[Paper Review] Demonstrating a superconducting dual-rail cavity qubit with erasure-detected logical measurements

Kevin Chou, Tali Shemma+32 more|arXiv (Cornell University)|Jul 6, 2023

Quantum Computing Algorithms and Architecture9 citations

TL;DR

The paper experimentally demonstrates a dual-rail superconducting cavity qubit with erasure-detected logical measurements, achieving high SPAM fidelity and converting most decay errors into erasures to enable efficient error correction benchmarks.

ABSTRACT

A critical challenge in developing scalable error-corrected quantum systems is the accumulation of errors while performing operations and measurements. One promising approach is to design a system where errors can be detected and converted into erasures. Such a system utilizing erasure qubits are known to have relaxed requirements for quantum error correction. A recent proposal aims to do this using a dual-rail encoding with superconducting cavities. However, experimental characterization and demonstration of a dual-rail cavity qubit has not yet been realized. In this work, we implement such a dual-rail cavity qubit; we demonstrate a projective logical measurement with integrated erasure detection and use it to measure dual-rail qubit idling errors. We measure logical state preparation and measurement errors at the $0.01\%$-level and detect over $99\%$ of cavity decay events as erasures. We use the precision of this new measurement protocol to distinguish different types of errors in this system, finding that while decay errors occur with probability $\sim 0.2\%$ per microsecond, phase errors occur 6 times less frequently and bit flips occur at least 140 times less frequently. These findings represent the first confirmation of the expected error hierarchy necessary to concatenate dual-rail erasure qubits into a highly efficient erasure code.

Motivation & Objective

• Motivate and realize erasure qubits to relax quantum error correction requirements.
• Implement a dual-rail cavity qubit in circuit QED with integrated erasure-detected logical measurements.
• Quantify SPAM and leakage detection performance and characterize idling error rates.
• Establish the error hierarchy (decay, phase, and bit-flip) to inform future erasure-code integration.

Proposed method

• Encode the qubit in a dual-rail of two cavities with an ancilla transmon for control and readout.
• Perform photon-number selective π-pulses to map cavity states to transmon states and dispersive readout to determine outcomes.
• Implement end-of-the-line erasure-detected logical measurements with one or more rounds of cavity measurements and a decoding strategy.
• Measure logical SPAM by preparing |01⟩ or |10⟩ and evaluating logical misassignment and erasure fractions.
• Test leakage-detection capability by intentionally preparing leakage states and quantifying detection errors.
• Use simulations and simplified error models to attribute observed errors to specific physical processes.

Experimental results

Research questions

• RQ1 Can a dual-rail cavity qubit provide erasure-detected logical measurements with ultra-low misassignment errors?
• RQ2 What is the efficacy of converting decay errors into erasures, and what is the leakage-detection efficiency (>99%)?
• RQ3 What are the dominant idling error rates (bit-flip and phase) in this architecture, and how do they compare to erasure rates?
• RQ4 How do multi-round measurement and decoding strategies affect logical misassignment and erasure rates?

Key findings

• Logical misassignment error: (1.8 ± 0.3) × 10^−4 averaged over state preparations.
• Erasure fraction: (6.03 ± 0.05) × 10^−2 for one-round SPAM measurement.
• Leakage-detection error: (7.7 ± 0.3) × 10^−3, yielding >99% conversion of leakage to erasures.
• Two-round measurements reduce logical misassignment to (4 ± 2) × 10^−5 and leakage-detection error to (1.2 ± 0.1) × 10^−3, with erasure fraction rising to (17 ± 0.1) × 10^−2.
• Cavity decay rate: ∼0.2% per microsecond; phase errors smaller by a factor of ~6; bit-flip errors at least 140× smaller than decay errors.
• Ramsey and echo dephasing rates: Γ_Rφ = 1/(2.2 ± 0.2 ms) and Γ_Eφ = 1/(2.7 ± 0.2 ms); phase-flip probabilities p_φ ≈ 0.023% and 0.019% per microsecond, respectively.