[Paper Review] Data and plotting code for 'Mid-circuit correction of correlated phase errors using an array of spectator qubits'

Kevin Singh, C. E. Bradley+4 more|arXiv (Cornell University)|Aug 24, 2022

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper demonstrates real-time mid-circuit correction of correlated phase errors in a neutral-atom quantum processor using an array of cesium spectator qubits to sense and coherently correct noise affecting rubidium data qubits. By performing single-shot mid-circuit readouts of spectator qubits and applying real-time feed-forward corrections, the protocol suppresses dephasing up to 11 mG, achieving a 97.4% data qubit fidelity when spectator contrast is ideal, enabling scalable error mitigation in noisy, correlated environments.

ABSTRACT

Scaling up invariably error-prone quantum processors is a formidable challenge. While quantum error correction ultimately promises fault-tolerant operation, the required qubit overhead and error thresholds are daunting, and many codes break down under correlated noise. Recent proposals have suggested a complementary approach based on co-located, auxiliary 'spectator' qubits. These act as in-situ probes of noise, and enable real-time, coherent corrections of the resulting errors on the data qubits. Here, we use an array of cesium spectator qubits to correct correlated phase errors on an array of rubidium data qubits. Crucially, by combining in-sequence readouts, data processing, and feed-forward operations, these correlated errors are suppressed within the execution of the quantum circuit. The protocol is broadly applicable to quantum information platforms, and our approach establishes key tools for scaling neutral-atom quantum processors: mid-circuit readout of atom arrays, real-time processing and feed-forward, and coherent mid-circuit reloading of atomic qubits.

Motivation & Objective

• To address the challenge of correlated noise in scalable quantum processors, which undermines traditional quantum error correction.
• To develop a real-time, in-situ error mitigation protocol that does not require prior knowledge of noise spectra or correlation times.
• To demonstrate mid-circuit readout, real-time processing, and feed-forward correction in a dual-species atom array with minimal disturbance to data qubits.
• To enable coherent reloading of spectator qubits within data qubit coherence times, supporting repeated error correction.
• To validate the protocol experimentally in a system with ~60 data and ~60 spectator qubits, showing suppression of dephasing up to 11 mG.

Proposed method

• Utilizes a dual-species array of laser-trapped rubidium (data qubits) and cesium (spectator qubits) atoms, with qubits encoded in hyperfine states.
• Performs mid-circuit, single-shot fluorescence readouts of spectator qubits to estimate globally correlated phase errors without disturbing data qubit coherence.
• Employs a classical control architecture to process spectator readout results in real time and apply feed-forward unitary corrections to data qubits.
• Relies on the correlation between noise-induced phase shifts on data and spectator qubits, assuming identical noise response across both species.
• Uses microwave Rabi oscillations to characterize qubit coherence and validate the protocol’s effectiveness under controlled noise injection.
• Implements a no-free-parameter model to simulate and predict system behavior, with adjustments for experimental discrepancies such as under-correction and finite pulse durations.

Experimental results

Research questions

• RQ1 Can mid-circuit readout and real-time feed-forward correction suppress correlated phase errors in a neutral-atom quantum processor?
• RQ2 To what extent can spectator qubits sense and enable correction of noise affecting data qubits without degrading their coherence?
• RQ3 How does the performance of the protocol depend on spectator qubit contrast and number of spectators?
• RQ4 What is the maximum noise strength (in mG) that the protocol can effectively suppress?
• RQ5 Can spectator qubits be replenished within the data qubit coherence time to enable repeated error correction?

Key findings

• The protocol successfully suppresses correlated phase errors up to 11 mG, with experimental results showing robustness up to this threshold.
• In the absence of injected noise, the data qubit fidelity is 88.0% with current experimental parameters (N=61 spectators, C=0.46), improving to 97.4% when spectator contrast C=1.
• Numerical simulations show that increasing the number of spectators to 165 improves fidelity to 95.6% (C=0.46) or 99.0% (C=1), indicating that limited contrast is the dominant error source.
• The protocol introduces minor sensitivity to noise at the edges of resonance features due to finite spectator readout time, but overall maintains strong suppression of decoherence.
• Spectator qubits can be reloaded within the data qubit coherence time, enabling repeated measurements and continuous operation.
• Discrepancies between experiment and simulation arise from non-linear noise synthesis and imperfect phase estimation, which can be mitigated by improving state preparation and reducing readout time.