Fault-tolerant fermionic quantum computation based on color code

2017/09/30 by Ying Li · 2 citations
Computer Science · Physics and Astronomy · #Computer science #Fermion #MAJORANA #Physics #Programming language #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum computer #Quantum error correction #Quantum information #Quantum mechanics #Qubit #Set (abstract data type) #Theoretical computer science #Topological Materials and Phenomena #Universal set #quant-ph

paper · pdf · doi:10.1103/physreva.98.012336

published as Phys. Rev. A 98, 012336 (2018) · 13 pages, 6 figures and 1 table; Version 2: References are updated

arxiv created 2017/11/03 · openalex publication_date 2018/07/31 · arxiv updated 2018/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

An important approach to fault-tolerant quantum computation is protecting logical information using quantum error correction. Usually, logical information is in the form of logical qubits, which are encoded in physical qubits using quantum error correction codes. Compared with qubit quantum computation, fermionic quantum computation has advantages in quantum simulations of fermionic systems, e.g., molecules. In this paper, we show that fermionic quantum computation can be universal and fault tolerant if we encode logical Majorana fermions in physical Majorana fermions. We take a color code as an example to demonstrate the universal set of fault-tolerant operations on logical Majorana fermions, and we numerically find that the fault-tolerance threshold is about 0.8%.

Citations

• Fault-tolerant quantum computing with color codes
• Quantum computing by color-code lattice surgery
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana qubit decoherence by quasiparticle poisoning
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Topological quantum memory
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Quantum algorithms for fermionic simulations
• Non-Abelian anyons and topological quantum computation
• Quantum Error Correction for Complex and Majorana Fermion Qubits
• Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping
• Quantum Computation and Quantum Information

Cited by

• Bandgap-assisted quantum control of topological edge states in a cavity
• Modeling noise and error correction for Majorana-based quantum computing