Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation

Abstract

Majorana zero modes (MZMs) promise a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations (e.g., braids) pose significant challenges. We introduce fermion-parity-based computation (FPBC): a measurement-based scheme, modeled on Pauli-based computation, that uses efficient classical processing to virtually increase the number of available MZMs and which, given magic state inputs, operates without transformations. FPBC requires all MZM parities to be measurable, but this conflicts with constraints in proposed MZM hardware. We thus introduce a design in which all parities are directly measurable and which is hence well suited for FPBC. While developing FPBC, we identify the "logical braid group" as the fermionic analog of the Clifford group.

12 pages, 4 figures; v2: accepted manuscript

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Cited by in corpus (7)

• Non-Stabilizerness of Sachdev-Ye-Kitaev Model
• Encoding Majorana codes
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Dissipationless topological quantum computation for Majorana objects in sparse-dense mixed encoding process
• Certification of two-qubit quantum systems with temporal inequality
• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions