Quantum data is any data source that occurs in a natural or artificial quantum system. This can be data generated by a quantum computer, like the samples gathered from the Sycamore processor for Google’s demonstration of quantum supremacy. Quantum data exhibits superposition and entanglement, leading to joint probability distributions that could require an exponential amount of classical computational resources to represent or store. The quantum supremacy experiment showed it is possible to sample from an extremely complex joint probability distribution of 2^53 Hilbert space.

Quantum Data

https://qiskit.org/textbook/ch-algorithms/grover.html

Grover's Search

https://qiskit.org/textbook/ch-algorithms/shor.html

Shor's Factorization

https://qiskit.org/textbook/ch-algorithms/quantum-fourier-transform.html

Quantum Fourier Transformation

Early quantum algorithms: 
* Deutsch, 
* Deutsch-Jozsa,
* Bernstein-Vazirani,
* Simon’s

Foundational quantum Algorithms:
* Grover’s Search
* Quantum Fourier Transform 
* Quantum Phase Estimation
* Shor’s Factorization

Cross-industry quantum algorithms
* Quantum Amplitude Estimation - Monte Carlo Simulations
* Quantum Support Vector Machine
* Quantum Generative Adversarial Networks (qGANs)
* Quantum Optimization


University of Michigan - Ann Arbor

Quantum computing is an emerging field that appears to be more and more difficult to avoid in a vast number of fields including physics, business, mathematics, chemistry, and more notably, data science. One such aspect of quantum computing that attracts the minds of many, especially data scientists, is its potential in advancing our knowledge in optimization problems. As such, it may be invaluable to understand the basics of quantum computing and how to start quantum programming now, even before the widespread availability of quantum computers. Even better, companies like Google, Microsoft, IBM, Rigetti, and more have developed their own open-source development kits to begin learning quantum computing. One such software package is called QuTip within Python.

Quantum Computing with Python

This is an open-source framework for quantum computing founded by IBM Research. This site is an excellent resource to not only learn how to use this package, but to learn about the basics and motivation behind quantum computing.

Qiskit is a quantum circuit construction, optimization, and execution engine. Additional algorithm and application layers within Qiskit leverage quantum circuits, often in concert with classical computing resources, to solve problems in optimization, quantum chemistry, physics, machine learning, and finance. 

Qiskit - https://qiskit.org/

This is a paper published in Nature that proposes and experimentally implements two quantum algorithms. The algorithms solve a problem of supervised learning: the construction of a classifier. It bridges the fields of machine learning and quantum computing.

Supervised learning with quantum-enhanced feature spaces

Quantum Algorithms

Circ is Google's open source framework for programming quantum computers. Cirq is a Python software library for writing, manipulating, and optimizing quantum circuits, and then running them on quantum computers and quantum simulators. Cirq provides useful abstractions for dealing with today’s noisy intermediate-scale quantum computers, where details of the hardware are vital to achieving state-of-the-art results.

Cirq

PennyLane is an open-source software framework built around the concept of quantum differentiable programming. It seamlessly integrates classical machine learning libraries with quantum simulators and hardware, giving users the power to train quantum circuits.

Classical computations, as well as optimization or training of models, are executed using one of the standard scientific computing or machine learning libraries. PennyLane provides an interface to these libraries, making them quantum-aware.

PennyLane’s standard interface is NumPy, but interfaces to powerful machine learning libraries like PyTorch, Tensorflow, and JAX are also available.

The quantum computations are sent to a device for execution. A device can be real quantum hardware or a classical simulator. PennyLane comes with default simulator devices, but is well-integrated with external software and hardware to run quantum circuits—such as Xanadu’s Strawberry Fields, Rigetti’s Forest, IBM’s Qiskit, or Google’s Cirq.

PennyLane

A quantum neural network (QNN) is used to describe a parameterized quantum computational model that is best executed on a quantum computer. This term is often interchangeable with parameterized quantum circuit (PQC).

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