Steering paths mid-flight for fault-tolerance in measurement-based holonomic gates

TL;DR

This paper presents a fault-tolerant, measurement-based holonomic quantum gate framework that uses real-time feedback and continuous measurements to suppress errors, correct non-adiabatic effects, and enable faster quantum gate implementation.

Contribution

It introduces a novel fault-tolerant protocol for measurement-based holonomic gates utilizing continuous measurement and real-time feedback to enhance speed and error correction.

Findings

Non-Markovian decoherence is suppressed via the quantum Zeno effect.

Measurement records enable detection of errors and steering of gate paths.

Protocol corrects non-adiabatic measurement-induced errors.

Abstract

Continuous measurement-based holonomic quantum computation provides a route to universal logical computation in quantum error correcting codes. We introduce a fault-tolerant framework for implementing measurement-based holonomic gates that leverages continuous measurements with real-time feedback. We show that non-Markovian decoherence is intrinsically suppressed through the quantum Zeno effect, while Markovian errors are identified by the decoding of measurement records to reveal the rotated syndrome subspace populated during the evolution. This information enables steering holonomic paths mid-flight to ensure that the final evolution realizes the target logical gate. We further demonstrate that non-adiabatic effects give rise to measurement-induced errors, and we show that these can also be corrected by an analogous protocol. This approach relaxes the stringent adiabaticity requirement and enables faster implementation of holonomic gates.