Schematic representation method for quantum circuits: an intuitive approach to quantum gate effects

AKKOYUN S.

Physics Education, cilt.61, sa.4, 2026 (Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 61 Sayı: 4
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1088/1361-6552/ae778f
  • Dergi Adı: Physics Education
  • Derginin Tarandığı İndeksler: Scopus, Aerospace Database, Agricultural & Environmental Science Database, EBSCO Education Source, Educational research abstracts (ERA), INSPEC, DIALNET, Academic Search Ultimate (EBSCO), Social Science Premium Collection (ProQuest), Education Collection (ProQuest), Education Source Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
  • Anahtar Kelimeler: quantum algorithm, quantum circuits, quantum computing, quantum gates
  • Sivas Cumhuriyet Üniversitesi Adresli: Evet

Özet

In quantum circuits, qubits and the quantum gates acting on them have traditionally been analysed using matrix algebra and Dirac notation. While powerful, these can be unintuitive for conceptual understanding and rapid problem solving. In this work, a new schematic representation method is developed that visualizes the effects of quantum gates on qubits without relying on complex mathematical operations. In the new notation, quantum bits (qubits) are represented using black (|0〉) and white (|1〉) circles. When a quantum gate is applied to a qubit, the circle representing the qubit is visually modified. For example, a Hadamard gate transforms a solid black or white circle into a half-black and half-white circle representing superposition. The work shows how this method simplifies the visualization of quantum algorithms, entanglement, and multi- qubit operations. The work proposes how this method can act as a visual aid to support the understanding of quantum algorithms, entanglement, and multi-qubit operations. Thus, the initial conceptual analysis of basic quantum circuits can be facilitated by simple schematic representations, reducing the immediate cognitive load of complex mathematical operations for beginners.