Quantum Information & Computation
Volume 25, Issue 4
RESEARCH ARTICLE Open access

A Resource-Efficient 4-Qubit Circuit for Bit-Flip Error Correction Using Feynman Gates

Dimitrios Gryllakis, Kyriakos N. Sgarbas

Author affiliations
  1. Electrical and Computer Engineering Department, University of Patras, Patras, Greece; AI-Hub, University of Patras, Patras, Greece

pp. 344-355 · 10.2478/qic-2025-0019

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Abstract

Quantum systems are inherently prone to errors caused by decoherence, noise, and imperfect gate operations. Effective error correction is essential to preserving quantum information, especially under hardware constraints. In this paper, we present a resource-efficient 4-qubit quantum circuit designed to detect and correct single-qubit bit-flip errors within a 3-qubit data block. The circuit uses Feynman (CNOT) and NOT gates alongside an ancillary qubit to implement full correction logic with minimal overhead. Compared to well-known approaches like the 9-qubit Shor code, our design achieves equivalent fidelity (100%) using fewer qubits, making it highly suitable for near-term quantum devices. Simulation results, obtained using IBM Quantum Composer and Qiskit, confirm the circuit’s correctness and reliability across all bit-flip scenarios. The design also introduces a reusable unitary block for efficient implementation. This work offers a scalable and practical solution to quantum error correction using minimal hardware resources.
Open accessCC BY-NC-ND 4.0

Keywords

  • ancilla qubit
  • controlled-NOT gate
  • quantum error detection
  • quantum fault tolerance
  • bit-flip error
  • quantum circuit design

Suggested citation

Dimitrios Gryllakis, Kyriakos N. Sgarbas (2025). A Resource-Efficient 4-Qubit Circuit for Bit-Flip Error Correction Using Feynman Gates. Quantum Information & Computation, 25(4), 344-355. https://doi.org/10.2478/qic-2025-0019

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