Quantum Computing with Majorana Fermion Codes

Abstract

We establish a unified framework for Majorana-based fault-tolerant quantum computation with Majorana surface codes and Majorana color codes. All logical Clifford gates are implemented with zero time overhead. This is done by introducing a protocol for Pauli product measurements with tetrons and hexons which only requires local 4-Majorana parity measurements. An analogous protocol is used in the fault-tolerant setting, where tetrons and hexons are replaced by Majorana surface code patches, and parity measurements are replaced by lattice surgery, still only requiring local few-Majorana parity measurements. To this end, we discuss twist defects in Majorana fermion surface codes and adapt the technique of twist-based lattice surgery to fermionic codes. Moreover, we propose a new family of codes that we refer to as Majorana color codes, which are obtained by concatenating Majorana surface codes with small Majorana fermion codes. Majorana surface and color codes can be used to decrease the space overhead and stabilizer weight compared to their bosonic counterparts.

Main text: 17 pages, 15 figures; Appendix: 11 pages, 16 figures

References in corpus (13)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Topological Quantum Distillation
• Quantized Majorana conductance
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Majorana box qubits
• Roadmap to Majorana surface codes
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Fault-tolerant logical gates in quantum error-correcting codes
• A magic state's fidelity can be superior to the operations that created it
• Dephasing of Majorana-based qubits
• Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes

Cited by in corpus (53)

• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer
• Signature of a pair of Majorana zero modes in superconducting gold surface states
• Majorana nanowires for topological quantum computation
• Hunting for Majoranas
• Entanglement spectroscopy of non-Abelian anyons: Reading off quantum dimensions of individual anyons
• Readout of Majorana Qubits
• Higher order topological superconductors as generators of quantum codes
• Performance of planar Floquet codes with Majorana-based qubits
• Time-induced second-order topological superconductors
• Foliated fracton order in the Majorana checkerboard model
• Equivalence between fermion-to-qubit mappings in two spatial dimensions
• A decoder for the triangular color code by matching on a Möbius strip
• Modeling noise and error correction for Majorana-based quantum computing
• Error generation and propagation in Majorana-based topological qubits
• $Z_4$ parafermion $\pm \pi /2$ modes in interacting periodically driven superconducting chain
• Majorana-Josephson Interferometer
• Feasibility of measurement-based braiding in the quasi-Majorana regime of semiconductor-superconductor heterostructures
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Optimizing Clifford gate generation for measurement-only topological quantum computation with Majorana zero modes
• Fidelity and visibility reduction in Majorana qubits by entanglement with environmental modes
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
• Non-Abelian statistics with mixed-boundary punctures on the toric code
• Characterizing Dynamic Majorana Hybridization for Universal Quantum Computing
• Quantum transport in coupled Majorana box systems
• Comparison of 2D topological codes and their decoding performances
• Encoding Majorana codes
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Long distance coherence of Majorana wires
• Topological ordering in the Majorana Toric Code
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Altermagnet-Superconductor Heterostructure: a Scalable Platform for Braiding of Majorana Modes
• Inverse Hamiltonian design of highly-entangled quantum systems
• Effective Potential for Emergent Majorana Fermions in Superconductor Systems
• Color codes with twists: construction and universal gate set implementation
• Investigating the Exchange of Ising Chains on a Digital Quantum Computer
• Dynamics of quantum resources in regular and Majorana fermion systems
• Quantum computation with charge-and-color permuting twists in qudit color codes
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• 1D Error Correcting Code for Majorana Qubits
• Majorana braiding simulations with projective measurements
• Edge Modes and Teleportation in a Topologically Insulating Quantum Wire
• Spin chains, defects, and quantum wires for the quantum-double edge
• Quantum-vacuum-protected topological edge polaritons
• Zero and Nonzero Energy Majorana Modes in an Extended Kitaev Chain
• Many-body wave function and edge magnetization of an open $p+is$ superconducting chain
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance
• Parity readout in Majorana box qubits from the dispersive to the resonant regime
• Interfacing a topological qubit with a spin qubit in a hybrid quantum system
• Partons from stabilizer codes
• Monte Carlo studies of modified scalable designs for quantum computation