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arXiv:0811.3734 · Nature Physics

Quantum error correction beyond qubits

Takao Aoki, Go Takahashi, Tadashi Kajiya, Jun-ichi Yoshikawa, Samuel L. Braunstein, Peter van Loock, Akira Furusawa

Published Jun 28, 2009• 144 citations
arXivHTMLPDF
DOI
10.1038/nphys1309

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Quantum error correction of a grid-state qubit with state preparation and measurement errors below 10−310^{-3}10−3
Grid state qubits offer a hardware-efficient approach to large-scale fault-tolerant quantum computing. They access the information redundancy required for quantum error correction by exploiting the large Hilbert space naturally available in harmonic oscillators. Superconducting architectures are particularly suitable to implement grid state qubits due to their fast and high-fidelity operations. Grid states in superconducting circuits enable quantum error correction (QEC) with performance beyond break-even. However, the state preparation and measurements (SPAM) errors of grid states has been a significant limitation to computational performances. In this work, we leverage high-performance QEC to enable repeat-until-success state preparation of both cardinal and magic states of the single-mode grid-state qubit. We combine this with an improved measurement protocol that corrects for both finite-energy envelope and auxiliary qubit readout errors, and increases robustness to photon loss. Our experiments, using both techniques, achieve a combined state-preparation and measurement error below 10−310^{-3}10−3. This represents two orders-of-magnitude improvement over the state of the art, bringing this platform on par with standard SPAM error levels measured in transmon qubits.
Quantum computers are highly susceptible to errors due to unintended interactions with their environment. It is crucial to correct these errors without gaining information about the quantum state, which would result in its destruction through back-action. Quantum Error Correction (QEC) provides information about occurred errors without compromising the quantum state of the system. However, the implementation of QEC has proven to be challenging due to the current performance levels of qubits -- break-even requires fabrication and operation quality that is beyond the state-of-the-art. Understanding how qubit performance factors into the success of a QEC code is a valuable exercise for tracking progress towards fault-tolerant quantum computing. Here we present qec_code_sim, an open-source, lightweight Python framework for studying the performance of small quantum error correcting codes under the influence of a realistic error model appropriate for superconducting transmon qubits, with the goal of enabling useful hardware studies and experiments. qec_code_sim requires minimal software dependencies and prioritizes ease of use, ease of change, and pedagogy over execution speed. As such, it is a tool well-suited to small teams studying systems on the order of one dozen qubits.