WeightedAdder

class qiskit.circuit.library.WeightedAdder(num_state_qubits=None, weights=None, name='adder')

Bases: BlueprintCircuit

A circuit to compute the weighted sum of qubit registers.

Given $n$ qubit basis states $q_0, \ldots, q_{n-1} \in \{0, 1\}$ and non-negative integer weights $\lambda_0, \ldots, \lambda_{n-1}$ , this circuit performs the operation

|q_0 \ldots q_{n-1}\rangle |0\rangle_s \mapsto |q_0 \ldots q_{n-1}\rangle |\sum_{j=0}^{n-1} \lambda_j q_j\rangle_s

where $s$ is the number of sum qubits required. This can be computed as

s = 1 + \left\lfloor \log_2\left( \sum_{j=0}^{n-1} \lambda_j \right) \right\rfloor

or $s = 1$ if the sum of the weights is 0 (then the expression in the logarithm is invalid).

For qubits in a circuit diagram, the first weight applies to the upper-most qubit. For an example where the state of 4 qubits is added into a sum register, the circuit can be schematically drawn as

           ┌────────┐
  state_0: ┤0       ├ | state_0 * weights[0]
           │        │ |
  state_1: ┤1       ├ | + state_1 * weights[1]
           │        │ |
  state_2: ┤2       ├ | + state_2 * weights[2]
           │        │ |
  state_3: ┤3       ├ | + state_3 * weights[3]
           │        │
    sum_0: ┤4       ├ |
           │  Adder │ |
    sum_1: ┤5       ├ | = sum_0 * 2^0 + sum_1 * 2^1 + sum_2 * 2^2
           │        │ |
    sum_2: ┤6       ├ |
           │        │
  carry_0: ┤7       ├
           │        │
  carry_1: ┤8       ├
           │        │
control_0: ┤9       ├
           └────────┘

Computes the weighted sum controlled by state qubits.

Parameters

num_state_qubits (Optional[int]) – The number of state qubits.
weights (Optional[List[int]]) – List of weights, one for each state qubit. If none are provided they default to 1 for every qubit.
name (str) – The name of the circuit.

Attributes

num_carry_qubits

The number of carry qubits required to compute the sum.

Note that this is not necessarily equal to the number of ancilla qubits, these can be queried using num_ancilla_qubits.

Returns

The number of carry qubits required to compute the sum.

num_control_qubits

The number of additional control qubits required.

Note that the total number of ancilla qubits can be obtained by calling the method num_ancilla_qubits.

Returns

The number of additional control qubits required (0 or 1).

num_state_qubits

The number of qubits to be summed.

Returns

The number of state qubits.

num_sum_qubits

The number of sum qubits in the circuit.

Returns

The number of qubits needed to represent the weighted sum of the qubits.

weights

The weights for the qubit states.

Returns

The weight for the qubit states.

name

Type: str

A human-readable name for the circuit.

Example

from qiskit import QuantumCircuit
 
qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)

my_circuit