Applications Based on Symmetry in Quantum Computing

Dear Colleagues,

Quantum computing is rapidly advancing, with algorithms, hardware, and hybrid systems maturing. At the same time, symmetry principles (in-group theory, topology, gauge invariance, time-reversal, lattice symmetries, etc.) have proven potent in physics, cryptography, materials science, and error correction. The intersection of symmetry and quantum information is fertile for breakthroughs. For instance, exploiting symmetry to reduce circuit depth, leveraging topological symmetry for fault tolerance, applying permutation symmetry in quantum simulation, employing gauge symmetries to constrain noise models, or using temporal symmetries for resource scheduling in quantum architectures. Next‑generation computing and communications are expected to be quantum‑enabled. Over the coming decade, first‑generation quantum computers are anticipated to emerge, while the 6G landscape will explore integration of a quantum internet with classical networks. Quantum computing is very different from regular computing, as it uses special ideas like superposition, entanglement, and teleportation. It also follows the no-cloning rule, which means that quantum data cannot be perfectly copied. These features help quantum computers solve problems faster and keep information more secure. They also allow new ways to handle and process data. As a result, quantum computing could bring big changes to both science and industry.

Despite these advantages, quantum computers remain nascent. Qubits are fragile; noise, decoherence, and crosstalk impose tight limits on circuit depth, and quantum error correction (QEC) introduces substantial overheads. To move forward in quantum computing, we need improvements at every level. This includes creating better devices and materials, controlling noise more effectively, and building systems that can grow and scale. In parallel, application development must identify where near-term, error-mitigated processors deliver clear value and how quantum computing will interoperate with classical infrastructure. Within this landscape, symmetry provides a powerful organizing principle and a practical lever for performance. Exploiting invariances reduces effective Hilbert-space dimension, preserves physical constraints, and improves robustness to noise.

This Special Issue invites contributions from academia and industry on symmetry-driven innovations in quantum computing, including but not limited to the following:

• New opportunities/challenges/use cases for symmetric in quantum computing;
• Quantum machine learning and data-efficient, symmetry-constrained model design;
• Symmetry in quantum networking: entanglement routing, verification, and cryptography for 6G/quantum‑internet convergence;
• Benchmarking and verification protocols based on conserved charges, symmetries, and Noether‑inspired constraints;
• Symmetry‑guided control, pulse design, and Hamiltonian engineering for high‑fidelity gates;
• Symmetry-based quantum algorithms (e.g., exploiting group invariance for quantumspeed-ups, symmetric subspace methods);
• Topological symmetry and fault-tolerant quantum computing (e.g., anyonic systems, twisted symmetries, lattice symmetries in error-correction);
• Symmetry in variational quantum algorithms and quantum machine learning (e.g.,symmetry as inductive bias, permutation invariance, equivariant quantum circuits);
• Symmetry-aware quantum compilation and circuit optimization (e.g., using symmetry to reduce gate counts, symmetry-preserving mappings);
• Symmetry in quantum simulation (e.g., simulation of symmetric Hamiltonians, symmetric initial states, exploiting symmetry to reduce resources);
• Symmetry in hardware architecture of quantum computers (e.g., symmetric coupling networks, lattice symmetries in superconducting qubits, symmetric control pulses, mirror symmetry in photonic circuits);
• Symmetry and error mitigation/noise modelling (e.g., leveraging symmetry for error detection, symmetric noise channels, symmetry-protected subspaces in NISQ devices);
• Symmetry in quantum communication and networks (e.g., symmetric entanglement distribution, symmetric quantum repeaters, symmetry in quantum network topologies);
• Emerging directions: spatio-temporal symmetries in quantum networks, gauge symmetries in quantum software/hardware co-design, symmetry in hybrid quantum-classical frameworks, symmetry-based benchmarking and certification of quantum devices.

This Special Issue distinguishes itself from prior collections by focusing explicitly on symmetry applied in quantum computing rather than symmetry in classical domains (statistics, biology, networks) or purely theoretical quantum symmetry work. It cuts across hardware, algorithms, and application layers, thereby offering an integrative platform. In particular,

• It emphasizes real-world quantum computing scenarios (NISQ, fault-tolerance, hybrid systems) rather than purely abstract symmetry theory;
• It fosters cross-disciplinary synergy between symmetry mathematics/groups, quantum
  algorithmics and quantum hardware architecture;
• It highlights emerging trends (e.g., symmetry-aware variational circuits, symmetric
  coupling networks, symmetry-based error mitigation) that are under-represented in
  existing special issues.

Dr. Simeon Okechukwu Ajakwe
Dr. Esmot Ara Tuli
Dr. Golam Mohtasin
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• trends in quantum computing
• quantum machine learning
• quantum error correction
• quantum optimization
• quantum cryptography