Efficient Preparation of Decoherence Free Subspace Basis States

• URL: http://arxiv.org/abs/2509.11544v1
• Date: Mon, 15 Sep 2025 03:27:00 GMT
• Title: Efficient Preparation of Decoherence Free Subspace Basis States
• Authors: Zi-Ming Li, Yu-xi Liu,
• Abstract summary: Decoherence-free subspace (DFS) provides a crucial mechanism for passive error mitigation in quantum computation.<n>DFS encodes information within symmetry-protected subspaces of the Hilbert space, which are immune from collective decoherence.<n>We propose a deterministic approach to prepare pure, orthogonal and complete DFS basis states for systems of arbitrary size composed of qubits.
• Score: 7.687716562071607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Decoherence-free subspace (DFS) provides a crucial mechanism for passive error mitigation in quantum computation by encoding information within symmetry-protected subspaces of the Hilbert space, which are immune from collective decoherence. Constructing a complete set of orthogonal basis states for the DFS is essential to realize fault-tolerant quantum computation by using the DFS codes. However, existing methods for preparing these basis states are often non-scalable, platform-specific, or yield mixed states. Here, we propose a deterministic approach to prepare pure, orthogonal and complete DFS basis states for systems of arbitrary size composed of qubits. Our method employs projective measurements and quantum circuits with single-qubit, two-qubit and Toffoli gates. We provide a rigorous resource cost analysis both mathematically and numerically. Meanwhile, we demonstrate the realizability of our method on NISQ devices by discussing how to implement our method on a superconducting chip. The proposed method offers a universal solution for preparing the DFS basis states across diverse quantum computing platforms and system sizes, which is realizable in the NISQ era.

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