Fault-tolerant quantum error detection

Abstract

Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent detection or correction of errors without destroying the logical state itself through direct measurement. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. The advantage persists in the face of large added error rates and experimental calibration errors.

17 pages, 4 figures, 1 table, 5 physical qubits, 2 logical qubits, 1 of which is fault-tolerant

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• A local and scalable lattice renormalization method for ballistic quantum computation
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• Optimal local unitary encoding circuits for the surface code
• The role of entropy in topological quantum error correction
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• Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm
• Continuous quantum error correction for evolution under time-dependent Hamiltonians
• Efficient and robust certification of genuine multipartite entanglement in noisy quantum error correction circuits
• Protecting solid-state spins from strongly coupled environment
• Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
• Scalable characterization of localizable entanglement in noisy topological quantum codes
• A cellular automaton decoder for a noise-bias tailored color code
• Engineering topological states and quantum-inspired information processing using classical circuits
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• Performance of Quantum Approximate Optimization with Quantum Error Detection
• Alibaba Cloud Quantum Development Platform: Surface Code Simulations with Crosstalk
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