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arXiv:1304.2910 · Nature Communications

Quantum replication at the Heisenberg limit

Giulio Chiribella, Yuxiang Yang, Andrew Chi-Chih Yao

Published Dec 5, 2013• 43 citations
arXivHTMLPDF
DOI
10.1038/ncomms3915

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The impossibility of superluminal communication is a fundamental principle of physics. Here we show that this principle underpins the performance of several fundamental tasks in quantum information processing and quantum metrology. In particular, we derive tight no-signaling bounds for probabilistic cloning and super-replication that coincide with the corresponding optimal achievable fidelities and rates known. In the context of quantum metrology, we derive the Heisenberg limit from the no-signaling principle for certain scenarios including reference frame alignment and maximum likelihood state estimation. We elaborate on the equivalence of assymptotic phase-covariant cloning and phase estimation for different figures of merit.
Current era quantum computers continue to grow in both capability and capacity. Despite these advancements, errors induced by environmental noise severely limit practical applicability. Current research into error mitigation and correction to bridge the gap between current-era quantum computers and the execution of noise-sensitive workloads. These methods have significant performance and resource overheads, thereby greatly limiting the real-world benefits of their use. Circuit replication, as a naive form of error mitigation, is not new and has largely been ignored given the resource constraints of current quantum hardware. However, its simplicity is attractive as a means to supplement modern methods, reducing the overall performance overhead while still preserving error-mitigation capabilities. In this paper, we profile the effects of simple circuit replication under real-world noise profiles to better establish replication's limits as a supplemental mitigation strategy. Quantum Approximate Optimization Algorithm (QAOA) for the Maxcut problem is explored for the analysis. For small graphs, we found that the average inference strength decreases by approximately 21.8% while the average standard deviation decreases by 108.8% compared to 6 replicates. For larger graphs, inference strength decreases by 35.4% while the average standard deviation decreased only 20.5%. Fewer replications did not affect smaller graphs, but degraded inference strength, with comparable benefits to standard deviation in larger graphs. These results show that replication has potential uses as a supplemental mitigation strategy for large-depth, highly variable workloads.