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.
Highlights
Physical realizations of large-scale quantum computers remain a paramount experimental challenge because of the unavoidable presence of environmental decoherence
Having discussed the implementation of the operations required of topological superconductor networks, we investigate error sources of Majorana Cooper pair boxes and how well they can be corrected by diamond color codes
We have devised a scalable architecture for universal fault-tolerant topological quantum computation, which can be realized with voltagecontrolled Majorana Cooper pair boxes as basic building blocks
Summary
Physical realizations of large-scale quantum computers remain a paramount experimental challenge because of the unavoidable presence of environmental decoherence. We show how parity measurements in topological superconductor networks can be used for fast multitarget CNOT gates, replacing multiple CNOT gates by a protocol that is as fast as a single CNOT Another advantage of Majorana-based qubits is ancillafree syndrome read-out. We demonstrate that networks of Majorana Cooper pair boxes are capable of performing the aforementioned required operations These can be implemented using proximitized semiconductor nanowires, on which recent experiments have focused, but possibly in other platforms such as hybrid structures based on quantum Hall, quantum spin Hall, or quantum anomalous Hall edge states. This article is by no means a review, but it is meant to lay the groundwork for color-code quantum computing with Majoranas in order to fully exploit the topological protection of Majoranabased qubits
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