# Artificial Intelligence Computing at the Quantum Level

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## Abstract

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## 1. Introduction

#### 1.1. Contributions

- This paper provides foundational concepts about QC and a comprehensive analysis of recent work, investigating the connection between physics and information science and assessing the area’s growth.
- We present flowcharts that summarize the field’s development and/or roadmap, as well as a comparison of common quantum bit technologies and open source development frameworks.
- We explore the field’s current (experimental and theoretical) problems in achieving fully scaled quantum devices. We also provide a summary of past developments as well as a progress report on quantum information science topics of interest.
- We provide a list of topics of interest, together with a high-quality list of reference resources for a more in-depth study of each subject, based on the preferences of the readers.

#### 1.2. Structure

## 2. Modern Physics and Artificial Intelligence

#### 2.1. Quantum Mechanics

#### Quantum Theory

#### 2.2. Machine Learning

## 3. Quantum Information Science

#### 3.1. Quantum Mechanics Postulates, Entanglement, Mixed States and Operations

- Postulate 1: State Space. The state of a quantum system is described by a unit vector $|\psi \rangle $ that lives in a Hilbert space $\mathcal{H}.$ This state contains all necessary information to characterize the system.
- Postulate 2: Evolution. A closed quantum system undergoes a time evolution $|\psi \left(t\right)\rangle $. This evolution is described by a unitary transformation that follows the Schrodinger Equation (1).
- Postulate 3: Measurement. Quantum measurements can be expressed using sets of measurement operators $\left\{{M}_{m}\right\}.$ In an experiment, m represents the possible measurement outcomes. Upon measuring a state, say $|\psi \left(t\right)\rangle $, the probability of an m outcome is $p\left(m\right)$.
- Postulate 4: Composite Systems. Two or more physical systems can be treated as a composite system. The state space of a composite system is the tensor product space of the states of the component physical systems.

#### Other Important Properties

- Superposition Linear combination of two states.
- Entanglement When the values of specific qualities of one system are correlated with the values of the corresponding properties of the other system, two quantum systems are said to be entangled.
- Speedup If the quantum algorithm requires fewer queries to solve a problem than the classical approach, the outcome is a quantum speedup [19].

#### 3.2. Quantum Information Science: An Overview

- Adiabatic quantum computing (AQC) is a computational model that employs adiabatic quantum mechanical processes [20].
- Quantum annealing (QA) is a technique for evaluating the minimum of an objective function that is built on AQC concepts but does not meet its stringent requirements [20].
- Quantum simulation (QS) is the use of a controllable quantum system to examine a less controllable or accessible quantum system [21].

- Gate-based quantum computing (GBQC) accepts data and modifies it by a unitary operation, which is expressed as a sequence of gate operations and measurements (i.e., the algorithm) and may be represented by a quantum circuit [22]. Quantum machine learning is the GBQC’s driving force.

#### 3.3. Quantum Computing System

#### 3.4. Q-Gates, Circuits, and Algorithms

#### 3.5. Common Quantum Applications

#### 3.5.1. Information Encoding

- Basis encoding;
- Amplitude encoding;
- Qsample encoding;
- Dynamic encoding.

#### 3.5.2. Quantum Teleportation

- Parties ${q}_{1}$ and ${q}_{2}$ create an entangled pair.
- ${q}_{1}$ applies a CNOT gate with the unknown state ${q}_{0}$.
- ${q}_{1}$ applies a Hadamard gate to the first qubit of the result in 2.
- ${q}_{1}$ measures the results from 3.
- ${q}_{1}$ communicates the measurement results with ${q}_{2}$.

#### 3.5.3. Quantum Cryptography

- No-cloning theorem;
- State collapse when measured;
- Irreversible measurement.

## 4. Quantum Computing Frameworks

#### 4.1. Comparing Common Types of Quantum Bit Technologies

#### 4.2. Challenges in the Field of Quantum Computation

#### 4.2.1. Experimental Challenges of Quantum Computing: Quantum Computers

- Putting atoms in precise quantum states;
- Manipulating the interactions of the atoms to carry out logical procedures;
- Obtaining the computational output by monitoring the resultant states.

#### 4.2.2. Theoretical Challenges of Quantum Computing: Quantum Simulators

## 5. Quantum Computing’s Chronology and Origin Sequence

#### 5.1. Quantum Computing Chronology

#### 5.2. From Physics to Quantum Computing

## 6. Discussion

#### 6.1. State of the Art

#### 6.2. Emerging Quantum Machine Learning Technology

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A Bloch sphere. This is used to visualize the qubit’s geometric state. It gives the angles and basis vectors for the $\psi $ representation.

**Figure 2.**One easy way to show the quantum mechanics postulates chart. P1 defines the state space, P2 defines the evolution, P3 defines the measurement, and P4 defines the composite system, where ${\psi}_{a}{\psi}_{b}\equiv {\psi}_{a}{\psi}_{b}$.

**Figure 3.**Quantum information science (QIS) chart. QIS is divided into three categories: quantum communication, quantum computing, and quantum sensing (and metrology). Quantum communication and quantum sensing have applications, such as quantum networking and quantum system design, respectively. The field of QC splits into analog and digital computing. An analog quantum computer could be any of three forms: adiabatic quantum computing, quantum annealing, or quantum simulation. A digital quantum computer exists in the form of gate-based quantum computing, using the features of QML for its operations.

**Figure 4.**Quantum computing system (QCS) Chart. QCS is a complete system that has two operational parts: hardware and software. The hardware of a QCS is essentially a quantum computer (with variations such as trapped ion qubits and superconducting qubits, among others). Generally, a quantum computer comprises essential components, which are quantum data planes, control and measurement planes, control processor plane, and a host processor. Similarly, the software of a QCS is composed of essential tools, which are simulation and debugging tools, optimization tools, and verification tools.

**Figure 5.**Programming quantum computers Chart. Quantum computers necessitate the use of two key features to run efficiently: programming languages and programming tools. A programming language can either be high level or low level. An example of low-level language programming is quantum assembly language (QASM). A high-level programming language is functional (example includes Quipper) and imperative (example includes ProjectQ).

**Figure 6.**A quantum circuit. The horizontal lines are referred to as wires representing qubits, while the boxes represent operators acting on the qubits. ${R}_{x}$ and H are the rotation operator and Hadamard gates, respectively.

**Figure 7.**Quantum teleportation circuit. There are three qubits (${q}_{0}$, ${q}_{1}$ and ${q}_{2}$) and two classical bits (represented by the / sign on the c wire). In addition, there are two Hadamard gates and two CNOT gates. Finally, measurements are made on the classical channels. Each dashed vertical line represents a barrier (B1, B2, and B3) to split some circuit parts for sequential order of operation.

**Figure 9.**Quantum computing journey from two fields of science: information science and quantum physics.

**Figure 10.**Query search used in Scopus database to generate data of the publications on the topics, quantum sensing, quantum communication, and quantum computing from 1996 to 2020.

**Figure 11.**Quantum information science progress report. This graph shows the progression of the number of published documents in the areas of quantum sensing and metrology, quantum computing and algorithms, and quantum communications, respectively. It dates from 1995 through 2020.

**Figure 12.**Quantum artificial intelligence is a superset of quantum machine learning and quantum deep learning.

Quantum Algorithms | |
---|---|

Quantum Fourier transform | Amplitude amplification |

Simon’s algorithm | Grover’s algorithm |

Shor’s algorithm | Quantum counting |

**Table 2.**Each quantum computing tool’s programming language, computing paradigm, and description are mentioned in the table.

Tool | Programming Language | Quantum Computing Paradigm | Framework Description |
---|---|---|---|

Cirq | Python | Discrete gate model | A library for creating, manipulating, and optimizing Noisy Intermediate Scale Quantum (NISQ) circuits, which can then be executed on quantum computers and simulators. |

dwave-system | Python | Quantum annealing | An API for using the D-Wave system as a sampler in the D-Wave Ocean software stack, either directly or via Leap’s cloud-based hybrid solvers. |

FermiLib | Python | Discrete gate model | An open-source software suite that makes it easier to create and test algorithms for quantum computer simulations of fermionic systems. |

Qbsolv | C | Quantum annealing | A deconstructing solver that splits a huge quadratic unconstrained binary optimization (QUBO) problem into pieces to obtain a minimal value. |

QGL.jl | Julia | Discrete gate model | A QGL compiler with a focus on performance. |

Qiskit.js | JavaScript | Discrete gate model | Quantum Information Science Kit for JavaScript. |

Qrack | C++ | Discrete gate model | A complete framework for constructing universal virtual quantum processors that is GPU accelerated. |

Quirk | JavaScript | Discrete gate model | A browser-based quantum circuit simulator with drag-and-drop functionality. A toy for experimenting with and learning about small quantum circuits. |

Strawberry Fields | Python | Continuous gate model | A Python library for developing, optimizing, and implementing photonic quantum computers. |

**Table 3.**A comparison of three qubit technologies: trapped ion, superconducting, and photonic qubits is shown in the table based on their operations and fundamental properties.

Trapped Ion Qubit | Superconducting Qubit | Photonic Qubit |
---|---|---|

To produce qubits, lasers are used to ionize atoms and trap them in electric potentials. The status of the qubits is then measured using an extra laser. | The qubits are created by combining a superconducting resonator with a nonlinear inductor to make an artificial atom. | The squeezed state (light working as qubit) is created by distributing laser light to an array of squeezers (microscopic devices comprised of relatively small ring resonators). |

Stable qubits can be generated using trapped ion technology, and forming an entangled state is simple. Working with large numbers of qubits in this system is challenging, and implementing a whole quantum algorithm is even more complicated. Decoherence is a difficult problem to solve. | Building and accurately measuring qubits with superconducting technology is simple. These qubits have a nanosecond time scale and a quick decoherence time. Qubits must be cooled to near absolute zero to function, and computation is subject to quantum noise. | Qubits are far more stable in photonic technology and can readily entangle a huge number of photons. It is possible to perform computation at room temperature, but it is less fault-tolerant, and error correction is harder. According to this technique, quantum supremacy is attained. |

Year | Activity | Reference |
---|---|---|

1935 | EPR Paradox | [34] |

1964 | Bell’s Inequality | [35] |

1982 | Quantum Computer envisaged by Richard Feynman | [36] |

1993 | Quantum Teleportation proposed | [37] |

1994 | Shor’s Factoring Algorithm | [38] |

2001 | Experimental factorization of 15 by IBM | [39] |

2014 | Data transfer by Quantum Teleportation | [40] |

2020 | Quantum Advantage: Jiuzhang | [41] |

2021 | Quantum communication over optical fibers over 600 km in length | [42] |

2021 | 127 Qubits Milestone: IBM | [43] |

**Table 5.**A collection of further reading resources encompassing subfields, such as quantum machine learning, quantum algorithms, and quantum ethics, is provided below.

Interesting Reads | Reference |
---|---|

Quantum Learning and Optimization | [56,57,58,59] |

Quantum Machine Learning | [19,32,33,44,54,60] |

Quantum Fault Tolerance and Error Correction | [61,62,63,64,65] |

Quantum System Simulation | [21,25,66,67,68,69] |

Quantum Algorithm Designs | [70,71,72,73,74,75] |

Quantum Hardware Test Development | [76,77,78,79,80] |

Quantum Cryptography | [81,82,83,84,85,86,87] |

Hybrid (Quantum–Classical) Computing | [54,55,88,89,90] |

Ethical Quantum Computing | [91,92,93] |

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**MDPI and ACS Style**

Ayoade, O.; Rivas, P.; Orduz, J.
Artificial Intelligence Computing at the Quantum Level. *Data* **2022**, *7*, 28.
https://doi.org/10.3390/data7030028

**AMA Style**

Ayoade O, Rivas P, Orduz J.
Artificial Intelligence Computing at the Quantum Level. *Data*. 2022; 7(3):28.
https://doi.org/10.3390/data7030028

**Chicago/Turabian Style**

Ayoade, Olawale, Pablo Rivas, and Javier Orduz.
2022. "Artificial Intelligence Computing at the Quantum Level" *Data* 7, no. 3: 28.
https://doi.org/10.3390/data7030028