Quantum Error Correction

Venkateswaran Kasirajan

Sangkha Borah, Bijita Sarma, Michael J. Kewming +3 more

Canonical discrete quantum error correction (DQEC) schemes use projective von Neumann measurements on stabilizers to discretize the error syndromes into a finite set, and fast unitary gates are applied to recover the corrupted information. Quantum error correction (QEC) based on continuous measurement, known as continuous quantum error correction (CQEC), in principle, can be executed faster than DQEC and can also be resource efficient. However, CQEC requires meticulous filtering of noisy continuous measurement data to reliably extract error syndromes on the basis of which errors could be detected. In this paper, we show that by constructing a measurement-based estimator (MBE) of the logical qubit to be protected, which is driven by the noisy continuous measurement currents of the stabilizers, it is possible to accurately track the errors occurring on the physical qubits in real time. We use this MBE to develop a continuous quantum error correction (MBE-CQEC) scheme that can protect the logical qubit to a high degree, surpassing the performance of DQEC, and also allows QEC to be conducted either immediately or in delayed time with instantaneous feedbacks.

Jincheng Zhang

Quantum error correction (QEC) is a crucial component of quantum computing, enabling the reliable transmission and manipulation of quantum information. Traditional QEC schemes often rely on fixed phase adjustments, which can be suboptimal in certain scenarios. This paper introduces a novel self-adaptive quantum error correction algorithm, termed "Quantum Phase Evolution," that dynamically adjusts quantum bit phases based on the observed error patterns. Our approach leverages a 'Quantum Phase Evolution' mechanism to optimize the error correction process by tailoring the qubit states in response to feedback loops generated during error correction. We demonstrate the effectiveness of this algorithm through simulations and preliminary experiments, achieving significant improvements in error correction fidelity compared to conventional methods. The core mechanism is to iteratively refine the quantum state based on the error patterns, offering a more adaptive and potentially more efficient approach to QEC.

Ray LaPierre

Daowen Qiu

Jincheng Zhang

Quantum error correction (QEC) is a critical component of quantum computing, enabling the reliable manipulation of quantum information. However, current QEC schemes often rely on a fixed number of qubits, limiting their scalability and error correction capabilities. This paper proposes a novel approach to QEC based on dynamically adjusting the dimensionality of the quantum state. We introduce a "quantum topology state" mechanism that leverages the unique properties of quantum error correction to dynamically control and optimize the quantum state, thereby significantly reducing quantum error rates. This design offers a pathway towards higher precision and improved error correction performance, addressing a critical limitation of existing QEC techniques.