Quantum Artificial Intelligence: A Brief Survey

TL;DR

Some major key findings on the feasability and the potential of using quantum computing for solving computationally hard problems in various subfields of AI, and vice versa, the leveraging of AI methods for building and operating quantum computing devices are summarized.

Abstract

Quantum Artificial Intelligence (QAI) is the intersection of quantum computing and AI, a technological synergy with expected significant benefits for both. In this paper, we provide a brief overview of what has been achieved in QAI so far and point to some open questions for future research. In particular, we summarize some major key findings on the feasability and the potential of using quantum computing for solving computationally hard problems in various subfields of AI, and vice versa, the leveraging of AI methods for building and operating quantum computing devices.

Figures (5)

• Figure 1: Quantum AI (QAI) as intersection of quantum computing and AI with subfields in relation to AI each covering both directions.
• Figure 2: Representation of a quantum state $|\psi\rangle$ on the Bloch sphere. The state is described by the angles $\theta$ and $\varphi$, where $\theta$ defines the polar angle from the $z$-axis and $\varphi$ defines the azimuthal angle in the $xy$-plane. The Bloch sphere provides a geometric representation of the pure states of a qubit, with $|0\rangle$ and $|1\rangle$ corresponding to the poles of the sphere.
• Figure 3: A simple quantum circuit demonstrating the combination of basic quantum gates. The circuit starts with a qubit in the $\ket{0}$ state. The Hadamard gate ($H$) is applied first, creating a superposition of $\ket{0}$ and $\ket{1}$. Following this, a Pauli-X gate ($X$) is applied, flipping the qubit's state. The circuit concludes with a measurement, represented by the meter symbol, which collapses the qubit's state into either $\ket{0}$ or $\ket{1}$, producing a classical output.
• Figure 4: A Hybrid Quantum-Classical Optimization Workflow (adapted from Maca23+). The diagram illustrates a hybrid quantum-classical optimization process. The quantum part involves three main stages: State Preparation: An initial quantum state is prepared using the unitary operator $U_S$. Computation: The prepared state is processed by a parameterized quantum circuit $U(\Theta)$ to search for the optimal solution $x$ based on the parameters $\Theta$. Measurement: The quantum state is measured to obtain the expectation value $\langle M \rangle$. The classical part includes three steps: Post-Processing: The measured expectation value $\langle M \rangle$ is processed to extract the classical variable $x$. Evaluation: The function $f(x)$ is evaluated based on the classical variable $x$. Update: The parameters $\Theta$ are updated using classical optimization algorithms to improve the search in the next iteration. The process iterates, with the updated parameters $\Theta_{i+1}$ being fed back into the quantum circuit, forming a closed-loop optimization cycle between the quantum and classical computations.
• Figure 5: Stack of tasks in the building and operation of quantum computing devices for which AI techniques (currently mainly from ML) are utilized.