The development of techniques for simulating quantum systems using classical computers is a paramount task for two primary reasons: i) there exist configurations for which classical computers are remarkably effective and will continue to be so, and ii) exploring the limits of classical computation facilitates the identification of the regimes of competence for quantum computers. In this work, we present MPStab, a quantum circuit simulator based on a hybrid formalism combining stabilizers and tensor networks, recently introduced in Ref. [1]. We present the package, its core functionalities, and explore its performances in a few interesting simulation regimes.
Giulio Crognaletti, Mattia Robbiano, Michele Grossi et al.· 1 citation
Approximate quantum error correction (AQEC) extends the framework of discrete- and continuous-variable quantum error correction beyond the Knill-Laflamme (KL) conditions, where the recovery performance is quantified by entanglement fidelity. Recent studies have enabled efficient evaluation of near-optimal entanglement fidelity using transpose-channel recovery. Yet, determining the global optimal recovery map and its entanglement fidelity for general codes beyond the KL conditions remains a major computational challenge. Direct optimization becomes prohibitive as the number of noise Kraus operators grows rapidly with system size, and existing approaches lack rigorous guarantees for reducing this optimization to a tractable dimension. Here, we derive an explicit characterization of the optimal environmental state of complement channel, which transforms the optimization over recovery channels into an equivalent optimization over quotient unitaries. For a broader class of codes that satisfy only the orthogonality part of the KL conditions, we show that the optimal recovery map admits an explicit analytical form. Building on this form, we derive novel rigorous lower bounds of entanglement fidelity that strictly improve upon the transpose-recovery bound. We further develop a novel recovery strategy based on principle components, and derive a rigorous bound on the error introduced by noise truncation. Our approach enables efficient searches for approximate recovery maps for AQEC codes, avoiding the need to optimize over the full Kraus-operator space.
Jing Wu, Michele Grossi, D. Kurkcuoglu et al.· 0 citations
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