# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""Compute the weighted sum of qubit states."""
from typing import List, Optional
import numpy as np
from qiskit.circuit import QuantumRegister, AncillaRegister, QuantumCircuit
from ..blueprintcircuit import BlueprintCircuit
[docs]class WeightedAdder(BlueprintCircuit):
r"""A circuit to compute the weighted sum of qubit registers.
Given :math:`n` qubit basis states :math:`q_0, \ldots, q_{n-1} \in \{0, 1\}` and non-negative
integer weights :math:`\lambda_0, \ldots, \lambda_{n-1}`, this circuit performs the operation
.. math::
|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 :math:`s` is the number of sum qubits required.
This can be computed as
.. math::
s = 1 + \left\lfloor \log_2\left( \sum_{j=0}^{n-1} \lambda_j \right) \right\rfloor
or :math:`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
.. parsed-literal::
┌────────┐
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 ├
└────────┘
"""
def __init__(
self,
num_state_qubits: Optional[int] = None,
weights: Optional[List[int]] = None,
name: str = "adder",
) -> None:
"""Computes the weighted sum controlled by state qubits.
Args:
num_state_qubits: The number of state qubits.
weights: List of weights, one for each state qubit. If none are provided they
default to 1 for every qubit.
name: The name of the circuit.
"""
super().__init__(name=name)
self._weights = None
self._num_state_qubits = None
self.weights = weights
self.num_state_qubits = num_state_qubits
@property
def num_sum_qubits(self) -> int:
"""The number of sum qubits in the circuit.
Returns:
The number of qubits needed to represent the weighted sum of the qubits.
"""
if sum(self.weights) > 0:
return int(np.floor(np.log2(sum(self.weights))) + 1)
return 1
@property
def weights(self) -> List[int]:
"""The weights for the qubit states.
Returns:
The weight for the qubit states.
"""
if self._weights:
return self._weights
if self.num_state_qubits:
return [1] * self.num_state_qubits
return None
@weights.setter
def weights(self, weights: List[int]) -> None:
"""Set the weights for summing the qubit states.
Args:
weights: The new weights.
Raises:
ValueError: If not all weights are close to an integer.
"""
if weights:
for i, weight in enumerate(weights):
if not np.isclose(weight, np.round(weight)):
raise ValueError("Non-integer weights are not supported!")
weights[i] = np.round(weight)
self._invalidate()
self._weights = weights
self._reset_registers()
@property
def num_state_qubits(self) -> int:
"""The number of qubits to be summed.
Returns:
The number of state qubits.
"""
return self._num_state_qubits
@num_state_qubits.setter
def num_state_qubits(self, num_state_qubits: int) -> None:
"""Set the number of state qubits.
Args:
num_state_qubits: The new number of state qubits.
"""
if self._num_state_qubits is None or num_state_qubits != self._num_state_qubits:
self._invalidate()
self._num_state_qubits = num_state_qubits
self._reset_registers()
def _reset_registers(self):
"""Reset the registers."""
self.qregs = []
if self.num_state_qubits:
qr_state = QuantumRegister(self.num_state_qubits, name="state")
qr_sum = QuantumRegister(self.num_sum_qubits, name="sum")
self.qregs = [qr_state, qr_sum]
if self.num_carry_qubits > 0:
qr_carry = AncillaRegister(self.num_carry_qubits, name="carry")
self.add_register(qr_carry)
if self.num_control_qubits > 0:
qr_control = AncillaRegister(self.num_control_qubits, name="control")
self.add_register(qr_control)
@property
def num_carry_qubits(self) -> int:
"""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.
"""
return self.num_sum_qubits - 1
@property
def num_control_qubits(self) -> int:
"""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).
"""
return int(self.num_sum_qubits > 2)
def _check_configuration(self, raise_on_failure=True):
"""Check if the current configuration is valid."""
valid = True
if self._num_state_qubits is None:
valid = False
if raise_on_failure:
raise AttributeError("The number of state qubits has not been set.")
if self._num_state_qubits != len(self.weights):
valid = False
if raise_on_failure:
raise ValueError("Mismatching number of state qubits and weights.")
return valid
def _build(self):
"""If not already built, build the circuit."""
if self._is_built:
return
super()._build()
num_result_qubits = self.num_state_qubits + self.num_sum_qubits
circuit = QuantumCircuit(*self.qregs)
qr_state = circuit.qubits[: self.num_state_qubits]
qr_sum = circuit.qubits[self.num_state_qubits : num_result_qubits]
qr_carry = circuit.qubits[num_result_qubits : num_result_qubits + self.num_carry_qubits]
qr_control = circuit.qubits[num_result_qubits + self.num_carry_qubits :]
# loop over state qubits and corresponding weights
for i, weight in enumerate(self.weights):
# only act if non-trivial weight
if np.isclose(weight, 0):
continue
# get state control qubit
q_state = qr_state[i]
# get bit representation of current weight
weight_binary = f"{int(weight):b}".rjust(self.num_sum_qubits, "0")[::-1]
# loop over bits of current weight and add them to sum and carry registers
for j, bit in enumerate(weight_binary):
if bit == "1":
if self.num_sum_qubits == 1:
circuit.cx(q_state, qr_sum[j])
elif j == 0:
# compute (q_sum[0] + 1) into (q_sum[0], q_carry[0])
# - controlled by q_state[i]
circuit.ccx(q_state, qr_sum[j], qr_carry[j])
circuit.cx(q_state, qr_sum[j])
elif j == self.num_sum_qubits - 1:
# compute (q_sum[j] + q_carry[j-1] + 1) into (q_sum[j])
# - controlled by q_state[i] / last qubit,
# no carry needed by construction
circuit.cx(q_state, qr_sum[j])
circuit.ccx(q_state, qr_carry[j - 1], qr_sum[j])
else:
# compute (q_sum[j] + q_carry[j-1] + 1) into (q_sum[j], q_carry[j])
# - controlled by q_state[i]
circuit.x(qr_sum[j])
circuit.x(qr_carry[j - 1])
circuit.mcx(
[q_state, qr_sum[j], qr_carry[j - 1]],
qr_carry[j],
qr_control,
mode="v-chain",
)
circuit.cx(q_state, qr_carry[j])
circuit.x(qr_sum[j])
circuit.x(qr_carry[j - 1])
circuit.cx(q_state, qr_sum[j])
circuit.ccx(q_state, qr_carry[j - 1], qr_sum[j])
else:
if self.num_sum_qubits == 1:
pass # nothing to do, since nothing to add
elif j == 0:
pass # nothing to do, since nothing to add
elif j == self.num_sum_qubits - 1:
# compute (q_sum[j] + q_carry[j-1]) into (q_sum[j])
# - controlled by q_state[i] / last qubit,
# no carry needed by construction
circuit.ccx(q_state, qr_carry[j - 1], qr_sum[j])
else:
# compute (q_sum[j] + q_carry[j-1]) into (q_sum[j], q_carry[j])
# - controlled by q_state[i]
circuit.mcx(
[q_state, qr_sum[j], qr_carry[j - 1]],
qr_carry[j],
qr_control,
mode="v-chain",
)
circuit.ccx(q_state, qr_carry[j - 1], qr_sum[j])
# uncompute carry qubits
for j in reversed(range(len(weight_binary))):
bit = weight_binary[j]
if bit == "1":
if self.num_sum_qubits == 1:
pass
elif j == 0:
circuit.x(qr_sum[j])
circuit.ccx(q_state, qr_sum[j], qr_carry[j])
circuit.x(qr_sum[j])
elif j == self.num_sum_qubits - 1:
pass
else:
circuit.x(qr_carry[j - 1])
circuit.mcx(
[q_state, qr_sum[j], qr_carry[j - 1]],
qr_carry[j],
qr_control,
mode="v-chain",
)
circuit.cx(q_state, qr_carry[j])
circuit.x(qr_carry[j - 1])
else:
if self.num_sum_qubits == 1:
pass
elif j == 0:
pass
elif j == self.num_sum_qubits - 1:
pass
else:
# compute (q_sum[j] + q_carry[j-1]) into (q_sum[j], q_carry[j])
# - controlled by q_state[i]
circuit.x(qr_sum[j])
circuit.mcx(
[q_state, qr_sum[j], qr_carry[j - 1]],
qr_carry[j],
qr_control,
mode="v-chain",
)
circuit.x(qr_sum[j])
self.append(circuit.to_gate(), self.qubits)