Entangling Four Logical Qubits beyond Break-Even in a Nonlocal Code.

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Error Correction

Background:

• Quantum error correction is essential for protecting quantum information from decoherence.
• Achieving the break-even point, where error-corrected logical qubits outperform physical qubits, is a key challenge for scalable quantum computers.

Purpose of the Study:

• To demonstrate the practical advantage of quantum error correction by encoding a Greenberger-Horne-Zeilinger (GHZ) state in logical qubits.
• To compare the fidelity of logical qubits with error correction against uncorrected physical qubits.

Main Methods:

• Encoding a GHZ state into four logical qubits using a ⟦25,4,3⟧ Tanner-transformed long-range-enhanced surface code on Quantinuum's H2 trapped-ion quantum processor.
• Implementing logical entangling gates via simple swap operations.
• Comparing the fidelity of the encoded logical GHZ state with a GHZ state prepared on four physical qubits.

Main Results:

• Achieved a fidelity of 99.5±0.15%–99.7±0.1% for the logical GHZ state after postselection.
• Prepared an uncorrected GHZ state on four physical qubits with a fidelity of 97.8±0.2%–98.7±0.2%.
• Demonstrated higher fidelity for error-corrected logical qubits compared to uncorrected physical qubits.

Conclusions:

• The results represent a critical step towards fault-tolerant quantum computation.
• This work paves the way for utilizing geometrically nonlocal quantum low-density parity check codes for robust quantum information processing.