update

unitary/alpha/__init__.py

@@ -43,8 +43,10 @@
 from unitary.alpha.qudit_effects import (
     Cycle,
     Flip,
+    Superpose,
     QuditCycle,
     QuditFlip,
+    QuditSuperpose,
 )
 
 from unitary.alpha.quantum_object import (

unitary/alpha/qudit_effects.py

@@ -18,12 +18,12 @@
 
 import cirq
 
-from unitary.alpha.qudit_gates import QuditPlusGate, QuditXGate
+from unitary.alpha.qudit_gates import QuditPlusGate, QuditXGate, QuditHadamardGate
 from unitary.alpha.quantum_effect import QuantumEffect
 
 
 class Cycle(QuantumEffect):
-    """Cycles a qubit from |0> to |1>, |1> to |2>, etc.
+    """Cycles a qudit from |0> to |1>, |1> to |2>, etc.
 
     Essentially adds `addend` to the state, where `addend`
     is the parameter supplied at creation.
@@ -55,15 +55,13 @@ def __init__(self, dimension, num=1):
 
 
 class Flip(QuantumEffect):
-    """Flips two states of a qubit, leaving all other states unchanged.
+    """Flips two states of a qudit, leaving all other states unchanged.
 
-    For instance, Flip(state0 = 0, state1=2) is a qutrit effect
+    For instance, Flip(state0 = 0, state1 = 2) is a qutrit effect
     that flips |0> to |2>, |2> to |0> and leaves
-    |1> alone.  This is also sometimes referred to as the X_0_2 gate.
+    |1> alone.  This is also sometimes referred as the X_02 gate.
 
     For a partial flip, use the `effect_fraction` argument.
-    Note that this is only applied so far on qubits and not yet for
-    qudits.
 
     These effects will be cumulative.  For instance, two quarter
     flips (effect_fraction=0.25) will be equivalent to a half
@@ -127,3 +125,32 @@ class QuditFlip(Flip):
 
     def __init__(self, dimension: int, state0: int, state1: int):
         super().__init__(state0=state0, state1=state1)
+
+
+class Superpose(QuantumEffect):
+    """Transforms each pure state to a (equal, in terms of absolute magnitude) superposition of
+    all pure states.
+    """
+
+    def __init__(self):
+        pass
+
+    def effect(self, *objects):
+        for q in objects:
+            if q.qubit.dimension == 2:
+                yield cirq.H(q.qubit)
+            else:
+                yield QuditHadamardGate(dimension=q.qubit.dimension)(
+                    q.qubit
+                )
+
+
+class QuditSuperpose(Superpose):
+    """Equivalent to Superpose.
+
+    Exists only for backwards compatibiltity.
+    Will be removed in 2024.
+    """
+
+    def __init__(self, dimension: int):
+        super().__init__()

unitary/alpha/qudit_effects_test.py

@@ -75,3 +75,14 @@ def test_qudit_flip(simulator, compile_to_qubits):
     alpha.QuditFlip(3, 0, 1)(piece)
     results = board.peek([piece], count=100)
     assert all(result == [StopLight.GREEN] for result in results)
+
+
+def test_qudit_superpose():
+    board = alpha.QuantumWorld(sampler=cirq.Simulator(), compile_to_qubits=False)
+    piece = alpha.QuantumObject("t", StopLight.GREEN)
+    board.add_object(piece)
+    alpha.QuditSuperpose(3)(piece)
+    results = board.peek([piece], count=100)
+    assert any(result == [StopLight.RED] for result in results)
+    assert any(result == [StopLight.YELLOW] for result in results)
+    assert any(result == [StopLight.GREEN] for result in results)

unitary/alpha/qudit_gates.py

@@ -24,8 +24,8 @@ class QuditXGate(cirq.Gate):
     'destination_state' parameter that is passed in.
     All other states are left alone.
 
-    For example, QuditXGate(dimension=3, state=1)
-    is a X_01 gate that leaves the |2〉 state alone.
+    For example, QuditXGate(dimension=3, source_state=0, destination_state=1)
+    is a X_01 gate that leaves the |2〉state alone.
     """
 
     def __init__(
@@ -34,28 +34,32 @@ def __init__(
         self.dimension = dimension
         self.source_state = source_state
         self.destination_state = destination_state
+        if self.source_state >= self.dimension:
+            raise ValueError("Source state must be smaller than dimension.")
+        if self.destination_state >= self.dimension:
+            raise ValueError("Destination state must be smaller than dimension.")
 
     def _qid_shape_(self):
         return (self.dimension,)
 
     def _unitary_(self):
-        arr = np.zeros((self.dimension, self.dimension))
-        arr[self.source_state, self.destination_state] = 1
-        arr[self.destination_state, self.source_state] = 1
-        for i in range(self.dimension):
-            if i != self.source_state and i != self.destination_state:
-                arr[i, i] = 1
+        arr = np.eye(self.dimension)
+        if self.source_state != self.destination_state:
+            arr[self.source_state, self.source_state] = 0
+            arr[self.destination_state, self.destination_state] = 0
+            arr[self.source_state, self.destination_state] = 1
+            arr[self.destination_state, self.source_state] = 1
         return arr
 
     def _circuit_diagram_info_(self, args):
         return f"X({self.source_state}_{self.destination_state})"
 
 
 class QuditPlusGate(cirq.Gate):
-    """Cycles all the states using a permutation gate.
+    """Cycles all the states by `addend` using a permutation gate.
 
-    This gate adds a number to each state.  For instance,
-    `QuditPlusGate(dimension=3, addend=1)`
+    This gate adds a number to each state. For instance,`QuditPlusGate(dimension=3, addend=1)`
+    will cycle state vector (a, b, c) to (c, a, b), and will cycle state |0> to |1>, |1> to |2>, |2> to |0>.
     """
 
     def __init__(self, dimension: int, addend: int = 1):
@@ -78,19 +82,16 @@ def _circuit_diagram_info_(self, args):
 class QuditControlledXGate(cirq.Gate):
     """A Qudit controlled-X gate.
 
-    This gate takes the dimension of the qudit (e.g. 3 for qutrits)
-    as well as the control and destination gates to produce a
+    This gate takes the dimension of the qudit as well as the control and destination states to produce a
     controlled-X 2-qudit gate.
 
-    Note that there are two parameters for this gate.  The first
-    is the control state, which determines when the X gate on the
-    second qudit is activated.  For instance, if this is set to 2,
-    then the X gate will be activated when the first qudit is
-    in the |2> state.
-
-    The state parameter specifies the destination state of the
-    second qudit.  For instance, if set to 1, it will perform a
-    X_01 gate when activated by the control.
+    Args:
+        dimension: dimension of the qudits, for instance, a dimension of 3 would be a qutrit.
+        control_state: the state of first qudit that when satisfied the X gate on the second qudit will be activated.  
+          For instance, if `control_state` is set to 2, then the X gate will be
+          activated when the first qudit is in the |2> state.
+        state: the destination state of the second qudit. For instance, if set to 1, it will perform a
+          X_01 gate when activated by `control_state`.
     """
 
     def __init__(self, dimension: int, control_state: int = 1, state: int = 1):
@@ -103,14 +104,12 @@ def _qid_shape_(self):
 
     def _unitary_(self):
         size = self.dimension * self.dimension
-        arr = np.zeros((size, size), dtype=np.complex64)
+        arr = np.eye(size, dtype=np.complex64)
         control_block_offset = self.control_state * self.dimension
+        arr[control_block_offset, control_block_offset] = 0
+        arr[control_block_offset + self.state, control_block_offset + self.state] = 0
         arr[control_block_offset, control_block_offset + self.state] = 1
         arr[control_block_offset + self.state, control_block_offset] = 1
-        for x in range(self.dimension):
-            for y in range(self.dimension):
-                if x != self.control_state or (y != self.state and y != 0):
-                    arr[x * self.dimension + y, x * self.dimension + y] = 1
         return arr
 
 
@@ -139,14 +138,14 @@ def _qid_shape_(self):
     def _unitary_(self):
         size = self.dimension * self.dimension
         arr = np.zeros((size, size), dtype=np.complex64)
+        g = np.exp(1j * np.pi * self.exponent / 2)
+        coeff = -1j * g * np.sin(np.pi * self.exponent / 2)
+        diag = g * np.cos(np.pi * self.exponent / 2)
         for x in range(self.dimension):
             for y in range(self.dimension):
                 if x == y:
                     arr[x * self.dimension + y][x * self.dimension + y] = 1
                     continue
-                g = np.exp(1j * np.pi * self.exponent / 2)
-                coeff = -1j * g * np.sin(np.pi * self.exponent / 2)
-                diag = g * np.cos(np.pi * self.exponent / 2)
                 arr[x * self.dimension + y, y * self.dimension + x] = coeff
                 arr[x * self.dimension + y, x * self.dimension + y] = diag
         return arr
@@ -186,13 +185,13 @@ def _qid_shape_(self):
     def _unitary_(self):
         size = self.dimension * self.dimension
         arr = np.zeros((size, size), dtype=np.complex64)
+        coeff = 1j * np.sin(np.pi * self.exponent / 2)
+        diag = np.cos(np.pi * self.exponent / 2)
         for x in range(self.dimension):
             for y in range(self.dimension):
                 if x == y:
                     arr[x * self.dimension + y][x * self.dimension + y] = 1
                     continue
-                coeff = 1j * np.sin(np.pi * self.exponent / 2)
-                diag = np.cos(np.pi * self.exponent / 2)
                 arr[x * self.dimension + y, y * self.dimension + x] = coeff
                 arr[x * self.dimension + y, x * self.dimension + y] = diag
 
@@ -202,3 +201,37 @@ def _circuit_diagram_info_(self, args):
         return cirq.CircuitDiagramInfo(
             wire_symbols=("iSwap", "iSwap"), exponent=self._diagram_exponent(args)
         )
+
+
+class QuditHadamardGate(cirq.Gate):
+    """Performs a Hadamard opperation on the given qudit.
+
+    This is the equivalent of a H gate for qubits. When applied to a given pure state,
+    the state will be transformed to a (equal, in terms of absolute magnitude) superposition of
+    all pure states.
+
+    Args:
+        dimension: dimension of the qudits, for instance,
+          a dimension of 3 would be a qutrit.
+    """
+
+    def __init__(self, dimension: int):
+        self.dimension = dimension
+
+    def _qid_shape_(self):
+        return (self.dimension,)
+
+    def _unitary_(self):
+        arr = 1.0 / np.sqrt(self.dimension) * np.ones((self.dimension, self.dimension), dtype=np.complex64)
+        w = np.exp(1j * 2 * np.pi / self.dimension)
+        # Note: this unitary matrice always has first row and first column elements equal to one,
+        # so we only do calculation for rest of the elements.
+        for i in range(1, self.dimension):
+            for j in range(1, self.dimension):
+                arr[i, j] *= w ** (i * j)
+        return arr
+
+    def _circuit_diagram_info_(self, args):
+        return cirq.CircuitDiagramInfo(
+            wire_symbols=("H", "H"), exponent=self._diagram_exponent(args)
+        )

unitary/alpha/qudit_gates_test.py

@@ -19,7 +19,7 @@
 import unitary.alpha.qudit_gates as qudit_gates
 
 
-@pytest.mark.parametrize("state", [1, 2])
+@pytest.mark.parametrize("state", [0, 1, 2])
 def test_qutrit_x(state: int):
     qutrit = cirq.NamedQid("a", dimension=3)
     sim = cirq.Simulator()
@@ -38,7 +38,7 @@ def test_qutrit_x(state: int):
     assert np.all(results.measurements["m"] == 0)
 
 
-@pytest.mark.parametrize("num_gates", [1, 2, 3, 4, 5, 6])
+@pytest.mark.parametrize("num_gates", [0, 1, 2, 3, 4, 5, 6])
 def test_qutrit_plus_one(num_gates: int):
     qutrit = cirq.NamedQid("a", dimension=3)
     c = cirq.Circuit()
@@ -50,7 +50,7 @@ def test_qutrit_plus_one(num_gates: int):
     assert np.all(results.measurements["m"] == num_gates % 3)
 
 
-@pytest.mark.parametrize("num_gates", [1, 2, 3, 4, 5, 6])
+@pytest.mark.parametrize("num_gates", [0, 1, 2, 3, 4, 5, 6])
 def test_qutrit_plus_addend(num_gates: int):
     qutrit = cirq.NamedQid("a", dimension=3)
     c = cirq.Circuit()
@@ -101,7 +101,7 @@ def test_control_x(control: int, dest: int):
     assert np.all(results.measurements["m1"] == 0)
 
     # Control is excited to a non-controlling state and has no effect.
-    non_active = 2 - control + 1
+    non_active = 3 - control
     c = cirq.Circuit(
         qudit_gates.QuditXGate(3, 0, non_active)(qutrit0),
         qudit_gates.QuditControlledXGate(3, control, dest)(qutrit0, qutrit1),
@@ -112,6 +112,18 @@ def test_control_x(control: int, dest: int):
     assert np.all(results.measurements["m0"] == non_active)
     assert np.all(results.measurements["m1"] == 0)
 
+    # 2nd qutrit is excited to a non-dest state and has no effect.
+    non_active = 3 - dest
+    c = cirq.Circuit(
+        qudit_gates.QuditXGate(3, 0, control)(qutrit0),
+        qudit_gates.QuditXGate(3, 0, non_active)(qutrit1),
+        qudit_gates.QuditControlledXGate(3, control, dest)(qutrit0, qutrit1),
+        cirq.measure(qutrit0, key="m0"),
+        cirq.measure(qutrit1, key="m1"),
+    )
+    results = sim.run(c, repetitions=1000)
+    assert np.all(results.measurements["m0"] == control)
+    assert np.all(results.measurements["m1"] == non_active)
 
 @pytest.mark.parametrize("dest", [1, 2])
 def test_control_of_0_x(dest: int):
@@ -162,6 +174,17 @@ def test_control_of_0_x(dest: int):
     assert np.all(results.measurements["m0"] == 2)
     assert np.all(results.measurements["m1"] == 0)
 
+    # 2nd qutrit is in the non-dest state and has no effect
+    non_active = 3 - dest
+    c = cirq.Circuit(
+        qudit_gates.QuditXGate(3, 0, non_active)(qutrit1),
+        qudit_gates.QuditControlledXGate(3, 0, dest)(qutrit0, qutrit1),
+        cirq.measure(qutrit0, key="m0"),
+        cirq.measure(qutrit1, key="m1"),
+    )
+    results = sim.run(c, repetitions=1000)
+    assert np.all(results.measurements["m0"] == 0)
+    assert np.all(results.measurements["m1"] == non_active)
 
 @pytest.mark.parametrize(
     "gate",
@@ -180,12 +203,14 @@ def test_control_of_0_x(dest: int):
         qudit_gates.QuditISwapPowGate(3),
         qudit_gates.QuditSwapPowGate(3, exponent=0.5),
         qudit_gates.QuditISwapPowGate(3, exponent=0.5),
+        qudit_gates.QuditHadamardGate(2),
+        qudit_gates.QuditHadamardGate(3),
+        qudit_gates.QuditHadamardGate(4),
     ],
 )
 def test_gates_are_unitary(gate: cirq.Gate):
     m = cirq.unitary(gate)
     np.set_printoptions(linewidth=200)
-    result = m.dot(m.T.conj())
     assert np.allclose(np.eye(len(m)), m.dot(m.T.conj()), atol=1e-6)
 
 
@@ -295,3 +320,18 @@ def test_sqrt_iswap(q0: int, q1: int):
     results = sim.run(c, repetitions=1000)
     assert np.all(results.measurements["m0"] == q1)
     assert np.all(results.measurements["m1"] == q0)
+
+
+@pytest.mark.parametrize(
+    "d, q0", [(2, 0), (2, 1), (3, 0), (3, 1), (3, 2), (4, 0), (4, 1), (4, 2), (4, 3)]
+)
+def test_hadamard(d: int, q0: int):
+    qutrit0 = cirq.NamedQid("q0", dimension=d)
+    c = cirq.Circuit()
+    c.append(qudit_gates.QuditPlusGate(d, addend=q0)(qutrit0))
+    c.append(qudit_gates.QuditHadamardGate(d)(qutrit0))
+    c.append(cirq.measure(qutrit0, key="m0"))
+    sim = cirq.Simulator()
+    results = sim.run(c, repetitions=1000)
+    for each_possible_outcome in range(d):
+        assert np.any(results.measurements["m0"] == each_possible_outcome)