Comparing Shor and Steane error correction using the Bacon-Shor code.

Area of Science:

• Quantum Information Science
• Quantum Computing
• Atomic Physics

Background:

• Quantum states are fragile and susceptible to environmental noise, leading to decoherence.
• Quantum error correction (QEC) is essential for maintaining quantum coherence.
• QEC encodes quantum information into redundant logical states with high symmetry.

Purpose of the Study:

• To experimentally compare the effectiveness of Shor and Steane quantum error correction methods.
• To evaluate the performance of these methods in correcting bit flip errors using the Bacon-Shor code.

Main Methods:

• Implementation of the Bacon-Shor code in a chain of 23 trapped atomic ions.
• Experimental comparison of Shor error correction, which uses separate ancillary qubits for each symmetry measurement.
• Experimental comparison of Steane error correction, which maps perturbations to a logical ancilla qubit for simultaneous symmetry measurement.

Main Results:

• The Steane error correction method resulted in fewer errors after a single correction round.
• The Steane method caused less disturbance to the data qubits compared to Shor error correction.
• Both methods utilize ancillary quantum states to measure symmetries without perturbing data qubits.

Conclusions:

• Steane error correction demonstrates superior performance in preserving quantum coherence and minimizing data disturbance.
• The experimental findings highlight the practical advantages of Steane error correction for quantum computing applications.
• The study validates the efficacy of QEC techniques in mitigating environmental noise in quantum systems.