Entangling four logical qubits beyond break-even in a nonlocal code

Abstract

Quantum error correction protects logical quantum information against environmental decoherence by encoding logical qubits into entangled states of physical qubits. One of the most important near-term challenges in building a scalable quantum computer is to reach the break-even point, where logical quantum circuits on error-corrected qubits achieve higher fidelity than equivalent circuits on uncorrected physical qubits. Using Quantinuum's H2 trapped-ion quantum processor, we encode the GHZ state in four logical qubits with fidelity $99.5\pm 0.15\%\le F\le 99.7\pm 0.1\%$ (after postselecting on over 98% of outcomes). Using the same quantum processor, we can prepare an uncorrected GHZ state on four physical qubits with fidelity $97.8\pm 0.2\%\le F\le 98.7\pm 0.2\%$. The logical qubits are encoded in a $[[25,4,3]]$ Tanner-transformed long-range-enhanced surface code. Logical entangling gates are implemented using simple swap operations. Our results are a first step towards realizing fault-tolerant quantum computation with logical qubits encoded in geometrically nonlocal quantum low-density parity check codes.

13 pages, 9 figures, 1 table. v2 changes: added classical simulation data and appendices

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Cited by in corpus (12)

• High-rate quantum LDPC codes for long-range-connected neutral atom registers
• Experiments with the 4D Surface Code on a QCCD Quantum Computer
• Low-density parity-check codes as stable phases of quantum matter
• Coprime Bivariate Bicycle Codes and Their Layouts on Cold Atoms
• Single-shot preparation of hypergraph product codes via dimension jump
• Quantum low-density parity-check codes for erasure-biased atomic quantum processors
• Fundamental thresholds for computational and erasure errors via the coherent information
• Non-local resources for error correction in quantum LDPC codes
• Towards self-correcting quantum codes for neutral atom arrays
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• Noise-Aware Circuit Compilations for a Continuously Parameterized Two-Qubit Gateset
• Scalable and fault-tolerant preparation of encoded k-uniform states