Continuous-time quantum error correction (CTQEC) is an approach to protecting quantum information from noise in which both the noise and the error correcting operations are treated as processes that are continuous in time. This chapter investigates CTQEC based on continuous weak measurements and feedback from the point of view of the subsystem principle, which states that protected quantum information is contained in a subsystem of the Hilbert space. We study how to approach the problem of constructing CTQEC protocols by looking at the evolution of the state of the system in an encoded basis in which the subsystem containing the protected information is explicit. This point of view allows us to reduce the problem to that of protecting a known state, and to design CTQEC procedures from protocols for the protection of a single qubit. We show how previously studied CTQEC schemes with both direct and indirect feedback can be obtained from strategies for the protection of a single qubit via weak measurements and weak unitary operations. We also review results on the performance of CTQEC with direct feedback in cases of Markovian and non-Markovian decoherence, where we have shown that due to the existence of a Zeno regime in non-Markovian dynamics, the performance of CTQEC can exhibit a quadratic improvement if the time resolution of the weak error-correcting operations is high enough to reveal the non-Markovian character of the noise process.
This paper proposes a novel approach to distributed quantum error correction (QEC) leveraging the concept of information entropy topology. Traditional QEC focuses on coding schemes and error detection/correction algorithms, often treating the underlying network topology as a secondary consideration. We argue that the topology itself can be fundamentally defined and optimized using information entropy, offering a new paradigm for constructing more robust and efficient QEC networks. We present a framework where quantum error correction nodes are viewed as points within an information entropy space, and their connectivity is determined by the geodesic distance – a measure derived from information entropy – between them. This approach allows for the direct optimization of the network topology to achieve superior error correction performance. The core claim is that utilizing information entropy to define and operate on quantum error correction networks significantly enhances their error resilience and correction capabilities. The key mechanism involves translating quantum error correction networks into a topological structure within an information entropy space, exploiting the geometric properties of information entropy to refine the design of error-correcting codes and optimize the error detection/correction processes. Specifically, we employ information entropy distances to define the relationships between correction nodes, creating networks with tailored error correction properties. We demonstrate, through theoretical analysis, that this entropy-based topology can outperform conventional approaches, particularly in scenarios with complex network geometries and high error rates. The research contributes to a deeper understanding of the interplay between information theory and quantum error correction, paving the way for the development of next-generation QEC systems.
Distributed Quantum Computing (DQC) and Quantum Error Correction (QEC) rely on dynamic circuits that include Mid-Circuit Measurements (MCMs) and classical feedback. These operations present a major bottleneck: MCMs suffer from high error rates that lead to real-time branching errors, while MCM and classical feedback latencies amplify decoherence errors. Current hardware controllers, qubit-state discriminators, and software error mitigation techniques fail to address these challenges holistically.
We propose MCMit, a hardware-software co-design to mitigate branching and latency-induced errors. MCMit introduces a scalable, constant-latency multi-control branch instruction for faster classical feedback and two qubit-state discriminators, a transformer, and a CNN, with high accuracy even under short measurement durations. On the software side, static MCM elimination and stochastic branching complement the hardware by mitigating residual branching errors that persist despite hardware improvements.
We implement MCMit on Qubic and evaluate it using experimentally extracted QPU readout traces. Our branch instruction reduces feedback latency by up to 70\%, improving circuit depths by up to
7× over Qubic. Our CNN discriminator achieves up to 62\% higher accuracy for short measurement durations than the baselines, driving
1.2−9.4× lower logical error rates in QEC. Last, our software mitigation improves fidelity by 18--30\% over baseline methods in DQC workloads.