Detecting bit-flip errors in a logical qubit using stabilizer measurements

Abstract

Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the smallest QEC codes, the information in one logical qubit is encoded in a two-dimensional subspace of a larger Hilbert space of multiple physical qubits. For each code, a set of non-demolition multi-qubit measurements, termed stabilizers, can discretize and signal physical qubit errors without collapsing the encoded information. Experimental demonstrations of QEC to date, using nuclear magnetic resonance, trapped ions, photons, superconducting qubits, and NV centers in diamond, have circumvented stabilizers at the cost of decoding at the end of a QEC cycle. This decoding leaves the quantum information vulnerable to physical qubit errors until re-encoding, violating a basic requirement for fault tolerance. Using a five-qubit superconducting processor, we realize the two parity measurements comprising the stabilizers of the three-qubit repetition code protecting one logical qubit from physical bit-flip errors. We construct these stabilizers as parallelized indirect measurements using ancillary qubits, and evidence their non-demolition character by generating three-qubit entanglement from superposition states. We demonstrate stabilizer-based quantum error detection (QED) by subjecting a logical qubit to coherent and incoherent bit-flip errors on its constituent physical qubits. While increased physical qubit coherence times and shorter QED blocks are required to actively safeguard quantum information, this demonstration is a critical step toward larger codes based on multiple parity measurements.

6 pages, 4 figures, 10 supplementary figures

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• Thermal and Residual Excited-State Population in a 3D Transmon Qubit
• Analysis of parametrically driven exchange-type (iSWAP) and two-photon (bSWAP) interactions between superconducting qubits
• Inductively shunted transmon qubit with tunable transverse and longitudinal coupling
• Measuring a transmon qubit in circuit QED: dressed squeezed states
• Experimental study of optimal measurements for quantum state tomography
• An argon ion beam milling process for native ${\text{AlO}}_{\text{x}}$ layers enabling coherent superconducting contacts
• Direct digital synthesis of microwave waveforms for quantum computing
• Modeling dynamics of entangled physical systems with superconducting quantum computer