# 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**(*int**| None*) – The number of state qubits.**weights**(*List**[**int**] | None*) – 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

### ancillas

Returns a list of ancilla bits in the order that the registers were added.

### calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`

### clbits

Returns a list of classical bits in the order that the registers were added.

### data

### extension_lib

Default value: `'include "qelib1.inc";'`

### global_phase

Return the global phase of the current circuit scope in radians.

### header

Default value: `'OPENQASM 2.0;'`

### instances

Default value: `159`

### layout

Return any associated layout information about the circuit

This attribute contains an optional `TranspileLayout`

object. This is typically set on the output from `transpile()`

or `PassManager.run()`

to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the `transpile()`

function, an initial layout which permutes the qubits based on the selected physical qubits on the `Target`

, and a final layout which is an output permutation caused by `SwapGate`

s inserted during routing.

### metadata

The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided `dict`

of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

### num_ancillas

Return the number of ancilla qubits.

### 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_clbits

Return number of classical bits.

### 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_parameters

### num_qubits

Return number of qubits.

### 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.

### op_start_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

**Returns**

List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`

.

**Raises**

**AttributeError** – When circuit is not scheduled.

### parameters

### prefix

Default value: `'circuit'`

### qregs

Type: `list[QuantumRegister]`

A list of the quantum registers associated with the circuit.

### qubits

Returns a list of quantum bits in the order that the registers were added.

### weights

The weights for the qubit states.

**Returns**

The weight for the qubit states.