## Five Key Benefits of Quantum Machine Learning

*Here, Dr. Amit Ray discusses the five key benefits of quantum machine learning. *

Quantum machine learning is evolving very fast and gaining enormous momentum due to its huge potential. Quantum machine learning is the key technology for future compassionate artificial intelligence. In our Compassionate AI Lab, we have conducted several experiments on quantum machine learning in the areas of drug-discovery, combating antibiotic resistance bacteria, and multi-omics data integration.

We have realized that in the area of drug design and multi-omics data integration, the power of deep learning is very much restricted in classical computer. Hence, with limited facilities, we have conducted many hybrid classical-quantum machine learning algorithm testing at our Compassionate AI Lab.

Earlier we have discussed top 10 properties of quantum machine learning, **Road-map for 1000 Qubits Fault-tolerant Quantum Computers,** **7 Core Qubit Technologies for Quantum Computing, 7 Key Requirements for Quantum Computing.** **Spin-orbit Coupling Qubits for Quantum Computing and AI, Quantum Computing Algorithms for Artificial Intelligence, Quantum Computing and Artificial Intelligence , Quantum Computing with Many World Interpretation Scopes and Challenges and Quantum Computer with Superconductivity at Room Temperature. **Here, primarily we focus on the five key benefits of quantum machine learning.

## What is Quantum Machine Learning?

In the book Quantum computing algorithms for artificial intelligence, we have defined quantum machine learning as:** “Quantum Machine Learning is ****defined as** the branch of science and technology that is concerned with the application of **quantum mechanical phenomena such as superposition, entanglement and tunneling** for designing software and hardware to provide machines the ability to learn insights and patterns from data and the environment, and the ability to adapt automatically to changing situations with high precision, accuracy and speed.”

The speed requirements for various machine learning applications grows with the complexity of the problems and the speed advantage of quantum computers are enormous compare to classical computers. ** The key to quantum computation speed is that every additional qubit doubles the potential computing power of a quantum machine. **Based on complexity theory, quantum computers can solve much complex problems in exponentially less time than classical computers. Quantum computers can provide faster solutions to factoring and searching, and other algorithms compare to the classical computers.

A classic computer processes bits, which at any given time can be in one of two states: 0 or 1. Quantum computers use qubits, which can exist in any superposition of states 0 and 1, and are represented by a complex number. When N qubits are in superposition, a combination of 2^{N} states is created. A classic computer can only hold one of these states at a time, while quantum computers can perform operations on many superposition of states. This quantum superposition of states allows the simultaneous manipulation of all possible combinations of a set of bits in a single operation, speeding up many algorithms exponentially when compared to a classical computers.

## Benefits of Quantum Machine Learning

The core of many machine learning applications is the repeated computation of a complex mathematical expression. Neural networks store weights in matrices. Deep learning is mostly comprised of matrix operations like matrix multiplication. Primarily, there are two types of quantum processing: 1) Gate model universal quantum processing and 2) Quantum Annealing processing. Both of them have their own advantages and limitations. Quantum machine learning can be implemented on both of them. The true benefits of quantum machine learning depends on many parameters like design selection, network architectures, software, and implementation criteria. However, the five common benefits of quantum machine learning techniques are as follows:

**1 QML Can speedup the training time:**

Quantum computers use quantum properties such as quantum coherence, superposition and entanglement to process information in ways that classical computers can not. The quantum computer exhibits a square root speed up over the classical computer. For example, quantum computers can search an unsorted database with N entries in time proportional to √N—that is O(√N)—where a classical computer given black-box access to the same database takes time proportional to N – that is O(N).

**2. QML Can handle complex network topology**

The quantum adiabatic computing approach allows deep learning network topologies to be much more complex than what is feasible with conventional classical computer architectures. Similarly, quantum associative memory algorithm (QAM) uses the exponential storage capacity of memory states. Here, complex network topology we mean bidirectional connections and looping connectivity between neural units. Complex topologies that can be trained on a quantum computer. There is no time-based performance penalty due to the addition of intra layer connections, though there may be a need to sample more often in order to reduce potential errors.

Quantum circuits are a special class of tensor networks. Complex neural networks can be implemented with tensor networks. The tensor networks of quantum circuit model is widely used for building quantum neural networks to describe quantum algorithms and their experimental implementations.

**3. QML Can automatically adjust network hyperparameters**

Hyperparameters in deep learning refer to the model parameters, such as learning rate, number of hidden layers, number of hidden nodes in each layer, kernel size, number of epochs. Currently the best deep learning models are discovered by creating, training, testing, and tuning many models on some well-known reference dataset and reporting the best model in the literature. It is difficult to know how to tune networks for optimal performance. GPU-based high performance computing provides some opportunity to automate but are very limited. The complexity of the hyper parameters scales exponentially with the system size. However, quantum computing promises to adjust the network hyperparameters automatically. Nonlocality, which is closely related to entanglement, is another important feature of quantum mechanics is powerful to determine the hyper-parameters.

**4. QML Can perform complex matrix and tensor manipulation at high speed**

In 2009, Harrow, Hassidim, and Lloyd developed a quantum algorithm (referred to as the HHL algorithm) that solves linear systems of equations in time * for -by- sparse matrices. The HHL algorithm is backbone of many traditional quantum machine learning algorithms. The **algorithm *seeks to solve **A x = b** using a *quantum* computer. In gate model, the quantum process consists of an input state, a quantum circuit and a measurement. Tensors are the fundamental bricks building up the quantum state, and quantum entanglement plays the role of the glue amongst the different pieces [11]. A tensor is a multi-dimensional array. Tensor Networks (TN) are originally designed for efficiently representing quantum many body wave function. Popular TNs include Matrix Product States (MPS), Tree Tensor Networks (TTN), Multi-scale Entanglement Renormalization Ansatz (MERA), projected entanglement pair states (PEPS).

Tensor networks can represent weights of the neural network structures. Quantum entanglement is a physical phenomenon in which measurements on one particle will instantaneously influence the state of another, even when the particles are spatially separated by a large distance—a phenomenon Albert Einstein called “spooky action at a distance.” Entanglement area law is crucial in the tensor-network representation of quantum many-body states and forms the backbone of numerous tensor-network-based algorithms. The number of parameters needed to describe quantum neural networks layers scales linearly with the system size rather than exponentially, as in a conventional tensor-network representation [5].

**5. QML Can use quantum tunneling to achieve true objective function goals**

Traditionally the classical computers uses gradient descent and its variants for the optimization of neural networks and other machine learning algorithms. Due to the local and deterministic nature of the search performed by gradient based schemes the problem of convergence to a local minima near the initial random starting point is always a problem. Moreover often the objective error function is nonconvex and highly multimodal and finding the global minimum is a NP complete problem and exact solution in classical computer is not practical. However, in the quantum computer the quantum tunneling phenomena of Quantum Mechanics allow the best global optimum solution of the objective function as it tunnel through the hills in the cost function.

## Quantum Computing Software Platforms

The six primary quantum computing software platforms are: Cirq from Google, Forest from Rigetti, pyQuil from Rigetti, QISKit from IBM, and ProjectQ from ETH Zurich and Quantum Development Kit from Microsoft. pyQuil is an open source Python library developed at Rigetti Computing that constructs programs for quantum computers. pyQuil produces programs in the Quantum Instruction Language (Quil). The figure shows the list of gate model quantum computing software.

## Present State of Quantum Computers

Presently, IBM, Google, Rigetti, D-Wave, and Microsoft are the key players in quantum computers. 50-qubit noisy machines have been developed, 100-qubit noisy machines are just knocking on the door, and even 1000-qubit machines are perhaps only a few years away. Presently, the largest operational gate-based quantum computer is a 20-qubit system from IBM Q with an average two-qubit gate error rate of about 5 percent. IBM, Intel, and Google each reported testing quantum processors containing 50, 49, and 72 qubits, respectively, all realized using superconducting circuits.

## Summary:

We have discussed the key benefits of quantum machine learning. The true benefits of quantum machine learning depends on design and implementation criteria. The technologies for machine learning are evolving rapidly and current progress is really impressive. The third wave of machine learning breakthroughs is bound to emerge, allowing us to solve a brand-new class of deep learning challenges.

The development of hybrid classical quantum machine learning algorithms can also be capable of exploiting the best of both the worlds. It is essential higher fidelity of the QPUs and better connectivity across the modules. Yet significant work remains, and many open questions and obstacles need to be tackled to achieve the goal of building large-scale quantum machine learning applications.

## Source Books:

- Compassionate Artificial Intelligence: Frameworks and Algorithms by Dr. Amit Ray
- Compassionate Superintelligence, AI 5.0 by Dr. Amit Ray
- Quantum Computing Algorithms for Artificial Intelligence By Dr. Amit Ray

## References:

1. Hybrid Programming for Near-term Quantum Computing Systems, A. J. McCaskey, 2018

2. Simulating Quantum Computers Using OpenCL, Adam Kelly, 2018

3. Quantum Computer Simulation Using CUDA, Alexander Smith, 2018

4. Overview and Comparison of Gate Level Quantum Software Platforms, Ryan LaRose, 2019

5. Machine learning meets quantum physics, Shankar Das Sharma, Physics Today, 2019

6. Quantum Algorithm for Linear Systems of Equations, Aram W. Harrow, Avinatan Hassidim, and Seth Lloyd. Phys. Rev. Lett. 103, 150502 – Published 7 October 2009

7. Quantum Machine Learning, Jacob Biamonte, 2018

8. Open source software in quantum computing, Mark Fingerhuth, PLOS ONE, 2018

9. Reconsider HHL algorithm and its related quantum machine learning algorithms

9. Hybrid quantum linear equation algorithm and its experimental test on IBM Quantum Experience Yonghae Lee, Jaewoo Joo & Soojoon Lee,Scientific Reports volume 9, Nature, 2019

10. Bayesian Deep Learning on a Quantum Computer, Zhikuan Zhao, 2018

11. Robust quantum network architectures and topologies for entanglement distribution

12. Tree Tensor Networks for Generative Modeling

13. Tensor networks for complex quantum systems

13 - 13Shares