Quantum Arithmetic Logic Units

An Introduction and Overview of the QALU Module

Introduction

As quantum computing continues to grow in importance and application, researchers and developers are creating tools and libraries to facilitate the implementation of quantum algorithms. One key challenge in quantum computing is the design and implementation of quantum arithmetic logic units (QALUs) that can perform basic arithmetic and logic operations efficiently. In this blog post, we will discuss the concept of QALUs and introduce the QALU module, which provides a set of functions for performing arithmetic and logic operations on quantum computers.

Quantum Arithmetic Logic Units (QALU)

A QALU is a fundamental building block of quantum computers that performs arithmetic and logic operations on quantum bits, or qubits. Unlike classical computing, where bits can be either 0 or 1, qubits can exist in a superposition of states, allowing quantum computers to perform calculations in parallel. To harness the potential of quantum computing, QALUs are designed to perform operations on qubits while maintaining their coherence and minimizing errors.

The QALU module

The QALU module is a Python package that provides a set of functions for implementing arithmetic and logic operations on quantum circuits. The module is designed to work with quantum computing frameworks, such as Qiskit or Cirq, that provide circuit objects for constructing and simulating quantum circuits. The QALU module simplifies the process of designing quantum circuits by providing a set of functions that perform common arithmetic and logic operations.

The following is an overview of the functions provided by the QALU module:

and_(circ, a, b, out)
nand_(circ, a, b, out)
or_(circ, a, b, out)
nor_(circ, a, b, out)
xor_(circ, a, b, out)
xnor_(circ, a, b, out)
half_adder(circ, a, b, carry, sum_)
full_adder(circ, a, b, c_in, c_out, sum_)
half_subtractor(circ, a, b, bor, diff)
full_subtractor(circ, a, b, b_in, b_out, diff)
multi_qubits_adder(circ, A, B, T, C)
multi_qubits_subtractor(circ, A, B, T, C)

These functions take a quantum circuit object, qubit indices, and other relevant parameters as input and apply the corresponding quantum gates to perform the specified operation. Additionally, the QALU module includes a utils class that provides utility functions for analyzing and interpreting the results of quantum circuits.

4-Qubits Adder

Here is an implementation of 4-qubits adder in QALU. By introducing quantum parallelism, all possible input combinations of addition is done simultaneously, namely, 256 addition operations are done simultaneously

from qiskit import QuantumCircuit,execute,Aer,QuantumRegister, ClassicalRegister
from qiskit.visualization import plot_state_qsphere,plot_bloch_multivector
from math import log
import numpy as np
from QALU import *
# Simulation environment for QC
be=Aer.get_backend(“statevector_simulator”)
# Create Multi Qubits Adder woth QALU
a=QuantumRegister(4,”a”)
b=QuantumRegister(4,”b”)
t=QuantumRegister(3,”t”)
c=QuantumRegister(5,”c”)
qc=QuantumCircuit(a,b,t,c)
qc.h([i for i in range(8)])
multi_qubits_subtractor(qc,(0,1,2,3),(4,5,6,7),(8,9,10),(11,12,13,14,15))
display(qc.draw(“mpl”,fold=-1))
sv=execute(qc,be).result()

Conclusion

The QALU module provides a convenient way to perform arithmetic and logic operations on quantum circuits. By abstracting the implementation details of quantum gates, the QALU module enables developers to focus on designing and optimizing quantum algorithms. As quantum computing continues to advance, tools like the QALU module will play a crucial role in simplifying the development process and making quantum computing more accessible to researchers, developers, and enthusiasts alike.