SciPost Physics

SciPost Phys. 16, 033 (2024) · published 26 January 2024

• doi: 10.21468/SciPostPhys.16.1.033
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Abstract

Utilizing the framework of $\mathbb{Z}_2$ lattice gauge theories in the context of Pauli stabilizer codes, we present methodologies for simulating fermions via qubit systems on a two-dimensional square lattice. We investigate the symplectic automorphisms of the Pauli module over the Laurent polynomial ring. This enables us to systematically increase the code distances of stabilizer codes while fixing the rate between encoded logical fermions and physical qubits. We identify a family of stabilizer codes suitable for fermion simulation, achieving code distances of d=2,3,4,5,6,7, allowing correction of any $\lfloor \frac{d-1}{2} \rfloor$-qubit error. In contrast to the traditional code concatenation approach, our method can increase the code distances without decreasing the (fermionic) code rate. In particular, we explicitly show all stabilizers and logical operators for codes with code distances of d=3,4,5. We provide syndromes for all Pauli errors and invent a syndrome-matching algorithm to compute code distances numerically.

• IV et al., Low-weight high-distance error-correcting fermionic encodings
  Phys. Rev. Research 6, 043123 (2024) [Crossref]
• Di Meglio et al., Quantum Computing for High-Energy Physics: State of the Art and Challenges
  PRX Quantum 5, 037001 (2024) [Crossref]
• Liang et al., Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions
  PRX Quantum 5, 030328 (2024) [Crossref]
• Carena et al., Quantum error thresholds for gauge-redundant digitizations of lattice field theories
  Phys. Rev. D 110, 054516 (2024) [Crossref]