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Fault-tolerant quantum error detection
N. M. Linke, M. Gutierrez, K. A. Landsman, C. Figgatt, S. Debnath, K. R. Brown, C. Monroe
TL;DR
The paper analyzes error rates in a quantum-computing experiment using an error model with artificially introduced stochastic errors. Under perfect gates, preparation, and measurement, both logical qubits have the same modeled error rate, while the resulting rates are 0.50%, 1.0%, and 1.4%.
Problem
The analysis addresses how logical-qubit error rates behave under a model of artificially introduced stochastic errors.
Method
The experiment uses a quantum computer with Raman-beam control and evaluates accepted experimental and simulated circuits under an artificial stochastic-error model.
Results
0.50%, 1.0%, and 1.4% are the resulting error-rate values obtained from accepted experimental and simulated circuits.
Takeaways & Limitations
Under perfect gates, preparation, and measurement, both logical qubits have the same error rate under the model.
Takeaways & Limitations
Some subsets are not sampled and their logical error rates are set to zero because their statistical importance is significant only at very high added error rates.
Abstract
from arXiv · showhide
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.
Materials and Methods
The experiment uses five trapped 171Yb+ ions to encode, manipulate, measure, and test a logical qubit with fault-tolerant error detection. It combines laser-controlled single- and two-qubit operations with error modeling and deliberately added Pauli errors.
- Experimental system: Five trapped 171Yb+ ions provide the physical-qubit platform, with optical pumping initialization and state-dependent fluorescence readout.Each ion supplies one physical qubit; single-ion detection reaches 99.4(1)% average fidelity.
- Qubit control: Single-qubit gates use resonant Rabi rotations, while two-qubit XX-gates create effective spin-spin interactions through transient motion-mediated entanglement.Pulse shaping leaves the motion disentangled from the qubit states at the end of the interaction.
- Artificial stochastic errors: The experiment prepares logical |00⟩L states, applies selected Pauli errors, measures the Sz stabilizer, and repeats the procedure across error configurations.Each X, Y, or Z error occurs with probability p/3 on a physical qubit.
- Error sampling: Error configurations are exhaustively covered at weights 0 and 1, 27 of 54 weight-2 configurations are sampled and reweighted, while weights 3 and 4 are omitted.The omission is justified in the stated model because their statistical importance is significant only at very high added error rates.
- Model comparison: In the limit of perfect gates, preparation, and measurement, the two logical qubits have the same error rate under the model.The physical error curve uses readout error r = 0.003 and spin-flip success probability Fx = 0.997.