Quantum error correction avoids pausing with new hardware design

Yuejie Xin and colleagues have demonstrated a leakage reduction unit (LRU) achieving 98.4% leakage removal during qubit measurement without adding time overhead, a critical step for improving quantum error correction. Adapted from a protocol called DDROP, the LRU utilizes simultaneous drives on the transmon and its readout resonator, actively returning qubits to a usable state. The LRU achieves a 98.4% leakage removal fraction without compromising the 2RO assignment fidelity (99.2%). The team combined this enhanced measurement with neural-network decoding to successfully suppress logical error rates in experiments with up to nine qubits.

Leakage Reduction Units Integrated with Superconducting Qubit Readout

A 98.4% leakage removal fraction was experimentally achieved without adding any time overhead to the standard two-level readout process, a critical advancement for scaling quantum error correction in superconducting circuits. This improvement stems from a newly developed Leakage Reduction Unit (LRU) integrated directly into the qubit measurement process, circumventing the need for additional processing steps that typically slow down computations. The LRU operates by simultaneously applying microwave pulses to both the transmon qubit and its associated readout resonator, actively driving leaked quantum information back into the usable computational state.

This active reset, combined with richer information gleaned from the readout, allows for more effective error correction. The design uses a protocol called DDROP, or Double-Drive Reset of Population, to manipulate the qubit’s state during measurement.

These simultaneous drives utilize the dispersive shift, a phenomenon where the qubit’s state alters the resonator’s frequency, to efficiently return qubits to a state where they can be reliably read. This approach differs from previous methods that often relied on post-processing or complex calibration routines, streamlining the error correction process and potentially reducing the overall latency of quantum algorithms. The team demonstrated that the LRU’s performance isn’t simply about reducing leakage; it’s about maintaining the integrity of the error correction itself, even as the amount of initial leakage increases.

This stability is important for building larger, more complex quantum processors, where errors are inevitable and must be actively mitigated. The LRU’s ability to maintain performance under increasing error rates indicates that it could be a key component in achieving fault-tolerant quantum computation.

The enhanced measurement provided by the LRU also feeds a neural network decoder, which then computes the necessary logical corrections with greater accuracy. The team validated the LRU’s effectiveness through two distinct error correction experiments: a memory experiment utilizing a distance-3 bit-flip repetition code and a seven-qubit stability experiment. These benchmarks assessed the LRU’s ability to both preserve quantum information over time and maintain the fidelity of computations in the face of errors.

The results demonstrated that combining the LRU with a three-level readout, which provides the decoder with significantly richer information, yields the best performance. Specifically, a readout result corresponding to heralds a leakage event at a known location and time, transforming a potentially disruptive error into a manageable one for the decoder.

The implications of this work extend to advanced quantum architectures like lattice surgery and logical qubit mobility, where minimizing the number of error correction cycles is paramount. The development of a high-fidelity and hardware-efficient LRU with zero time overhead for 2RO represents a step toward building practical, scalable superconducting quantum computers.

4% Leakage Removal Achieves High-Fidelity 2RO & 3RO

The new leakage reduction unit (LRU) maintains 99.2% assignment fidelity during two-level readout while removing 98.4% of qubit leakage, a performance level previously requiring additional processing steps. The protocol uses the dispersive shift between the transmon qubit and its readout resonator, creating a directional process that actively returns the qubit to its computational state. This approach establishes a one-way path from leakage states back to usable states through simultaneous microwave drives applied to both the qubit and resonator.

Population transfer matrices confirm the LRU’s effectiveness; the matrices demonstrate a clear shift in probability from leakage states to the computational state, with the bottom row of the data showing the LRU actively returning the qubit when it begins in a leaked state. Specifically, the probability of transitioning from a leaked state to the computational state increases by 61%, 33%, and 90% at various measurement parameters.

This improvement is important because the LRU not only removes leakage but also preserves the error-suppression rate during stability experiments, making it independent of the rate at which leakage is injected. Without leakage removal, the error-suppression rate degrades as leakage increases, but the LRU maintains a nearly constant rate even with increased leakage. The LRU’s performance extends to three-level readout, consistently providing the best performance across studied leakage rates.

Simulations suggest the observed non-exponential curvature at low rounds in the stability experiments is not due to insufficient leakage removal by the LRU, nor leakage on the central data qubit, but potentially due to leakage to higher excited states beyond the primary computational space. Assignment fidelity with the LRU using three-level readout reached 96.3%. Well-separated state clusters were observed on the I-Q plane, and average three-level readout assignment fidelities reached 96.3% for the LRU-enhanced measurement.

LRU-Enhanced Measurement Improves Neural-Network Decoding

The design of the LRU prioritizes maintaining qubit fidelity during the leakage removal process; assignment fidelity between qubit states remained uncompromised, registering at 99.2% during testing. This is achieved by carefully shaping the transmon drive pulse to only induce transitions between specific states, ideally leaving the ground state unaffected, and by optimizing the timing between resonator and transmon drives.

Integrating this LRU-enhanced measurement into two QEC benchmarks, a distance-3 bit-flip repetition code memory experiment and a Stability-7 experiment, demonstrated its practical value. In the memory experiment, the logical error rate decreased most significantly when using three-level readout, with the LRU providing further improvements even with injected leakage.

More notably, the Stability-7 experiment revealed the LRU’s ability to mitigate the spread of leakage-induced correlated errors, preserving the error-suppression rate even as injected leakage increased. Calibration of the LRU involved optimizing both assignment fidelity and leakage removal efficiency using a dedicated circuit. The transmon drive pulse utilizes a sine-squared envelope, while the resonator drive is a square pulse, with a total measurement duration typical for the system.

Varying the delay between the resonator and transmon drives revealed a trade-off between performance and fidelity, with initial increases in delay improving assignment fidelity until limited by the transmon’s natural relaxation time. Analysis of single-shot I-Q data and readout assignment matrices confirmed the LRU-enhanced measurement’s performance.

Stabilized Logical Error Rates in Memory & Stability QEC

A high-fidelity leakage removal fraction of 98.4% was observed in stability experiments utilizing a new Leakage Reduction Unit (LRU) compared to standard two-level readout, demonstrating a significant benefit even without intentionally introducing errors. This improvement stems from the LRU’s ability to concurrently reduce leakage and provide leakage information to a neural network decoder, enhancing the performance of quantum error correction (QEC) protocols. The design actively returns qubits to a usable state during readout, a critical function for maintaining data integrity in increasingly complex quantum computations.

This simultaneous action distinguishes it from previous methods, which often addressed leakage as a separate, sequential step, introducing delays and potential for further errors. Researchers found that the LRU achieves a 98.4% leakage removal fraction without diminishing the accuracy of the initial two-level readout, maintaining a 99.2% assignment fidelity.

This preservation of readout fidelity is important, as it allows the neural network decoder to accurately interpret the qubit state, even in the presence of residual leakage. Without the LRU, the error suppression degrades as leakage accumulates, highlighting the unit’s effectiveness in reducing the long-lived, time-correlated errors caused by leaked states.

Stability experiments, designed to test the movement of logical observables, are particularly vulnerable to these time-correlated errors, making the LRU’s performance in this context especially noteworthy. The team demonstrated this benefit across a range of leakage rates, with the combination of three-level readout and the LRU consistently delivering the best results.

In a distance-3 bit-flip repetition code memory experiment, utilizing three-level readout alongside the LRU further reduced logical error rates at finite injected leakage, while in Stability-7 experiments, the LRU successfully mitigated the propagation of leakage-induced correlated errors. This was evidenced by a sustained error-suppression factor, even at baseline leakage levels, and its stabilization against all levels of injected leakage. The researchers performed these tests with up to nine qubits.

Scalable LRU Design Uses Existing Superconducting Processor Architecture

The LRU’s design uses existing components common to most superconducting quantum processors, specifically, a dispersively coupled readout resonator, minimizing the need for specialized hardware or additional control lines. The LRU operates on a principle of directional reset, specifically targeting leakage from the ground and first excited states to the second excited state in transmon qubits. This targeted approach addresses a significant error channel that can propagate through two-qubit gates, creating temporally and spatially correlated errors detrimental to logical qubit performance.

The researchers detail in their published work, noting the schematic omits a Purcell filter present in their processor, which did not impede the LRU’s effectiveness. Combining the LRU with three-level readout (3RO) yielded the highest logical performance across all tested conditions, demonstrating a synergistic benefit between active error removal and richer error syndrome information.

Experiments utilized a processor with a standard circuit quantum electrodynamics architecture, where each transmon is dispersively coupled to a dedicated readout resonator. This architecture allowed for seamless integration of the LRU protocol, which requires no additional local oscillators or mixers. The team demonstrated that this LRU-enhanced measurement has zero time overhead compared to standard 2RO, which is an important factor for scalability. The researchers achieved an average assignment fidelity of 99.2% with the LRU operating in conjunction with 2RO, and 96.3% with 3RO, demonstrating high accuracy in qubit state determination.

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