1,232 research outputs found

    Fast Quantum Algorithms for Trace Distance Estimation

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    In quantum information, trace distance is a basic metric of distinguishability between quantum states. However, there is no known efficient approach to estimate the value of trace distance in general. In this paper, we propose efficient quantum algorithms for estimating the trace distance within additive error ε\varepsilon between mixed quantum states of rank rr. Specifically, we first provide a quantum algorithm using rO~(1/ε2)r \cdot \widetilde O(1/\varepsilon^2) queries to the quantum circuits that prepare the purifications of quantum states. Then, we modify this quantum algorithm to obtain another algorithm using O~(r2/ε5)\widetilde O(r^2/\varepsilon^5) samples of quantum states, which can be applied to quantum state certification. These algorithms have query/sample complexities that are independent of the dimension NN of quantum states, and their time complexities only incur an extra O(log(N))O(\log (N)) factor. In addition, we show that the decision version of low-rank trace distance estimation is BQP\mathsf{BQP}-complete.Comment: Final version. Improve proof details, add BQP-completeness. 31 pages, 2 algorithms, 2 tables, 2 figure

    Model and Integrate Medical Resource Available Times and Relationships in Verifiably Correct Executable Medical Best Practice Guideline Models (Extended Version)

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    Improving patient care safety is an ultimate objective for medical cyber-physical systems. A recent study shows that the patients' death rate is significantly reduced by computerizing medical best practice guidelines. Recent data also show that some morbidity and mortality in emergency care are directly caused by delayed or interrupted treatment due to lack of medical resources. However, medical guidelines usually do not provide guidance on medical resource demands and how to manage potential unexpected delays in resource availability. If medical resources are temporarily unavailable, safety properties in existing executable medical guideline models may fail which may cause increased risk to patients under care. The paper presents a separately model and jointly verify (SMJV) architecture to separately model medical resource available times and relationships and jointly verify safety properties of existing medical best practice guideline models with resource models being integrated in. The SMJV architecture allows medical staff to effectively manage medical resource demands and unexpected resource availability delays during emergency care. The separated modeling approach also allows different domain professionals to make independent model modifications, facilitates the management of frequent resource availability changes, and enables resource statechart reuse in multiple medical guideline models. A simplified stroke scenario is used as a case study to investigate the effectiveness and validity of the SMJV architecture. The case study indicates that the SMJV architecture is able to identify unsafe properties caused by unexpected resource delays.Comment: full version, 12 page
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