A symbolic model of the quantum Grover search algorithm for the simplest two-qubit systems is proposed, which simultaneously utilizes the capabilities of the Maple computer mathematics system and the Quirk quantum browser simulator. The model is developed with a focus on its application in engineering education for modern quantum computing courses. It enables generalization to systems with more qubits, as well as cases involving multiple target states. It can serve as a foundation for developing laboratory work. This model is among the first attempts to go beyond the limitations of Python-based quantum simulators. Maple, whose programming language is based on Java, interacts effectively with the Quirk quantum simulator, which is based on JavaScript. Keywords: Grover's quantum algorithm, Maple, Quirk, simulation of quantum algorithms, symbolic modeling.
A symbolic model of the quantum Grover search algorithm for the simplest two-qubit systems is proposed, which simultaneously utilizes the capabilities of the Maple computer mathematics system and the Quirk quantum browser simulator. The model is developed with a focus on its application in engineering education for modern quantum computing courses. It enables generalization to systems with more qubits, as well as cases involving multiple target states. It can serve as a foundation for developing laboratory work. This model is among the first attempts to go beyond the limitations of Python-based quantum simulators. Maple, whose programming language is based on Java, interacts effectively with the Quirk quantum simulator, which is based on JavaScript. Keywords: Grover's quantum algorithm, Maple, Quirk, simulation of quantum algorithms, symbolic modeling.
In this work we study Grover's algorithm for quantum computers. This algorithm promises to search in an unstructured database in time comparable with a square root of the number of objects. A description of basic quantum computer principles is followed by the original Grover's formulation and a proof of the algorithm, as well as a later geometrical description of the algorithm. We also mention their suitability for educational purposes. We also include a description of the Grover's algorithm in a programming language, which makes it possible to simulate a quantum computing on classical computers.
A general quantum simulation language on a classical computer provides the opportunity to compare an experiential result from the development of quantum computers with mathematical theory. The intention of this research is to develop a program language that is able to make simulations of all quantum algorithms in same framework. This study examines the simulation of quantum algorithms on a classical computer with a symbolic programming language. We use the language Mathematica to make simulations of well-known quantum algorithms. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational methods. This gives us an uncomplicated and clear language for the implementations of algorithms. The computational language includes essential formulations such as quantum state, superposition and quantum operator. This symbolic programming language provides a universal framework for examining the existing as well as future quantum algorithms. This study contributes with an implementation of a quantum algorithm in a program code where the substance is applicable in other simulations of quantum algorithms.
Quantum computing represents the leading edge of computational technology, leveraging the principles of quantum mechanics to execute targeted computations much faster than classical computers. In contrast to classical bits, which are limited to representing either 0 or 1, qubits, or quantum bits, exhibit the extraordinary property of superposition. This distinctive characteristic enables qubits to simultaneously occupy multiple states, empowering quantum computers to explore numerous potential solutions to a problem concurrently. This feature makes quantum computing particularly potent for specific tasks. Recent research endeavors have been sparked by the potential of advanced quantum computing technology, leading to the creation of simulations of quantum computers using classical hardware. Grover's quantum search algorithm serves as a notable illustration of quantum computing application, enabling quantum computers to conduct a database search within an unsorted array with a quadratic speedup in time efficiency compared to classical computers. This document presents the quantum Grover search algorithm and its application through 5-qubit quantum circuits, as well as a design framework to simplify the creation of an oracle for a greater number of qubits.
Understanding the high-level conceptual structure of quantum algorithms from their low-level circuit representations is a critical task for verification, debugging, and education. While traditional numerical simulators can calculate output probabilities, they do not explicitly surface the underlying algorithmic logic, such as the function of an oracle or embedded symmetries. In this work, we shift the focus from numerical simulation to symbolic analysis , investigating whether large language models (LLMs) can automatically interpret quantum circuits and articulate their logic in a human-readable format. We introduce GroverGPT+, a model that leverages Chain-of-Thought reasoning and quantum-native tokenization to analyze Grover’s search algorithm. We use Grover’s algorithm as a controlled testbed, as its well-defined analytical properties allow for rigorous verification of the model’s reasoning process. Our primary finding is that GroverGPT+ successfully identifies the oracle and its marked states directly from circuit representations. The model’s key output is not a final probability, but a structured, interpretable reasoning trace that mirrors human expert analysis, effectively translating procedural circuit steps into conceptual insights. Furthermore, we establish a structured benchmark for this symbolic analysis task and explore its empirical extrapolation, describing the model’s performance as the number of qubits increases. These findings position LLMs as powerful tools for automated quantum algorithm analysis and verification. More fundamentally, this work offers a first step towards using such models as scientific probes, suggesting that an algorithm’s “learnability" by a classical model can provide a new, complementary perspective on its conceptual complexity, a topic of core interest to quantum information science.
Early researchers attempting to simulate complex quantum mechanical interactions on digital computers discovered that they very quickly consumed the computers’ available memory\nresources, because the state space of a quantum system typically grows exponentially with problem size. Consequently, Richard Feynman proposed in 1982 that perhaps the only way to simulate complex quantum mechanical situations was by simulating them on some quantum mechanical system. Quantum computers attempt to exploit this idea incorporating the special properties of quantum mechanics, such as the superposition of states and entanglement, into a computing device. Two key algorithms have been discovered which would run on this new type of computer, Shor’s factorization algorithm discovered in 1994, which provides an exponential speedup over classical algorithms and Grover’s search algorithm in 1996, which provides a quadratic speedup. Following this in 1999 Meyer initiated the field of quantum game theory by introducing quantum mechanical states into the framework of classical game theory. In this thesis, we firstly investigate the phase estimation procedure, due to its importance as the basis for Shor’s factorization algorithm, for which a new error formula is found using an improved symmetrical definition of the error. Unlike other existing error formulas which require approximations in their derivation, our result is obtained analytically. The work on the phase estimation procedure then motivates the development of computer software written in the Java programming language, which can simulate the common algorithms and visually display their behavior on a circuit board type layout. The software is found useful in verifying the new error formula described above and to test ideas for new algorithms. Being written in Java, it is envisaged that it could be placed online and used as a learning tool for new students to the field. We then investigate the second key algorithm of quantum computing, the Grover search algorithm. It is already known that the Grover search is an SU(2) rotation but the idea is extended by deriving the three generators in terms of the two non-orthogonal basis vectors, representing the solution and initial states. We then demonstrate that the Grover search is equivalent to the precession of the polarization axis of a spin- 1/2 particle in a magnetic field. At this point we introduce geometric algebra (GA), because of its efficient implementation of rotations and its associated visual representation, and hence ideal to describe the Grover search process. It was found to provide a simple algebraic solution to the exact Grover search problem as well providing a simple visual picture describing the general solution to Meyer’s quantum penny flip game, which is a simple two-player quantum game based on the manipulation of a single qubit and hence closely analogous to the Grover search process. We then extend the work on quantum games developing two-player, three-player and N player quantum games in the context of an EPR type experiment, which has the advantage of providing a sound physical basis to quantum games avoiding the common criticism of other quantum game frameworks regarding the proper embedding of the classical game. Using the algebraic approach of GA, we solve the general N player game, without requiring the use of matrices which become unworkable for large N. Games based on non-factorisable joint probabilities were then also developed which provided a more general framework for both classical and quantum games, and allows the field of quantum games to be accessible to nonphysicists, as it does not employ Dirac’s bra-ket notation. In summary, several new results in the field of Quantum computing were produced, including an improved error formula for phase estimation [JMCL11b], a general solution to Meyer’s quantum penny flip game [CILVS09] and a paper producing quantum games from non-factorisable joint probabilities [CIA10], as well as an EPR framework for quantum games [JMCL11a], refer attached papers.
The development of programming languages for quantum computing has increased rapidly over the last few years, making it practical for a hands-on approach in teaching quantum computation. In this paper, I introduce the standard textbook example of searching for one item out of four using Grover's search algorithm and extend it by including a quantum database. In addition to explaining how to include a quantum database using a quantum circuit model, I give a complete program implementing the algorithm written in the quantum computing language Qiskit from IBM. If presented in the classroom, this extension of Grover's search algorithm alleviates some unsatisfying aspects of the standard textbook example. If given as an exercise to students, it allows them to extend the standard example and provides experience in developing quantum algorithms. I also outline searching for one (or more) items out of eight with a quantum database, which could be used for student projects.