Fault-tolerant fermionic quantum computation based on color code

Abstract

An important approach to the fault-tolerant quantum computation is protecting the logical information using the quantum error correction. Usually, the logical information is in the form of logical qubits, which are encoded in physical qubits using quantum error correction codes. Compared with the qubit quantum computation, the fermionic quantum computation has advantages in quantum simulations of fermionic systems, e.g. molecules. In this paper, we show that the 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%.

13 pages, 6 figures and 1 table; Version 2: References are updated

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Cited by in corpus (13)

• Anyon condensation and the color code
• A decoder for the triangular color code by matching on a Möbius strip
• Bandgap-Assisted Quantum Control of Topological Edge States in a Cavity
• Modeling noise and error correction for Majorana-based quantum computing
• Quantum Operations in an Information Theory for Fermions
• Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Decoding quantum color codes with MaxSAT
• Topological Dynamical Decoupling
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• 1D Error Correcting Code for Majorana Qubits
• Quantum science with arrays of metastable helium-3 atoms
• Quantum operation of fermionic systems and process tomography using Majorana fermion gates