate.n_qubits(gate) == n
31 
+
32 
+
33 
+@given(n_qubit_gates)
34 
+def test_n_qubits_invalid(gate):
35 
+    # Not a numpy array
36 
+    with pytest.raises(ValueError):
37 
+        qsim.gate.n_qubits(list(map(list, gate)))
38 
+    # Not complex
39 
+    with pytest.raises(ValueError):
40 
+        qsim.gate.n_qubits(gate.real)
41 
+    # Not square
42 
+    with pytest.raises(ValueError):
43 
+        qsim.gate.n_qubits(gate[:-2])
44 
+    # Not size 2**n, n > 0
45 
+    with pytest.raises(ValueError):
46 
+        qsim.gate.n_qubits(gate[:-1, :-1])
47 
+    # Not unitary
48 
+    nonunitary_part = np.zeros_like(gate)
49 
+    nonunitary_part[0, -1] = 1j
50 
+    with pytest.raises(ValueError):
51 
+        qsim.gate.n_qubits(gate + nonunitary_part)
52 
+
53 
+
54 
+@given(n_qubits, n_qubit_gates)
55 
+def test_controlled(n, gate):
56 
+    nq = 2 ** n
57 
+    controlled_gate = qsim.gate.controlled(gate)
58 
+    assert controlled_gate.shape[0] == 2 * nq
59 
+    assert np.all(controlled_gate[:nq, :nq] == np.identity(nq))
60 
+    assert np.all(controlled_gate[nq:, nq:] == gate)
61 
+
62 
+
63 
+@given(phases)
64 
+def test_phase_gate_inverse(phi):
65 
+    assert np.allclose(
66 
+        qsim.gate.phase_shift(phi) @ qsim.gate.phase_shift(-phi), np.identity(2)
67 
+    )
68 
+
69 
+
70 
+@given(phases, st.integers())
71 
+def test_phase_gate_periodic(phi, n):
72 
+    atol = np.finfo(complex).resolution * abs(n)
73 
+    assert np.allclose(
74 
+        qsim.gate.phase_shift(phi),
75 
+        qsim.gate.phase_shift(phi + 2 * np.pi * n),
76 
+        atol=atol,
77 
+    )
78 
+
79 
+
80 
+@given(single_qubit_gates)
81 
+def test_id(gate):
82 
+    assert np.all(qsim.gate.id @ gate == gate)
83 
+    assert np.all(gate @ qsim.gate.id == gate)
84 
+
85 
+
86 
+def test_pauli_gates_are_involutary():
87 
+    pauli_gates = [qsim.gate.x, qsim.gate.y, qsim.gate.z]
88 
+    assert np.all(qsim.gate.x == qsim.gate.not_)
89 
+    for gate in pauli_gates:
90 
+        assert np.all(gate @ gate == qsim.gate.id)
91 
+    assert np.all(-1j * qsim.gate.x @ qsim.gate.y @ qsim.gate.z == qsim.gate.id)
92 
+
93 
+
94 
+def test_sqrt_not():
95 
+    assert np.all(qsim.gate.sqrt_not @ qsim.gate.sqrt_not == qsim.gate.not_)
96 
+
97 
+
98 
+def test_deutch():
99 
+    assert np.allclose(qsim.gate.deutsch(np.pi / 2), qsim.gate.toffoli)
100 
+
101 
+
102 
+def test_swap():
103 
+    assert np.all(qsim.gate.swap @ qsim.gate.swap == np.identity(4))