Add test for bug fix for issue #7335

crates/circuit/src/operations.rs

@@ -359,6 +359,16 @@ impl StandardGate {
     pub fn get_name(&self) -> &str {
         self.name()
     }
+
+    pub fn __eq__(&self, other: &Bound<PyAny>) -> Py<PyAny> {
+        let py = other.py();
+        let Ok(other) = other.extract::<Self>() else { return py.NotImplemented() };
+        (*self == other).into_py(py)
+    }
+
+    pub fn __hash__(&self) -> isize {
+        *self as isize
+    }
 }
 
 // This must be kept up-to-date with `StandardGate` when adding or removing

qiskit/circuit/library/standard_gates/x.py

@@ -952,8 +952,8 @@ class C4XGate(SingletonControlledGate):
     of the relative phase version of c3x, the rc3x [2].
 
     References:
-        [1] Barenco et al., 1995. https://arxiv.org/pdf/quant-ph/9503016.pdf
-        [2] Maslov, 2015. https://arxiv.org/abs/1508.03273
+        1. Barenco et al., 1995. https://arxiv.org/pdf/quant-ph/9503016.pdf
+        2. Maslov, 2015. https://arxiv.org/abs/1508.03273
     """
 
     def __init__(
@@ -1320,9 +1320,14 @@ def _define(self):
 class MCXRecursive(MCXGate):
     """Implement the multi-controlled X gate using recursion.
 
-    Using a single ancilla qubit, the multi-controlled X gate is recursively split onto
-    four sub-registers. This is done until we reach the 3- or 4-controlled X gate since
-    for these we have a concrete implementation that do not require ancillas.
+    Using a single clean ancilla qubit, the multi-controlled X gate is split into
+    four sub-registers, each one of them uses the V-chain method.
+
+    The method is based on Lemma 9 of [2], first shown in Lemma 7.3 of [1].
+
+    References:
+        1. Barenco et al., 1995. https://arxiv.org/pdf/quant-ph/9503016.pdf
+        2. Iten et al., 2015. https://arxiv.org/abs/1501.06911
     """
 
     def __init__(
@@ -1378,32 +1383,35 @@ def _define(self):
             qc._append(C4XGate(), q[:], [])
             self.definition = qc
         else:
-            for instr, qargs, cargs in self._recurse(q[:-1], q_ancilla=q[-1]):
-                qc._append(instr, qargs, cargs)
-            self.definition = qc
+            num_ctrl_qubits = len(q) - 1
+            q_ancilla = q[-1]
+            q_target = q[-2]
+            middle = ceil(num_ctrl_qubits / 2)
+            first_half = [*q[:middle]]
+            second_half = [*q[middle : num_ctrl_qubits - 1], q_ancilla]
+
+            qc._append(
+                MCXVChain(num_ctrl_qubits=len(first_half), dirty_ancillas=True),
+                qargs=[*first_half, q_ancilla, *q[middle : middle + len(first_half) - 2]],
+                cargs=[],
+            )
+            qc._append(
+                MCXVChain(num_ctrl_qubits=len(second_half), dirty_ancillas=True),
+                qargs=[*second_half, q_target, *q[: len(second_half) - 2]],
+                cargs=[],
+            )
+            qc._append(
+                MCXVChain(num_ctrl_qubits=len(first_half), dirty_ancillas=True),
+                qargs=[*first_half, q_ancilla, *q[middle : middle + len(first_half) - 2]],
+                cargs=[],
+            )
+            qc._append(
+                MCXVChain(num_ctrl_qubits=len(second_half), dirty_ancillas=True),
+                qargs=[*second_half, q_target, *q[: len(second_half) - 2]],
+                cargs=[],
+            )
 
-    def _recurse(self, q, q_ancilla=None):
-        # recursion stop
-        if len(q) == 4:
-            return [(C3XGate(), q[:], [])]
-        if len(q) == 5:
-            return [(C4XGate(), q[:], [])]
-        if len(q) < 4:
-            raise AttributeError("Something went wrong in the recursion, have less than 4 qubits.")
-
-        # recurse
-        num_ctrl_qubits = len(q) - 1
-        middle = ceil(num_ctrl_qubits / 2)
-        first_half = [*q[:middle], q_ancilla]
-        second_half = [*q[middle:num_ctrl_qubits], q_ancilla, q[num_ctrl_qubits]]
-
-        rule = []
-        rule += self._recurse(first_half, q_ancilla=q[middle])
-        rule += self._recurse(second_half, q_ancilla=q[middle - 1])
-        rule += self._recurse(first_half, q_ancilla=q[middle])
-        rule += self._recurse(second_half, q_ancilla=q[middle - 1])
-
-        return rule
+            self.definition = qc
 
 
 class MCXVChain(MCXGate):

qiskit/primitives/backend_estimator_v2.py

@@ -72,7 +72,7 @@ class _PreprocessedData:
 
 
 class BackendEstimatorV2(BaseEstimatorV2):
-    """Evaluates expectation values for provided quantum circuit and observable combinations
+    r"""Evaluates expectation values for provided quantum circuit and observable combinations.
 
     The :class:`~.BackendEstimatorV2` class is a generic implementation of the
     :class:`~.BaseEstimatorV2` interface that is used to wrap a :class:`~.BackendV2`
@@ -87,7 +87,19 @@ class BackendEstimatorV2(BaseEstimatorV2):
     precludes doing any provider- or backend-specific optimizations.
 
     This class does not perform any measurement or gate mitigation, and, presently, is only
-    compatible with Pauli-based observables.
+    compatible with Pauli-based observables. More formally, given an observable of the type
+    :math:`O=\sum_{i=1}^Na_iP_i`, where :math:`a_i` is a complex number and :math:`P_i` is a
+    Pauli operator, the estimator calculates the expectation :math:`\mathbb{E}(P_i)` of each
+    :math:`P_i` and finally calculates the expectation value of :math:`O` as
+    :math:`\mathbb{E}(O)=\sum_{i=1}^Na_i\mathbb{E}(P_i)`. The reported ``std`` is calculated
+    as
+
+    .. math::
+
+        \frac{\sum_{i=1}^{n}|a_i|\sqrt{\textrm{Var}\big(P_i\big)}}{\sqrt{N}}\:,
+
+    where :math:`\textrm{Var}(P_i)` is the variance of :math:`P_i`, :math:`N=O(\epsilon^{-2})` is
+    the number of shots, and :math:`\epsilon` is the target precision [1].
 
     Each tuple of ``(circuit, observables, <optional> parameter values, <optional> precision)``,
     called an estimator primitive unified bloc (PUB), produces its own array-based result. The
@@ -104,6 +116,12 @@ class BackendEstimatorV2(BaseEstimatorV2):
 
     * ``seed_simulator``: The seed to use in the simulator. If None, a random seed will be used.
       Default: None.
+
+    **Reference:**
+
+    [1] O. Crawford, B. van Straaten, D. Wang, T. Parks, E. Campbell, St. Brierley,
+    Efficient quantum measurement of Pauli operators in the presence of finite sampling error.
+    `Quantum 5, 385 <https://doi.org/10.22331/q-2021-01-20-385>`_
     """
 
     def __init__(
@@ -254,8 +272,8 @@ def _postprocess_pub(
             for pauli, coeff in bc_obs[index].items():
                 expval, variance = expval_map[param_index, pauli]
                 evs[index] += expval * coeff
-                variances[index] += variance * coeff**2
-        stds = np.sqrt(variances / shots)
+                variances[index] += np.abs(coeff) * variance**0.5
+        stds = variances / np.sqrt(shots)
         data_bin = DataBin(evs=evs, stds=stds, shape=evs.shape)
         return PubResult(data_bin, metadata={"target_precision": pub.precision})
 

qiskit/qasm3/ast.py

@@ -456,39 +456,23 @@ class SubroutineBlock(ProgramBlock):
     pass
 
 
-class QuantumArgument(QuantumDeclaration):
-    """
-    quantumArgument
-        : 'qreg' Identifier designator? | 'qubit' designator? Identifier
-    """
-
-
-class QuantumGateSignature(ASTNode):
+class QuantumGateDefinition(Statement):
     """
-    quantumGateSignature
-        : quantumGateName ( LPAREN identifierList? RPAREN )? identifierList
+    quantumGateDefinition
+        : 'gate' quantumGateSignature quantumBlock
     """
 
     def __init__(
         self,
         name: Identifier,
-        qargList: List[Identifier],
-        params: Optional[List[Expression]] = None,
+        params: Tuple[Identifier, ...],
+        qubits: Tuple[Identifier, ...],
+        body: QuantumBlock,
     ):
         self.name = name
-        self.qargList = qargList
         self.params = params
-
-
-class QuantumGateDefinition(Statement):
-    """
-    quantumGateDefinition
-        : 'gate' quantumGateSignature quantumBlock
-    """
-
-    def __init__(self, quantumGateSignature: QuantumGateSignature, quantumBlock: QuantumBlock):
-        self.quantumGateSignature = quantumGateSignature
-        self.quantumBlock = quantumBlock
+        self.qubits = qubits
+        self.body = body
 
 
 class SubroutineDefinition(Statement):