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

TL;DR

This paper demonstrates entangling four logical qubits beyond the quantum error correction break-even point using a trapped-ion quantum processor, showing logical qubits outperform physical qubits in fidelity.

Contribution

It reports the first experimental entanglement of four logical qubits with higher fidelity than physical qubits using a nonlocal surface code.

Findings

Logical four-qubit GHZ state fidelity: 99.5-99.7%

Physical four-qubit GHZ state fidelity: 97.8-98.7%

First step towards fault-tolerant quantum computing with nonlocal codes

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.