Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks

Abstract

We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes, and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and present protocols for realizing topologically protected Clifford gates. These hexagonal cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome readout and logical $T$-gates via magic state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but could also be realized in alternative settings such as quantum Hall-superconductor hybrids.

24 pages, 24 figures

References in corpus (27)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Charge insensitive qubit design derived from the Cooper pair box
• Surface codes: Towards practical large-scale quantum computation
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Introduction to topological superconductivity and Majorana fermions
• Topological Quantum Distillation
• Roads towards fault-tolerant universal quantum computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Magic state distillation with low overhead
• Measurement-Only Topological Quantum Computation
• Majorana box qubits
• Topological Kondo effect with Majorana fermions
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Universal transversal gates with color codes - a simplified approach
• Roadmap to Majorana surface codes
• Transport signatures of quasiparticle poisoning in a Majorana island
• Fault-tolerant logical gates in quantum error-correcting codes
• Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes
• Quantum computing by color-code lattice surgery
• Quantum Error Correction for Complex and Majorana Fermion Qubits
• Fast readout of a single Cooper-pair box using its quantum capacitance
• Extensible 3D architecture for superconducting quantum computing
• Small Majorana Fermion Codes

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• Weak measurement protocols for Majorana bound state identification
• Quasi-one-dimensional Quantum Anomalous Hall Systems as New Platforms for Scalable Topological Quantum Computation
• Neural network decoder for topological color codes with circuit level noise
• Anyon condensation and the color code
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Hybridization of sub-gap states in one-dimensional superconductor/semiconductor Coulomb islands
• Braiding by Majorana Tracking and Long-Range CNOT Gates with Color Codes
• Parity-to-charge conversion in Majorana qubit readout
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• Topological Quantum Computing Using Nanowire Devices
• Driven Dissipative Majorana Dark Spaces
• Observation of 2e-periodic Supercurrents in Nanowire Single-Cooper-Pair Transistors
• Building topological quantum circuits: Majorana nanowire junctions
• Towards dark space stabilization and manipulation in driven dissipative Majorana platforms
• Evidence of Majorana Zero Modes in Josephson Trijunctions
• Modeling noise and error correction for Majorana-based quantum computing
• Magnetotransport signatures of three-dimensional topological insulator nanostructures
• Control and detection of Majorana bound states in quantum dot arrays
• Absence of supercurrent sign reversal in a topological junction with a quantum dot
• Parafermionic generalization of the topological Kondo effect
• Simulating topological tensor networks with Majorana qubits
• Fault-tolerant fermionic quantum computation based on color code
• Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates
• Fidelity and visibility reduction in Majorana qubits by entanglement with environmental modes
• Observation of Gapped Topological Surface States and Isolated Surface Resonances in PdTe${}_2$ Ultrathin Films
• Localization and oscillations of Majorana fermions in a two-dimensional electron gas coupled with $d$-wave superconductors
• Scalable Fermionic Error Correction in Majorana Surface Codes
• Quantum phase transitions of the Majorana toric code in the presence of finite Cooper-pair tunneling
• Non-Abelian defects in Fracton phase of matter
• Dispersive sensing in hybrid InAs/Al nanowires
• Subradiant edge states in an atom chain with waveguide-mediated hopping
• Quantum transport in coupled Majorana box systems
• Multi-level effects in quantum-dot based parity-to-charge conversion of Majorana box qubits
• Long distance coherence of Majorana wires
• Topological Phases in Nodeless Tetragonal Superconductors
• Exfoliated hexagonal BN as gate dielectric for InSb nanowire quantum dots with improved gate hysteresis and charge noise
• Topological ordering in the Majorana Toric Code
• Simulating spin systems with Majorana networks
• Charge response of the Majorana toric code
• The domain wall color code
• 1D Error Correcting Code for Majorana Qubits
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Quantum-vacuum-protected topological edge polaritons
• Lattice Surgery Compilation Beyond the Surface Code
• Pinned QMA: The power of fixing a few qubits in proofs
• Parity readout in Majorana box qubits from the dispersive to the resonant regime
• Monte Carlo studies of modified scalable designs for quantum computation