Abstract Quantum computers operate in a manner so different from classical computers that our intuition for understanding the process of quantum computation is challenged. This not only makes it hard to develop new quantum algorithms, but also makes quantum computation a difficult subject for students. Here, we show that the time evolution of a particle on a ring with a coil through it performs the key quantum algorithm known as quantum phase estimation. The example uses the Aharonov–Bohm effect, and the aim is to help students build a physical intuition for quantum algorithms.
Abstract Quantum computers operate in a manner so different from classical computers that our intuition for understanding the process of quantum computation is challenged. This not only makes it hard to develop new quantum algorithms, but also makes quantum computation a difficult subject for students. Here, we show that the time evolution of a particle on a ring with a coil through it performs the key quantum algorithm known as quantum phase estimation. The example uses the Aharonov–Bohm effect, and the aim is to help students build a physical intuition for quantum algorithms.
We consider the time evolution of a particle on a ring with a long solenoid through and show that due to the Aharonov-Bohm effect this system naturally makes up a physical implementation of the quantum phase estimation algorithm for a U(1) unitary operator. The implementation of the full quantum phase estimation algorithm with a U(N) unitary operator is realized through the non-Abelian Aharonov-Bohm effect. The implementation allows for a more physically intuitive understanding of the algorithm. As an example we use the path integral formulation of the implemented quantum phase estimation algorithm to analyze the classical limit $\ensuremath{\hbar}\ensuremath{\rightarrow}0$.
This work reports an effort to introduce a few advanced concepts in quantum physics to undergraduate students who have only a minimal familiarity with wave mechanics. The geometric phase is not introduced in most introductory courses on quantum mechanics. It is of pivotal significance for the understanding of topological phase transitions which are becoming increasingly important in a large number of physical phenomena, including those that involve platforms for robust quantum computing. This article would provide a gentle introduction to the geometric phase. Toward this goal, Feynman’s path integral approach to quantum mechanics and its application in the interpretation of the wondrous Aharonov–Bohm effect is introduced in a gentle manner. A computer simulation of this interesting phenomenology is presented to help gain an early insight into some advanced concepts.
This technical note gives a self-contained exposition of the Aharonov–Bohm effect, aimed at advanced undergraduate students. Starting from the role of electromagnetic potentials in classical electrodynamics, it introduces gauge freedom, the quantum Hamiltonian with minimal coupling, and the gauge covariance of the Schrödinger equation. It then derives the Aharonov–Bohm phase for both the time-dependent scalar configuration and the magnetic configuration, showing how a charged particle acquires an observable phase shift while travelling only through regions where the electromagnetic field vanishes. The final part reviews the experimental evidence, from the early electron-interference experiments of Chambers and of Möllenstedt and Bayh to the 1986 toroidal-magnet experiment of Tonomura and collaborators. In that experiment, superconducting shielding confined the magnetic flux completely and closed the leakage-field loophole, while flux quantization produced the characteristic half-fringe shift. The note is expository and pedagogical: it does not present original research results and has not been peer reviewed. Originally developed from study notes prepared for the PHYS02 scientific talk at Lady Margaret Hall, Oxford, in July 2026; an earlier version of the notes has been publicly available on GitHub since August 2026. Corrections and comments are more than welcome at giancarminesparso@gmail.com.
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates and make quantum algorithms fundamentally different from their classical counterparts. Based on this unique principle of quantum computing, we develop an algorithmic toolbox, quantum phase processing, that can directly apply arbitrary trigonometric transformations to eigenphases of a unitary operator. The quantum phase processing circuit is constructed simply, consisting of single-qubit rotations and controlled unitaries, typically using only one ancilla qubit. Besides the capability of phase transformation, quantum phase processing in particular can extract the eigeninformation of quantum systems by simply measuring the ancilla qubit, making it naturally compatible with indirect measurement. Quantum phase processing complements another powerful framework known as quantum singular value transformation and leads to more intuitive and efficient quantum algorithms for solving problems that are particularly phase related. As a notable application, we propose a quantum phase estimation algorithm without quantum Fourier transform, which requires the fewest ancilla qubits and matches the best performance so far. We further exploit the power of our method by investigating a plethora of applications in Hamiltonian simulation, entanglement spectroscopy, and quantum entropy estimation, demonstrating improvements or optimality for almost all cases.
Quantum phenomena have become directly observable with the development of advanced techniques such as coherent field-emission electron beams, sensitive detectors, and microlithography. Examples are the single-electron build-up of an interference pattern, which contains, as R. Feynman describes in his textbook, the heart of quantum mechanics, and the Aharonov–Bohm (AB) effect, which indicates the physical significance of gauge fields. Using the AB effect, i.e., the fundamental principle behind the interaction of an electron wave with electromagnetic fields, new ways to directly observe previously unobservable microscopic quantum objects and phenomena were developed by detecting the phase of electrons.
Quantum computing poses unique challenges for computer science students due to the field's reliance on mathematical formalism, abstract physical concepts, and unfamiliar notation. While computer science students are typically proficient in algorithmic thinking and systems design, they often lack the background in quantum mechanics and linear algebra necessary to navigate the field's conceptual landscape. This mismatch can result in a form of disciplinary dissonance, a ‘Quantum Babel', where understanding breaks down due to divergent cognitive and notational frameworks. This paper proposes a layered, analogy-driven pedagogical framework that re-contextualizes quantum concepts using metaphors and structures familiar to CS learners. Grounded in cognitive load theory and analogical reasoning, the approach aims to reduce extraneous cognitive load through metaphorical scaffolding. For example, the quantum Hamiltonian is recast as an operating system task scheduler, facilitating intuitive understanding of time evolution and energy landscapes in quantum systems. We present a series of conceptual mappings and illustrative examples that enable learners to build quantum intuition using analogies drawn from classical computing domains such as signal processing, debugging, and resource scheduling. Our goal is to foster quantum intuition in learners without requiring a deep background in physics, supporting the emergence of a new generation of quantum-literate computer scientists. This work contributes to the growing field of quantum software engineering education and lays the foundation for empirically validated, cross-disciplinary teaching tools.